SlideShare a Scribd company logo
1 of 57
Download to read offline
Evaluation of Models for predicting the average monthly
Euro versus Norwegian krone exchange rate from financial
and commodity information
Raju RImal
Norwegian University of Life Sciences
(NMBU)
April 22, 2015
Raju RImal (NMBU) Masters Thesis April 22, 2015 1 / 23
Table of Contents
1 The BIG picture
2 Part I
Exchange rate determination
Factors affecting exchange rate
Foreign currency and Exchange
rate
Balance of Payment Account
Relevant Variables
3 Part II
Statistical Models
Linear Models
Multicollinearity Problem
PCR and PLS regression Model
Ridge Regression
Cross-validation and Prediction
4 Part III
Comparison of Models
Comments on Model
Comparison
Discussions and Conclusions
Raju RImal (NMBU) Masters Thesis April 22, 2015 2 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial and
commodity variables
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial and
commodity variables
2 Make prediction using different models
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
The BIG picture
The BIG picture
1 Identify functional relationship of Exchange rate with financial and
commodity variables
2 Make prediction using different models
3 Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
Part I
Identify functional relationship of Exchange rate
with financial and commodity variables
Raju RImal (NMBU) Masters Thesis April 22, 2015 4 / 23
Part I Exchange rate determination
Exchange rate determination
Exchange Rate is a price of one currency in terms of another
Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
Part I Exchange rate determination
Exchange rate determination
Exchange Rate is a price of one currency in terms of another
Determined from the demand and supply of the currency in Money
Market (ForEx)
−1. 1. 2. 3. 4. 5. 6. 7. 8.
−1.
1.
2.
3.
4.
5.
6.
7.
0
Demand of Currency
Supply of Currency
Quantity
ExchangeRate
Equilibrium Point
Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
∆Inf = Inflation differential between
two countries S0
D0
ValueofEUROperNOK
Quantity of EURO
9.10
9.97
S1
D1
QEuro
Upward shift in Demand
of Euro due to inflation in
Norway
Downward shift in supply
of Euro purchasing NOK
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
∆Inf = Inflation differential between
two countries
∆Int = Interest Rate differential be-
tween two countries
Quantity of Euro
(purchasing Norwegian Krone)
PriceofEuro(EUR/NOK)
S0
S1
D0
D1
QEuro
NOK
8.72
NOK
9.10
Demand Shift
Supply Shift
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
∆Inf = Inflation differential between
two countries
∆Int = Interest Rate differential be-
tween two countries
∆Inc = Income differential between
two countries
Quantity of Euro
(purchasing Norwegian Krone)
PriceofEuro(EUR/NOK)
S0
D0
D1
Q◦(Euro)
NOK
8.72
NOK
9.10
Increased demand of for-
eign goods due to in-
creased income levels
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
∆Inf = Inflation differential between
two countries
∆Int = Interest Rate differential be-
tween two countries
∆Inc = Income differential between
two countries
∆Gc = Government Control differen-
tial between two countries
Variable Selected:
Consumer Price Index
(CPI)
Interest Rate (Norway
and Euro Zone)
Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Factors affecting exchange rate
Factors affecting exchange rate
e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1)
∆Inf = Inflation differential between
two countries
∆Int = Interest Rate differential be-
tween two countries
∆Inc = Income differential between
two countries
∆Gc = Government Control differen-
tial between two countries
∆Exp = Expectation differential be-
tween two countries
Variable Selected:
Consumer Price Index
(CPI)
Interest Rate (Norway
and Euro Zone)
Loan Interest Rate
Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Foreign currency and Exchange rate
Involvement of Foreign Currency and Exchange Rate
Exchange
Rate Involve
during
Foreign Investment
Trading of Goods
and Services
Travelling and
many other
activities
Import Export
All these activities involve exchange of currency. These activities are
recorded as Balance of Payments account.
Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Current Account
Payments for merchandise and services
Factor Income payments
Transfer payments
Capital and Financial Account
Direct foreign investment
Portfolio investment
Other Capital Investment
Errors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Current Account
Payments for merchandise and services
Imports and Exports of Merchandise (tangible
products) and Services(tourism, consulting
service etc)
The difference is referred as Balance of trade
Import and Export of Good (Merchandise)
which are only availiable in Monthly format
are considered in this thesis
Factor Income payments
Transfer payments
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Current Account
Payments for merchandise and services
Factor Income payments
Income as Interest and Dividents
received by domestic investors on foreign
investments
payed to foreign investors on domestic
investments
Transfer payments
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Current Account
Payments for merchandise and services
Factor Income payments
Transfer payments
Represents aid, grands and gifts from one country to
another
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Capital and Financial Account
Direct foreign investment
Includes investment in fixed assets in foreign
countries
Portfolio investment
Other Capital Investment
Errors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Capital and Financial Account
Direct foreign investment
Portfolio investment
Includes long term transaction of long term
financial assets such as bonds and stocks
Other Capital Investment
Errors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Capital and Financial Account
Direct foreign investment
Portfolio investment
Other Capital Investment
Includes short term financial assets such as
money market securities
Errors, Omissions and Reserves
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Capital and Financial Account
Direct foreign investment
Portfolio investment
Other Capital Investment
Errors, Omissions and Reserves
Includes adjustment for negative balance in
current account
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Balance of Payment Account
Balance of Payment Account
Balance of Payment has two components - Current Account and Capital
Account;
Current Account
Payments for merchandise and services
Factor Income payments
Transfer payments
Capital and Financial Account
Direct foreign investment
Portfolio investment
Other Capital Investment
Errors, Omissions and Reserves
Variable Selected
Import
Oil Platform, Old Ship,
New Ship, Excluding Oil
and Ship Platform
Export
Condense Fuel, Crude oil,
Natural gas, Oil platform,
Old and new ships,
Excluding Ships and oil
platform
Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
Part I Relevant Variables
Some relevant variables selected for analysis
Financial Variables
Key Policy Rate of Norway (KeyIntRate)
Overnight lending rate (LoanIntRate)
Money market interest rates of Euro Area
(EuroIntRate)
Consumer Price Index (CPI)
Price Variable
Europe Brent Spot Price (OilSpotPrice)
Lagged Variables
First lag of Exchange Rate (ly.var)
Second lag of Exchange Rate (l2y.var)
First lag of Consumer Price Index (l.CPI)
Import Variables
Old Ship (ImpOldShip)
New Ship (ImpNewShip)
Oil Platform (ImpOilPlat)
Excluding Ship and Oil Platform
(ImpExShipOilPlat)
Export Variables
Crude Oil (ExpCrdOil)
Natural Gas (ExpNatGas)
Condensed Fuel (ExpCond)
Old Ship (ExpOldShip)
New Ship (ExpNewShip)
Oil Platform (ExpOilPlat)
Excluding Ship and Oil Platform
(ExpExShipOilPlat)
Raju RImal (NMBU) Masters Thesis April 22, 2015 9 / 23
Part II
Making prediction using different models
Raju RImal (NMBU) Masters Thesis April 22, 2015 10 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,
Multiple Linear Model
Y = β0 + β1X1 + . . . + βpXp
The OLS estimate of β is,
ˆβ = Xt
X
−1
Xt
Y
Ridge Regression
Principal Component Regression
Partial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,
Multiple Linear Model
Ridge Regression
Larger estimates due to multicollinearity is settled by using modified
OLS estimate in case of Ridge Regression as,
ˆβridge = λIp + Xt
X
−1
Xt
Y
Here, ridge parameter λ is estimated by minimizing RMSEP through
cross validation
Principal Component Regression
Partial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,
Multiple Linear Model
Ridge Regression
Principal Component Regression
A new set of variables Z1, . . . Zk called principal components are
constructed from linear combination of predictor variables
The variation present on predictor variables are accumulated on first
few principal components
Partial Least Square Regression
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Statistical Models
Models in use
Following models are used for prediction of Exchange Rate,
Multiple Linear Model
Ridge Regression
Principal Component Regression
Partial Least Square Regression
A new set of latent variables Z1, . . . , Zk are constructed.
The variables tries to capture most information in predictor variable
that is useful for explaining response.
Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results with
few significant variables (EuroIntRate, ly.var and l2y.var).
Subset models are created from the full model using following criteria,
Minimum Mallow’s Cp and Maximum adjusted R2
Minimum AIC and BIC
Stepwise procedure (Forward and Backward) based on F-value
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results with
few significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Minimum Mallow’s Cp and Maximum adjusted R2
1.2
0.04
