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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