0
0
−0.23
−0.03
1.1
R−Sq = 0.914
Adj R−Sq = 0.911
Sigma = 0.112
F = 264.8 (6,149)
0
5
10
15
(Intercept)
EuroIntRate
ExpCrdOil
ImpOldShip
l2y.var
LoanIntRate
ly.var
T−Value
0.65
0.06
0
0
0
0
0.01
−0.22
−0.03
1.08
0
R−Sq = 0.917
Adj R−Sq = 0.912
Sigma = 0.112
F = 160.9 (6,149)
0
5
10
15
(Intercept)
EuroIntRate
ExpCrdOil
ExpOilPlat
ImpNewShip
ImpOldShip
l.CPI
l2y.var
LoanIntRate
ly.var
OilSpotPrice
T−Value
Subset of linear model selected from criteria of minimum Mallow’s Cp (left) and maximum
adjusted R2 (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results with
few significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Minimum AIC and BIC
0.65
0.06
0
0
0
0
0.01
−0.22
−0.03
1.08
0
R−Sq = 0.917
Adj R−Sq = 0.912
Sigma = 0.112
F = 160.9 (6,149)
0
5
10
15
(Intercept)
EuroIntRate
ExpCrdOil
ExpOilPlat
ImpNewShip
ImpOldShip
l.CPI
l2y.var
LoanIntRate
ly.var
OilSpotPrice
T−Value
0.67
0
−0.22
1.14
R−Sq = 0.91
Adj R−Sq = 0.909
Sigma = 0.114
F = 514.1 (6,149)
0
5
10
15
(Intercept)
ImpOldShip
l2y.var
ly.var
T−Value
Subset of linear model selected from criteria of minimum AIC (left) and BIC (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results with
few significant variables (EuroIntRate, ly.var and l2y.var).
Subset Model with criteria of
Stepwise procedure (Forward and Backward) based on F-value
0.67
0
−0.22
1.14
R−Sq = 0.91
Adj R−Sq = 0.909
Sigma = 0.114
F = 514.1 (6,149)
0
5
10
15
(Intercept)
ImpOldShip
l2y.var
ly.var
T−Value
1.2
0.04
0
0
−0.23
−0.03
1.1
R−Sq = 0.914
Adj R−Sq = 0.911
Sigma = 0.112
F = 264.8 (6,149)
0
5
10
15
(Intercept)
EuroIntRate
ExpCrdOil
ImpOldShip
l2y.var
LoanIntRate
ly.var
T−Value
Subset of linear model selected from F-test based criteria through forward selection procedure
(left) and backward elimination procedure (right)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Linear Models
Linear Models
Multiple Linear regression with full set of predictor variable results with
few significant variables (EuroIntRate, ly.var and l2y.var).
Following pairs of model are found equivalent as they constitute of same
set of variables,
Model selected from minimum AIC (aicMdl) and maximum Adjusted
R2 (r2.model)
Model selected from F-based backward elimination procedure
(backward) and minimum Mallow’s Cp (cp.model)
Model selected from minimum BIC (bicMdl) and F-based Forward
selected procedure (forward)
Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
Part II Multicollinearity Problem
Multicollinearity Problem
Linear model with full set of predictor variable has serious
multicollinearity problem
subset model selected from minimum AIC and Maximum Adjusted R2
criteria also have problems with multicollinearity.
0.0e+00
2.5e+08
5.0e+08
7.5e+08
1.0e+09
KeyIntRate
LoanIntRate
EuroIntRate
CPI
OilSpotPrice
ImpOldShip
ImpNewShip
ImpOilPlat
ImpExShipOilPlat
ExpCrdOil
ExpNatGas
ExpCond
ExpOldShip
ExpNewShip
ExpOilPlat
ExpExShipOilPlat
TrBal
TrBalExShipOilPlat
TrBalMland
ly.var
l2y.var
l.CPI
Variables
VIF
Linear Model
0.0
2.5
5.0
7.5
10.0
LoanIntRate
EuroIntRate
OilSpotPrice
ImpOldShip
ImpNewShip
ExpCrdOil
ExpOilPlat
ly.var
l2y.var
l.CPI
Variables
VIF
Model selected (criteria:AIC)
Using models such as PCR and PLS can solve this problem
Raju RImal (NMBU) Masters Thesis April 22, 2015 13 / 23
Part II PCR and PLS regression Model
PCR and PLS Regression
0
25
50
75
100
0 5 10 15 20
Components
VariationExplained
X PerEURO
Variation Explained by PCR Model
25
50
75
100
0 5 10 15 20
Components
VariationExplained
X PerEURO
Variation Explained by PLS Model
More than 90 percent of variation present in Exchange Rate is
explained by 16 components of PCR model while PLS has explained
that much of variation by 6 components.
However, PCR model has captured most of the variation present in
predictor with fewer components than PLS model.
Raju RImal (NMBU) Masters Thesis April 22, 2015 14 / 23
Part II Ridge Regression
Ridge Regression
Also known as shrinkage
methods as it shrinks the
estimate that are enlarged by
Multicollinearity.
The ridge parameter λ is
estimated by minimizing the
Root mean square error
(RMSECV) using
cross-validation technique.
Here, λ is found to be 0.005
0.1350
0.1375
0.1400
0.1425
0.0000 0.0025 0.0050 0.0075 0.0100
λ
RMSEP
Setting up λ that minimize the RMSEP
Raju RImal (NMBU) Masters Thesis April 22, 2015 15 / 23
Part II Cross-validation and Prediction
Cross-valudation and Prediction
All the models seemed to work fine with observations included, but how it
behave with new observation – here comes the role of cross-validation.
Jan 2000 – Dec 2012
Training dataset
Jan 2013 – Nov 2014
Test dataset
Dataset is splitted into calibration set and test set as in figure above
Models fitted with training set were analysed for its behaviour with
new observations through cross-validation with consecutive segment of
length 12
2000 2001 . . . 2012
Training Set
Raju RImal (NMBU) Masters Thesis April 22, 2015 16 / 23
Part III
Compare the models
Raju RImal (NMBU) Masters Thesis April 22, 2015 17 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fit
Model AIC BIC R.Sq R.Sq.Adj Sigma F.value
linear -207.178 -133.982 0.919 0.906 0.116 68.594
cp.model -230.323 -205.925 0.914 0.911 0.112 264.849
r2.model -227.995 -191.397 0.917 0.912 0.112 160.906
aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906
bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106
forward -229.234 -213.985 0.910 0.909 0.114 514.106
backward -230.323 -205.925 0.914 0.911 0.112 264.849
Selected Linear Models, Ridge Model, PCR model and PLS models are
then compared on the basis of predictability
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fit
Model AIC BIC R.Sq R.Sq.Adj Sigma F.value
linear -207.178 -133.982 0.919 0.906 0.116 68.594
cp.model -230.323 -205.925 0.914 0.911 0.112 264.849
r2.model -227.995 -191.397 0.917 0.912 0.112 160.906
aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906
bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106
forward -229.234 -213.985 0.910 0.909 0.114 514.106
backward -230.323 -205.925 0.914 0.911 0.112 264.849
As prediction is objective, aicMdl or r2.model can be selected since they
have smallest residual standard error and explain the variation in exchange
rate better than other
Selected Linear Models, Ridge Model, PCR model and PLS models are then
compared on the basis of predictability
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comparison of Models
Comparison of Models
Linear Models are compared on the bases of their goodness of fit
Selected Linear Models, Ridge Model, PCR model and PLS models are
then compared on the basis of predictability
O
O
O
O O
O
RMSEP R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Models
Value(RMSEP/R−sqpred)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,
Linear Models predicts well for observations
included in the model
O
O
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Models
Value(RMSEP/R−sqpred)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,
Linear Models predicts well for observations
included in the model
Ridge regression perform moderately but
has predicted closer than some linear
models for new observations
O
O
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Models
Value(RMSEP/R−sqpred)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,
Linear Models predicts well for observations
included in the model
Ridge regression perform moderately but
has predicted closer than some linear
models for new observations
PCR and PLS models have made more
accurate prediction than other linear models
both in the case of cross-validation and test
dataset
O
O
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Models
Value(RMSEP/R−sqpred)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Comments on Model Comparison
Some Comments on model comparison
Figure alongside shows that,
Linear Models predicts well for observations
included in the model
Ridge regression perform moderately but
has predicted closer than some linear
models for new observations
PCR and PLS models have made more
accurate prediction than other linear models
both in the case of cross-validation and test
dataset
PLS model with 7 components has least
RMSEP while PCR model with 16
components ave least RMSECV
O
O
O
O O
O
RMSEP
R2pred
0.10
0.11
0.12
0.13
0.14
0.84
0.87
0.90
Linear
AICModel
BICModel
BackModel
Ridge
PCR.Comp15
PCR.Comp16
PCR.Comp17
PLS.Comp6
PLS.Comp7
PLS.Comp8
PLS.Comp9
Models
Value(RMSEP/R−sqpred)
train test cv
Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
Part III Discussions and Conclusions
Discussions and Conclusions
This thesis has attempted to make prediction in time series data
Some subset of linear model considered are free from multicollinearity
In case of multicollinearity problem, latent variable models like PLS
and PCR can deal with the situation
PLS and PCR models also outperformed in predicting new
observations that are not included in the model
Autocorrelation is inevitable in time series data, including lagged
dependent variable in the model has corrected the problem
Residuals obtained from selected model (pls.comp7) does not contain
any autocorrelation PACF plot
More practices are recommented to study the performance of latent
variable model in time-series data
Next
Raju RImal (NMBU) Masters Thesis April 22, 2015 20 / 23
Part III Discussions and Conclusions
Partial Autocorrelation Function
Linear Ridge
PCR.16 PLS.7
−0.1
0.0
0.1
0.2
−0.1
0.0
0.1
0.2
0 5 10 15 20 0 5 10 15 20
Var1
PACF
Partial Autocorrelation Function (PACF)
Raju RImal (NMBU) Masters Thesis April 22, 2015 21 / 23
Part III Discussions and Conclusions
Acknoledgement
Thanks to my Supervisors,
Ellen Sandberg and Trygve Almøy
and professor
Solve Sæbø
for their guidance and encouragements
Raju RImal (NMBU) Masters Thesis April 22, 2015 22 / 23
THANK YOU

More Related Content

What's hot

Balance of Payments Basics - 2015 (India)
Balance of Payments Basics - 2015 (India)Balance of Payments Basics - 2015 (India)
Balance of Payments Basics - 2015 (India)Suryansh Bansal
 
National income and related aggregates
National income and  related aggregatesNational income and  related aggregates
National income and related aggregatesAmiteshYadav7
 
Methods of foreign currency translation (current rate, current and non curren...
Methods of foreign currency translation (current rate, current and non curren...Methods of foreign currency translation (current rate, current and non curren...
Methods of foreign currency translation (current rate, current and non curren...Sundar B N
 
BALANCE OF PAYMENTS
BALANCE OF PAYMENTSBALANCE OF PAYMENTS
BALANCE OF PAYMENTSsairajch10
 
Current Account Deficit
Current Account DeficitCurrent Account Deficit
Current Account DeficitCp Prasad
 
Balanace of payment
Balanace of paymentBalanace of payment
Balanace of paymentIsaf Ali
 
Analysis for Balance of payments in Egypt
Analysis for Balance of payments in EgyptAnalysis for Balance of payments in Egypt
Analysis for Balance of payments in EgyptAhmad Bakr
 
A2 Macro: Balance of Payments and Exchange Rates
A2 Macro: Balance of Payments and Exchange RatesA2 Macro: Balance of Payments and Exchange Rates
A2 Macro: Balance of Payments and Exchange Ratestutor2u
 
Indices of economic trends
Indices of economic trendsIndices of economic trends
Indices of economic trendsHrishikesh Epte
 
"Do Current Account Deficits Matter?"
"Do Current Account Deficits Matter?""Do Current Account Deficits Matter?"
"Do Current Account Deficits Matter?"mkcrookham
 
Macroecos - Definition, scope, trade cycles, national income concepts
Macroecos - Definition, scope, trade cycles, national income conceptsMacroecos - Definition, scope, trade cycles, national income concepts
Macroecos - Definition, scope, trade cycles, national income conceptsPrabha Panth
 
Balance Of Payment
Balance Of Payment Balance Of Payment
Balance Of Payment Ajeesh Mk
 
Current account deficit of india
Current account deficit of indiaCurrent account deficit of india
Current account deficit of indiaSunanda Sarker
 
India's Current Account Deficit- A report
India's Current Account Deficit- A reportIndia's Current Account Deficit- A report
India's Current Account Deficit- A reportGurpreet Singh
 
U.S current account deficit
U.S current account deficitU.S current account deficit
U.S current account deficitTazeen Azeem
 
Analysis of foreign exchange exposure
Analysis of foreign exchange exposureAnalysis of foreign exchange exposure
Analysis of foreign exchange exposureStudsPlanet.com
 

What's hot (20)

Balance of Payments Basics - 2015 (India)
Balance of Payments Basics - 2015 (India)Balance of Payments Basics - 2015 (India)
Balance of Payments Basics - 2015 (India)
 
National income and related aggregates
National income and  related aggregatesNational income and  related aggregates
National income and related aggregates
 
Methods of foreign currency translation (current rate, current and non curren...
Methods of foreign currency translation (current rate, current and non curren...Methods of foreign currency translation (current rate, current and non curren...
Methods of foreign currency translation (current rate, current and non curren...
 
BALANCE OF PAYMENTS
BALANCE OF PAYMENTSBALANCE OF PAYMENTS
BALANCE OF PAYMENTS
 
Current Account Deficit
Current Account DeficitCurrent Account Deficit
Current Account Deficit
 
Balanace of payment
Balanace of paymentBalanace of payment
Balanace of payment
 
Analysis for Balance of payments in Egypt
Analysis for Balance of payments in EgyptAnalysis for Balance of payments in Egypt
Analysis for Balance of payments in Egypt
 
A2 Macro: Balance of Payments and Exchange Rates
A2 Macro: Balance of Payments and Exchange RatesA2 Macro: Balance of Payments and Exchange Rates
A2 Macro: Balance of Payments and Exchange Rates
 
Indices of economic trends
Indices of economic trendsIndices of economic trends
Indices of economic trends
 
"Do Current Account Deficits Matter?"
"Do Current Account Deficits Matter?""Do Current Account Deficits Matter?"
"Do Current Account Deficits Matter?"
 
Macroecos - Definition, scope, trade cycles, national income concepts
Macroecos - Definition, scope, trade cycles, national income conceptsMacroecos - Definition, scope, trade cycles, national income concepts
Macroecos - Definition, scope, trade cycles, national income concepts
 
Balance of payment
Balance of paymentBalance of payment
Balance of payment
 
Balance Of Payment
Balance Of Payment Balance Of Payment
Balance Of Payment
 
Current account deficit of india
Current account deficit of indiaCurrent account deficit of india
Current account deficit of india
 
BALANCE OF PAYMENTS
BALANCE OF PAYMENTSBALANCE OF PAYMENTS
BALANCE OF PAYMENTS
 
India's Current Account Deficit- A report
India's Current Account Deficit- A reportIndia's Current Account Deficit- A report
India's Current Account Deficit- A report
 
U.S current account deficit
U.S current account deficitU.S current account deficit
U.S current account deficit
 
Analysis of foreign exchange exposure
Analysis of foreign exchange exposureAnalysis of foreign exchange exposure
Analysis of foreign exchange exposure
 
Bhagyashree H. Chauhan (GST)
Bhagyashree H. Chauhan (GST)Bhagyashree H. Chauhan (GST)
Bhagyashree H. Chauhan (GST)
 
accounting standard
 accounting standard accounting standard
accounting standard
 

Similar to Exchange Rate Prediction Euro vs NOK from financial and commodity information

Trc q2 2015 earnings slides final
Trc q2 2015 earnings slides finalTrc q2 2015 earnings slides final
Trc q2 2015 earnings slides finaltrcsolutions
 
Valmet's Interim Review January-September 2015
Valmet's Interim Review January-September 2015Valmet's Interim Review January-September 2015
Valmet's Interim Review January-September 2015Valmet Oyj
 
HeidelbergCement: Q1 2015 Presentation
HeidelbergCement: Q1 2015 PresentationHeidelbergCement: Q1 2015 Presentation
HeidelbergCement: Q1 2015 PresentationHeidelbergCement
 
Macroeconomic trends and near-term policy challenges in Emerging Asia
Macroeconomic trends and near-term policy challenges in Emerging AsiaMacroeconomic trends and near-term policy challenges in Emerging Asia
Macroeconomic trends and near-term policy challenges in Emerging AsiaOECD Development Centre, Paris
 
Q2 2015 3 m earnings presentation
Q2 2015 3 m earnings presentationQ2 2015 3 m earnings presentation
Q2 2015 3 m earnings presentationInvestors_3M
 
State of economy - economic survey of India 2013-14
State of economy - economic survey of India 2013-14State of economy - economic survey of India 2013-14
State of economy - economic survey of India 2013-14Swapnil Soni
 
LinkedIn Q2 2014 Earnings Call
LinkedIn Q2 2014 Earnings CallLinkedIn Q2 2014 Earnings Call
LinkedIn Q2 2014 Earnings CallLinkedIn
 
4 q15 external earnings_presentation_2016-02-04_final
4 q15 external earnings_presentation_2016-02-04_final4 q15 external earnings_presentation_2016-02-04_final
4 q15 external earnings_presentation_2016-02-04_finalLevel3_Communications
 
3 Q 2015 External Earnings Presentation 2015-10-28-Final
3 Q 2015 External Earnings Presentation 2015-10-28-Final3 Q 2015 External Earnings Presentation 2015-10-28-Final
3 Q 2015 External Earnings Presentation 2015-10-28-FinalLevel3_Communications
 
EIBTM Trends Watch Report 2014
EIBTM Trends Watch Report 2014EIBTM Trends Watch Report 2014
EIBTM Trends Watch Report 2014Rob Davidson
 
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)State of the Bangladesh Economy in Fiscal Year 2015 (first reading)
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)Centre for Policy Dialogue (CPD)
 
Trc q3 2015 earnings slides final
Trc q3 2015 earnings slides finalTrc q3 2015 earnings slides final
Trc q3 2015 earnings slides finaltrcsolutions
 
Tools for spending review in Japan and the use of key performance indicators ...
Tools for spending review in Japan and the use of key performance indicators ...Tools for spending review in Japan and the use of key performance indicators ...
Tools for spending review in Japan and the use of key performance indicators ...OECD Governance
 
Presentation debt sales event Berlin Nov 2015
Presentation debt sales event Berlin Nov 2015Presentation debt sales event Berlin Nov 2015
Presentation debt sales event Berlin Nov 2015Casper Sonnega
 
Relationship Between Vietnamese Stock Price Relative On...
Relationship Between Vietnamese Stock Price Relative On...Relationship Between Vietnamese Stock Price Relative On...
Relationship Between Vietnamese Stock Price Relative On...Karina Thomas
 
Public Budget Analysis Project: Queensland, Australia
Public Budget Analysis Project: Queensland, AustraliaPublic Budget Analysis Project: Queensland, Australia
Public Budget Analysis Project: Queensland, AustraliaRaul A. Lujan Anaya
 
Trc q1 2015 earnings slides final
Trc q1 2015 earnings slides finalTrc q1 2015 earnings slides final
Trc q1 2015 earnings slides finaltrcsolutions
 
Enbridge Inc. Third Quarter 2014 Financial Results
Enbridge Inc. Third Quarter 2014 Financial ResultsEnbridge Inc. Third Quarter 2014 Financial Results
Enbridge Inc. Third Quarter 2014 Financial ResultsEnbridge Inc.
 

Similar to Exchange Rate Prediction Euro vs NOK from financial and commodity information (20)

Trc q2 2015 earnings slides final
Trc q2 2015 earnings slides finalTrc q2 2015 earnings slides final
Trc q2 2015 earnings slides final
 
Valmet's Interim Review January-September 2015
Valmet's Interim Review January-September 2015Valmet's Interim Review January-September 2015
Valmet's Interim Review January-September 2015
 
HeidelbergCement: Q1 2015 Presentation
HeidelbergCement: Q1 2015 PresentationHeidelbergCement: Q1 2015 Presentation
HeidelbergCement: Q1 2015 Presentation
 
Macroeconomic trends and near-term policy challenges in Emerging Asia
Macroeconomic trends and near-term policy challenges in Emerging AsiaMacroeconomic trends and near-term policy challenges in Emerging Asia
Macroeconomic trends and near-term policy challenges in Emerging Asia
 
Q2 2015 3 m earnings presentation
Q2 2015 3 m earnings presentationQ2 2015 3 m earnings presentation
Q2 2015 3 m earnings presentation
 
State of economy - economic survey of India 2013-14
State of economy - economic survey of India 2013-14State of economy - economic survey of India 2013-14
State of economy - economic survey of India 2013-14
 
LinkedIn Q2 2014 Earnings Call
LinkedIn Q2 2014 Earnings CallLinkedIn Q2 2014 Earnings Call
LinkedIn Q2 2014 Earnings Call
 
4 q15 external earnings_presentation_2016-02-04_final
4 q15 external earnings_presentation_2016-02-04_final4 q15 external earnings_presentation_2016-02-04_final
4 q15 external earnings_presentation_2016-02-04_final
 
3 Q 2015 External Earnings Presentation 2015-10-28-Final
3 Q 2015 External Earnings Presentation 2015-10-28-Final3 Q 2015 External Earnings Presentation 2015-10-28-Final
3 Q 2015 External Earnings Presentation 2015-10-28-Final
 
EIBTM Trends Watch Report 2014
EIBTM Trends Watch Report 2014EIBTM Trends Watch Report 2014
EIBTM Trends Watch Report 2014
 
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)State of the Bangladesh Economy in Fiscal Year 2015 (first reading)
State of the Bangladesh Economy in Fiscal Year 2015 (first reading)
 
Trc q3 2015 earnings slides final
Trc q3 2015 earnings slides finalTrc q3 2015 earnings slides final
Trc q3 2015 earnings slides final
 
Tools for spending review in Japan and the use of key performance indicators ...
Tools for spending review in Japan and the use of key performance indicators ...Tools for spending review in Japan and the use of key performance indicators ...
Tools for spending review in Japan and the use of key performance indicators ...
 
Presentation debt sales event Berlin Nov 2015
Presentation debt sales event Berlin Nov 2015Presentation debt sales event Berlin Nov 2015
Presentation debt sales event Berlin Nov 2015
 
Relationship Between Vietnamese Stock Price Relative On...
Relationship Between Vietnamese Stock Price Relative On...Relationship Between Vietnamese Stock Price Relative On...
Relationship Between Vietnamese Stock Price Relative On...
 
Public Budget Analysis Project: Queensland, Australia
Public Budget Analysis Project: Queensland, AustraliaPublic Budget Analysis Project: Queensland, Australia
Public Budget Analysis Project: Queensland, Australia
 
BI&P- Indusval- 1Q14 Earnings Release
BI&P- Indusval- 1Q14 Earnings ReleaseBI&P- Indusval- 1Q14 Earnings Release
BI&P- Indusval- 1Q14 Earnings Release
 
Trc q1 2015 earnings slides final
Trc q1 2015 earnings slides finalTrc q1 2015 earnings slides final
Trc q1 2015 earnings slides final
 
2 q15 earnings presentation
2 q15 earnings presentation2 q15 earnings presentation
2 q15 earnings presentation
 
Enbridge Inc. Third Quarter 2014 Financial Results
Enbridge Inc. Third Quarter 2014 Financial ResultsEnbridge Inc. Third Quarter 2014 Financial Results
Enbridge Inc. Third Quarter 2014 Financial Results
 

Recently uploaded

Stock Market Brief Deck for March 19 2024.pdf
Stock Market Brief Deck for March 19 2024.pdfStock Market Brief Deck for March 19 2024.pdf
Stock Market Brief Deck for March 19 2024.pdfMichael Silva
 
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.KumarJayaraman3
 
20240315 _E-Invoicing Digiteal. .pptx
20240315 _E-Invoicing Digiteal.    .pptx20240315 _E-Invoicing Digiteal.    .pptx
20240315 _E-Invoicing Digiteal. .pptxFinTech Belgium
 
Taipei, A Hidden Jewel in East Asia - PR Strategy for Tourism
Taipei, A Hidden Jewel in East Asia - PR Strategy for TourismTaipei, A Hidden Jewel in East Asia - PR Strategy for Tourism
Taipei, A Hidden Jewel in East Asia - PR Strategy for TourismBrian Lin
 
Work and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingWork and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingHenry Tapper
 
LIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxLIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxsonamyadav7097
 
The unequal battle of inflation and the appropriate sustainable solution | Eu...
The unequal battle of inflation and the appropriate sustainable solution | Eu...The unequal battle of inflation and the appropriate sustainable solution | Eu...
The unequal battle of inflation and the appropriate sustainable solution | Eu...Antonis Zairis
 
20240314 Calibre March 2024 Investor Presentation (FINAL).pdf
20240314 Calibre March 2024 Investor Presentation (FINAL).pdf20240314 Calibre March 2024 Investor Presentation (FINAL).pdf
20240314 Calibre March 2024 Investor Presentation (FINAL).pdfAdnet Communications
 
Monthly Market Risk Update: March 2024 [SlideShare]
Monthly Market Risk Update: March 2024 [SlideShare]Monthly Market Risk Update: March 2024 [SlideShare]
Monthly Market Risk Update: March 2024 [SlideShare]Commonwealth
 
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoRWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoCoinGecko
 
Stock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfStock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfMichael Silva
 
Contracts with Interdependent Preferences
Contracts with Interdependent PreferencesContracts with Interdependent Preferences
Contracts with Interdependent PreferencesGRAPE
 
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...Matthews Bantsijang
 
What Key Factors Should Risk Officers Consider When Using Generative AI
What Key Factors Should Risk Officers Consider When Using Generative AIWhat Key Factors Should Risk Officers Consider When Using Generative AI
What Key Factors Should Risk Officers Consider When Using Generative AI360factors
 
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdf
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdfLundin Gold March 2024 Corporate Presentation - PDAC v1.pdf
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdfAdnet Communications
 
Mphasis - Schwab Newsletter PDF - Sample 8707
Mphasis - Schwab Newsletter PDF - Sample 8707Mphasis - Schwab Newsletter PDF - Sample 8707
Mphasis - Schwab Newsletter PDF - Sample 8707harshan90
 
Hungarys economy made by Robert Miklos
Hungarys economy   made by Robert MiklosHungarys economy   made by Robert Miklos
Hungarys economy made by Robert Miklosbeduinpower135
 
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptx
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptxSlideshare - ONS Economic Forum Slidepack - 18 March 2024.pptx
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptxOffice for National Statistics
 
The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?Stephen Perrenod
 
Stock Market Brief Deck for 3/22/2024.pdf
Stock Market Brief Deck for 3/22/2024.pdfStock Market Brief Deck for 3/22/2024.pdf
Stock Market Brief Deck for 3/22/2024.pdfMichael Silva
 

Recently uploaded (20)

Stock Market Brief Deck for March 19 2024.pdf
Stock Market Brief Deck for March 19 2024.pdfStock Market Brief Deck for March 19 2024.pdf
Stock Market Brief Deck for March 19 2024.pdf
 
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
ACCOUNTING FOR BUSINESS.II DEPARTMENTAL ACCOUNTS.
 
20240315 _E-Invoicing Digiteal. .pptx
20240315 _E-Invoicing Digiteal.    .pptx20240315 _E-Invoicing Digiteal.    .pptx
20240315 _E-Invoicing Digiteal. .pptx
 
Taipei, A Hidden Jewel in East Asia - PR Strategy for Tourism
Taipei, A Hidden Jewel in East Asia - PR Strategy for TourismTaipei, A Hidden Jewel in East Asia - PR Strategy for Tourism
Taipei, A Hidden Jewel in East Asia - PR Strategy for Tourism
 
Work and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB fundingWork and Pensions report into UK corporate DB funding
Work and Pensions report into UK corporate DB funding
 
LIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptxLIC PRIVATISATION its a bane or boon.pptx
LIC PRIVATISATION its a bane or boon.pptx
 
The unequal battle of inflation and the appropriate sustainable solution | Eu...
The unequal battle of inflation and the appropriate sustainable solution | Eu...The unequal battle of inflation and the appropriate sustainable solution | Eu...
The unequal battle of inflation and the appropriate sustainable solution | Eu...
 
20240314 Calibre March 2024 Investor Presentation (FINAL).pdf
20240314 Calibre March 2024 Investor Presentation (FINAL).pdf20240314 Calibre March 2024 Investor Presentation (FINAL).pdf
20240314 Calibre March 2024 Investor Presentation (FINAL).pdf
 
Monthly Market Risk Update: March 2024 [SlideShare]
Monthly Market Risk Update: March 2024 [SlideShare]Monthly Market Risk Update: March 2024 [SlideShare]
Monthly Market Risk Update: March 2024 [SlideShare]
 
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGeckoRWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
RWA Report 2024: Rise of Real-World Assets in Crypto | CoinGecko
 
Stock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdfStock Market Brief Deck for March 26.pdf
Stock Market Brief Deck for March 26.pdf
 
Contracts with Interdependent Preferences
Contracts with Interdependent PreferencesContracts with Interdependent Preferences
Contracts with Interdependent Preferences
 
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...
Remembering my Totem _Unity is Strength_ growing in Bophuthatswana_Matthews B...
 
What Key Factors Should Risk Officers Consider When Using Generative AI
What Key Factors Should Risk Officers Consider When Using Generative AIWhat Key Factors Should Risk Officers Consider When Using Generative AI
What Key Factors Should Risk Officers Consider When Using Generative AI
 
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdf
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdfLundin Gold March 2024 Corporate Presentation - PDAC v1.pdf
Lundin Gold March 2024 Corporate Presentation - PDAC v1.pdf
 
Mphasis - Schwab Newsletter PDF - Sample 8707
Mphasis - Schwab Newsletter PDF - Sample 8707Mphasis - Schwab Newsletter PDF - Sample 8707
Mphasis - Schwab Newsletter PDF - Sample 8707
 
Hungarys economy made by Robert Miklos
Hungarys economy   made by Robert MiklosHungarys economy   made by Robert Miklos
Hungarys economy made by Robert Miklos
 
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptx
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptxSlideshare - ONS Economic Forum Slidepack - 18 March 2024.pptx
Slideshare - ONS Economic Forum Slidepack - 18 March 2024.pptx
 
The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?The Power Laws of Bitcoin: How can an S-curve be a power law?
The Power Laws of Bitcoin: How can an S-curve be a power law?
 
Stock Market Brief Deck for 3/22/2024.pdf
Stock Market Brief Deck for 3/22/2024.pdfStock Market Brief Deck for 3/22/2024.pdf
Stock Market Brief Deck for 3/22/2024.pdf
 

Exchange Rate Prediction Euro vs NOK from financial and commodity information

  • 1. Evaluation of Models for predicting the average monthly Euro versus Norwegian krone exchange rate from financial and commodity information Raju RImal Norwegian University of Life Sciences (NMBU) April 22, 2015 Raju RImal (NMBU) Masters Thesis April 22, 2015 1 / 23
  • 2. Table of Contents 1 The BIG picture 2 Part I Exchange rate determination Factors affecting exchange rate Foreign currency and Exchange rate Balance of Payment Account Relevant Variables 3 Part II Statistical Models Linear Models Multicollinearity Problem PCR and PLS regression Model Ridge Regression Cross-validation and Prediction 4 Part III Comparison of Models Comments on Model Comparison Discussions and Conclusions Raju RImal (NMBU) Masters Thesis April 22, 2015 2 / 23
  • 3. The BIG picture The BIG picture 1 Identify functional relationship of Exchange rate with financial and commodity variables Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
  • 4. The BIG picture The BIG picture 1 Identify functional relationship of Exchange rate with financial and commodity variables 2 Make prediction using different models Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
  • 5. The BIG picture The BIG picture 1 Identify functional relationship of Exchange rate with financial and commodity variables 2 Make prediction using different models 3 Compare the models Raju RImal (NMBU) Masters Thesis April 22, 2015 3 / 23
  • 6. Part I Identify functional relationship of Exchange rate with financial and commodity variables Raju RImal (NMBU) Masters Thesis April 22, 2015 4 / 23
  • 7. Part I Exchange rate determination Exchange rate determination Exchange Rate is a price of one currency in terms of another Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
  • 8. Part I Exchange rate determination Exchange rate determination Exchange Rate is a price of one currency in terms of another Determined from the demand and supply of the currency in Money Market (ForEx) −1. 1. 2. 3. 4. 5. 6. 7. 8. −1. 1. 2. 3. 4. 5. 6. 7. 0 Demand of Currency Supply of Currency Quantity ExchangeRate Equilibrium Point Raju RImal (NMBU) Masters Thesis April 22, 2015 5 / 23
  • 9. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 10. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) ∆Inf = Inflation differential between two countries S0 D0 ValueofEUROperNOK Quantity of EURO 9.10 9.97 S1 D1 QEuro Upward shift in Demand of Euro due to inflation in Norway Downward shift in supply of Euro purchasing NOK Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 11. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) ∆Inf = Inflation differential between two countries ∆Int = Interest Rate differential be- tween two countries Quantity of Euro (purchasing Norwegian Krone) PriceofEuro(EUR/NOK) S0 S1 D0 D1 QEuro NOK 8.72 NOK 9.10 Demand Shift Supply Shift Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 12. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) ∆Inf = Inflation differential between two countries ∆Int = Interest Rate differential be- tween two countries ∆Inc = Income differential between two countries Quantity of Euro (purchasing Norwegian Krone) PriceofEuro(EUR/NOK) S0 D0 D1 Q◦(Euro) NOK 8.72 NOK 9.10 Increased demand of for- eign goods due to in- creased income levels Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 13. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) ∆Inf = Inflation differential between two countries ∆Int = Interest Rate differential be- tween two countries ∆Inc = Income differential between two countries ∆Gc = Government Control differen- tial between two countries Variable Selected: Consumer Price Index (CPI) Interest Rate (Norway and Euro Zone) Loan Interest Rate Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 14. Part I Factors affecting exchange rate Factors affecting exchange rate e = f (∆Inf, ∆Int, ∆Inc, ∆Gc, ∆Exp) (1) ∆Inf = Inflation differential between two countries ∆Int = Interest Rate differential be- tween two countries ∆Inc = Income differential between two countries ∆Gc = Government Control differen- tial between two countries ∆Exp = Expectation differential be- tween two countries Variable Selected: Consumer Price Index (CPI) Interest Rate (Norway and Euro Zone) Loan Interest Rate Raju RImal (NMBU) Masters Thesis April 22, 2015 6 / 23
  • 15. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 16. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 17. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 18. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 19. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 20. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 21. Part I Foreign currency and Exchange rate Involvement of Foreign Currency and Exchange Rate Exchange Rate Involve during Foreign Investment Trading of Goods and Services Travelling and many other activities Import Export All these activities involve exchange of currency. These activities are recorded as Balance of Payments account. Raju RImal (NMBU) Masters Thesis April 22, 2015 7 / 23
  • 22. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Current Account Payments for merchandise and services Factor Income payments Transfer payments Capital and Financial Account Direct foreign investment Portfolio investment Other Capital Investment Errors, Omissions and Reserves Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 23. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Current Account Payments for merchandise and services Imports and Exports of Merchandise (tangible products) and Services(tourism, consulting service etc) The difference is referred as Balance of trade Import and Export of Good (Merchandise) which are only availiable in Monthly format are considered in this thesis Factor Income payments Transfer payments Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 24. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Current Account Payments for merchandise and services Factor Income payments Income as Interest and Dividents received by domestic investors on foreign investments payed to foreign investors on domestic investments Transfer payments Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 25. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Current Account Payments for merchandise and services Factor Income payments Transfer payments Represents aid, grands and gifts from one country to another Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 26. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Capital and Financial Account Direct foreign investment Includes investment in fixed assets in foreign countries Portfolio investment Other Capital Investment Errors, Omissions and Reserves Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 27. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Capital and Financial Account Direct foreign investment Portfolio investment Includes long term transaction of long term financial assets such as bonds and stocks Other Capital Investment Errors, Omissions and Reserves Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 28. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Capital and Financial Account Direct foreign investment Portfolio investment Other Capital Investment Includes short term financial assets such as money market securities Errors, Omissions and Reserves Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 29. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Capital and Financial Account Direct foreign investment Portfolio investment Other Capital Investment Errors, Omissions and Reserves Includes adjustment for negative balance in current account Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 30. Part I Balance of Payment Account Balance of Payment Account Balance of Payment has two components - Current Account and Capital Account; Current Account Payments for merchandise and services Factor Income payments Transfer payments Capital and Financial Account Direct foreign investment Portfolio investment Other Capital Investment Errors, Omissions and Reserves Variable Selected Import Oil Platform, Old Ship, New Ship, Excluding Oil and Ship Platform Export Condense Fuel, Crude oil, Natural gas, Oil platform, Old and new ships, Excluding Ships and oil platform Raju RImal (NMBU) Masters Thesis April 22, 2015 8 / 23
  • 31. Part I Relevant Variables Some relevant variables selected for analysis Financial Variables Key Policy Rate of Norway (KeyIntRate) Overnight lending rate (LoanIntRate) Money market interest rates of Euro Area (EuroIntRate) Consumer Price Index (CPI) Price Variable Europe Brent Spot Price (OilSpotPrice) Lagged Variables First lag of Exchange Rate (ly.var) Second lag of Exchange Rate (l2y.var) First lag of Consumer Price Index (l.CPI) Import Variables Old Ship (ImpOldShip) New Ship (ImpNewShip) Oil Platform (ImpOilPlat) Excluding Ship and Oil Platform (ImpExShipOilPlat) Export Variables Crude Oil (ExpCrdOil) Natural Gas (ExpNatGas) Condensed Fuel (ExpCond) Old Ship (ExpOldShip) New Ship (ExpNewShip) Oil Platform (ExpOilPlat) Excluding Ship and Oil Platform (ExpExShipOilPlat) Raju RImal (NMBU) Masters Thesis April 22, 2015 9 / 23
  • 32. Part II Making prediction using different models Raju RImal (NMBU) Masters Thesis April 22, 2015 10 / 23
  • 33. Part II Statistical Models Models in use Following models are used for prediction of Exchange Rate, Multiple Linear Model Y = β0 + β1X1 + . . . + βpXp The OLS estimate of β is, ˆβ = Xt X −1 Xt Y Ridge Regression Principal Component Regression Partial Least Square Regression Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
  • 34. Part II Statistical Models Models in use Following models are used for prediction of Exchange Rate, Multiple Linear Model Ridge Regression Larger estimates due to multicollinearity is settled by using modified OLS estimate in case of Ridge Regression as, ˆβridge = λIp + Xt X −1 Xt Y Here, ridge parameter λ is estimated by minimizing RMSEP through cross validation Principal Component Regression Partial Least Square Regression Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
  • 35. Part II Statistical Models Models in use Following models are used for prediction of Exchange Rate, Multiple Linear Model Ridge Regression Principal Component Regression A new set of variables Z1, . . . Zk called principal components are constructed from linear combination of predictor variables The variation present on predictor variables are accumulated on first few principal components Partial Least Square Regression Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
  • 36. Part II Statistical Models Models in use Following models are used for prediction of Exchange Rate, Multiple Linear Model Ridge Regression Principal Component Regression Partial Least Square Regression A new set of latent variables Z1, . . . , Zk are constructed. The variables tries to capture most information in predictor variable that is useful for explaining response. Raju RImal (NMBU) Masters Thesis April 22, 2015 11 / 23
  • 37. Part II Linear Models Linear Models Multiple Linear regression with full set of predictor variable results with few significant variables (EuroIntRate, ly.var and l2y.var). Subset models are created from the full model using following criteria, Minimum Mallow’s Cp and Maximum adjusted R2 Minimum AIC and BIC Stepwise procedure (Forward and Backward) based on F-value Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
  • 38. Part II Linear Models Linear Models Multiple Linear regression with full set of predictor variable results with few significant variables (EuroIntRate, ly.var and l2y.var). Subset Model with criteria of Minimum Mallow’s Cp and Maximum adjusted R2 1.2 0.04 0 0 −0.23 −0.03 1.1 R−Sq = 0.914 Adj R−Sq = 0.911 Sigma = 0.112 F = 264.8 (6,149) 0 5 10 15 (Intercept) EuroIntRate ExpCrdOil ImpOldShip l2y.var LoanIntRate ly.var T−Value 0.65 0.06 0 0 0 0 0.01 −0.22 −0.03 1.08 0 R−Sq = 0.917 Adj R−Sq = 0.912 Sigma = 0.112 F = 160.9 (6,149) 0 5 10 15 (Intercept) EuroIntRate ExpCrdOil ExpOilPlat ImpNewShip ImpOldShip l.CPI l2y.var LoanIntRate ly.var OilSpotPrice T−Value Subset of linear model selected from criteria of minimum Mallow’s Cp (left) and maximum adjusted R2 (right) Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
  • 39. Part II Linear Models Linear Models Multiple Linear regression with full set of predictor variable results with few significant variables (EuroIntRate, ly.var and l2y.var). Subset Model with criteria of Minimum AIC and BIC 0.65 0.06 0 0 0 0 0.01 −0.22 −0.03 1.08 0 R−Sq = 0.917 Adj R−Sq = 0.912 Sigma = 0.112 F = 160.9 (6,149) 0 5 10 15 (Intercept) EuroIntRate ExpCrdOil ExpOilPlat ImpNewShip ImpOldShip l.CPI l2y.var LoanIntRate ly.var OilSpotPrice T−Value 0.67 0 −0.22 1.14 R−Sq = 0.91 Adj R−Sq = 0.909 Sigma = 0.114 F = 514.1 (6,149) 0 5 10 15 (Intercept) ImpOldShip l2y.var ly.var T−Value Subset of linear model selected from criteria of minimum AIC (left) and BIC (right) Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
  • 40. Part II Linear Models Linear Models Multiple Linear regression with full set of predictor variable results with few significant variables (EuroIntRate, ly.var and l2y.var). Subset Model with criteria of Stepwise procedure (Forward and Backward) based on F-value 0.67 0 −0.22 1.14 R−Sq = 0.91 Adj R−Sq = 0.909 Sigma = 0.114 F = 514.1 (6,149) 0 5 10 15 (Intercept) ImpOldShip l2y.var ly.var T−Value 1.2 0.04 0 0 −0.23 −0.03 1.1 R−Sq = 0.914 Adj R−Sq = 0.911 Sigma = 0.112 F = 264.8 (6,149) 0 5 10 15 (Intercept) EuroIntRate ExpCrdOil ImpOldShip l2y.var LoanIntRate ly.var T−Value Subset of linear model selected from F-test based criteria through forward selection procedure (left) and backward elimination procedure (right) Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
  • 41. Part II Linear Models Linear Models Multiple Linear regression with full set of predictor variable results with few significant variables (EuroIntRate, ly.var and l2y.var). Following pairs of model are found equivalent as they constitute of same set of variables, Model selected from minimum AIC (aicMdl) and maximum Adjusted R2 (r2.model) Model selected from F-based backward elimination procedure (backward) and minimum Mallow’s Cp (cp.model) Model selected from minimum BIC (bicMdl) and F-based Forward selected procedure (forward) Raju RImal (NMBU) Masters Thesis April 22, 2015 12 / 23
  • 42. Part II Multicollinearity Problem Multicollinearity Problem Linear model with full set of predictor variable has serious multicollinearity problem subset model selected from minimum AIC and Maximum Adjusted R2 criteria also have problems with multicollinearity. 0.0e+00 2.5e+08 5.0e+08 7.5e+08 1.0e+09 KeyIntRate LoanIntRate EuroIntRate CPI OilSpotPrice ImpOldShip ImpNewShip ImpOilPlat ImpExShipOilPlat ExpCrdOil ExpNatGas ExpCond ExpOldShip ExpNewShip ExpOilPlat ExpExShipOilPlat TrBal TrBalExShipOilPlat TrBalMland ly.var l2y.var l.CPI Variables VIF Linear Model 0.0 2.5 5.0 7.5 10.0 LoanIntRate EuroIntRate OilSpotPrice ImpOldShip ImpNewShip ExpCrdOil ExpOilPlat ly.var l2y.var l.CPI Variables VIF Model selected (criteria:AIC) Using models such as PCR and PLS can solve this problem Raju RImal (NMBU) Masters Thesis April 22, 2015 13 / 23
  • 43. Part II PCR and PLS regression Model PCR and PLS Regression 0 25 50 75 100 0 5 10 15 20 Components VariationExplained X PerEURO Variation Explained by PCR Model 25 50 75 100 0 5 10 15 20 Components VariationExplained X PerEURO Variation Explained by PLS Model More than 90 percent of variation present in Exchange Rate is explained by 16 components of PCR model while PLS has explained that much of variation by 6 components. However, PCR model has captured most of the variation present in predictor with fewer components than PLS model. Raju RImal (NMBU) Masters Thesis April 22, 2015 14 / 23
  • 44. Part II Ridge Regression Ridge Regression Also known as shrinkage methods as it shrinks the estimate that are enlarged by Multicollinearity. The ridge parameter λ is estimated by minimizing the Root mean square error (RMSECV) using cross-validation technique. Here, λ is found to be 0.005 0.1350 0.1375 0.1400 0.1425 0.0000 0.0025 0.0050 0.0075 0.0100 λ RMSEP Setting up λ that minimize the RMSEP Raju RImal (NMBU) Masters Thesis April 22, 2015 15 / 23
  • 45. Part II Cross-validation and Prediction Cross-valudation and Prediction All the models seemed to work fine with observations included, but how it behave with new observation – here comes the role of cross-validation. Jan 2000 – Dec 2012 Training dataset Jan 2013 – Nov 2014 Test dataset Dataset is splitted into calibration set and test set as in figure above Models fitted with training set were analysed for its behaviour with new observations through cross-validation with consecutive segment of length 12 2000 2001 . . . 2012 Training Set Raju RImal (NMBU) Masters Thesis April 22, 2015 16 / 23
  • 46. Part III Compare the models Raju RImal (NMBU) Masters Thesis April 22, 2015 17 / 23
  • 47. Part III Comparison of Models Comparison of Models Linear Models are compared on the bases of their goodness of fit Model AIC BIC R.Sq R.Sq.Adj Sigma F.value linear -207.178 -133.982 0.919 0.906 0.116 68.594 cp.model -230.323 -205.925 0.914 0.911 0.112 264.849 r2.model -227.995 -191.397 0.917 0.912 0.112 160.906 aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906 bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106 forward -229.234 -213.985 0.910 0.909 0.114 514.106 backward -230.323 -205.925 0.914 0.911 0.112 264.849 Selected Linear Models, Ridge Model, PCR model and PLS models are then compared on the basis of predictability Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
  • 48. Part III Comparison of Models Comparison of Models Linear Models are compared on the bases of their goodness of fit Model AIC BIC R.Sq R.Sq.Adj Sigma F.value linear -207.178 -133.982 0.919 0.906 0.116 68.594 cp.model -230.323 -205.925 0.914 0.911 0.112 264.849 r2.model -227.995 -191.397 0.917 0.912 0.112 160.906 aicMdl -227.995 -191.397 0.917 0.912 0.112 160.906 bicMdl -229.234 -213.985 0.910 0.909 0.114 514.106 forward -229.234 -213.985 0.910 0.909 0.114 514.106 backward -230.323 -205.925 0.914 0.911 0.112 264.849 As prediction is objective, aicMdl or r2.model can be selected since they have smallest residual standard error and explain the variation in exchange rate better than other Selected Linear Models, Ridge Model, PCR model and PLS models are then compared on the basis of predictability Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
  • 49. Part III Comparison of Models Comparison of Models Linear Models are compared on the bases of their goodness of fit Selected Linear Models, Ridge Model, PCR model and PLS models are then compared on the basis of predictability O O O O O O RMSEP R2pred 0.10 0.11 0.12 0.13 0.14 0.84 0.87 0.90 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Models Value(RMSEP/R−sqpred) train test cv Raju RImal (NMBU) Masters Thesis April 22, 2015 18 / 23
  • 50. Part III Comments on Model Comparison Some Comments on model comparison Figure alongside shows that, Linear Models predicts well for observations included in the model O O O O O O RMSEP R2pred 0.10 0.11 0.12 0.13 0.14 0.84 0.87 0.90 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Models Value(RMSEP/R−sqpred) train test cv Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
  • 51. Part III Comments on Model Comparison Some Comments on model comparison Figure alongside shows that, Linear Models predicts well for observations included in the model Ridge regression perform moderately but has predicted closer than some linear models for new observations O O O O O O RMSEP R2pred 0.10 0.11 0.12 0.13 0.14 0.84 0.87 0.90 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Models Value(RMSEP/R−sqpred) train test cv Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
  • 52. Part III Comments on Model Comparison Some Comments on model comparison Figure alongside shows that, Linear Models predicts well for observations included in the model Ridge regression perform moderately but has predicted closer than some linear models for new observations PCR and PLS models have made more accurate prediction than other linear models both in the case of cross-validation and test dataset O O O O O O RMSEP R2pred 0.10 0.11 0.12 0.13 0.14 0.84 0.87 0.90 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Models Value(RMSEP/R−sqpred) train test cv Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
  • 53. Part III Comments on Model Comparison Some Comments on model comparison Figure alongside shows that, Linear Models predicts well for observations included in the model Ridge regression perform moderately but has predicted closer than some linear models for new observations PCR and PLS models have made more accurate prediction than other linear models both in the case of cross-validation and test dataset PLS model with 7 components has least RMSEP while PCR model with 16 components ave least RMSECV O O O O O O RMSEP R2pred 0.10 0.11 0.12 0.13 0.14 0.84 0.87 0.90 Linear AICModel BICModel BackModel Ridge PCR.Comp15 PCR.Comp16 PCR.Comp17 PLS.Comp6 PLS.Comp7 PLS.Comp8 PLS.Comp9 Models Value(RMSEP/R−sqpred) train test cv Raju RImal (NMBU) Masters Thesis April 22, 2015 19 / 23
  • 54. Part III Discussions and Conclusions Discussions and Conclusions This thesis has attempted to make prediction in time series data Some subset of linear model considered are free from multicollinearity In case of multicollinearity problem, latent variable models like PLS and PCR can deal with the situation PLS and PCR models also outperformed in predicting new observations that are not included in the model Autocorrelation is inevitable in time series data, including lagged dependent variable in the model has corrected the problem Residuals obtained from selected model (pls.comp7) does not contain any autocorrelation PACF plot More practices are recommented to study the performance of latent variable model in time-series data Next Raju RImal (NMBU) Masters Thesis April 22, 2015 20 / 23
  • 55. Part III Discussions and Conclusions Partial Autocorrelation Function Linear Ridge PCR.16 PLS.7 −0.1 0.0 0.1 0.2 −0.1 0.0 0.1 0.2 0 5 10 15 20 0 5 10 15 20 Var1 PACF Partial Autocorrelation Function (PACF) Raju RImal (NMBU) Masters Thesis April 22, 2015 21 / 23
  • 56. Part III Discussions and Conclusions Acknoledgement Thanks to my Supervisors, Ellen Sandberg and Trygve Almøy and professor Solve Sæbø for their guidance and encouragements Raju RImal (NMBU) Masters Thesis April 22, 2015 22 / 23