The document discusses analyzing the effect of different economic factors on India's Net Domestic Product (NDP) over time. It outlines collecting annual data on factor incomes from 1980-2013 and representing the data in time series curves. Preliminary analysis found some factors like agriculture and manufacturing decreasing in impact while others like construction and services increased. The author proposes using time series techniques like ADF tests, ARMA/GARCH modeling to test for stationarity, fit appropriate models, check for volatility and predict future values of incomes and their impact on NDP. Notations are introduced for the different income variables to be analyzed.

1. A vision into the economic
structure of India
EFFECT ON
DIFFERENT
ECONOMIC FACTORS
ON NDP(NATIONAL
DOMESTIC PRODUCT)

2. Motivation Of The
Project.
The global economic
structure of India is changing
from the post independence
era. Though it mainly relies
on Agriculture in the
beginning , but nowadays it
relies more on other
economic factors. The main
objective of my project is to
see how the different factors
incomes impact the Net
Domestic Product of Our
Country and also predict
some future values. Also we
will see that How much the
factor incomes effect NDP in
the future.

3. Methodology for the Analysis
For the analysis we shall follow the following process:
Data Collection Data Representation
Data AnalysisBring out our
Inferences

4. Data Collection:
For this Analysis we collected the data on factor Incomes from different websites.
Some of Them are given below:
• http://mospi.nic.in / (Indian Planning Commission)
• http://www.rbi.org.in/ (Reserve Bank Of India Website)
• http://databank.worldbank.org/(World Bank Data Website)

5. Data Analysis:
For the Analysis we shall use statistical techniques like
1. Time Series Analysis:
This includes fitting of time series models (like
ARIMA,GARCH,etc) and predicting future values through this model.
2. Multivariate Time Series Analysis:
This method helps in seeing the effects of the time series
covariates all at a time.
Before Carrying Our Usual Analysis we have to get in aquaintance with the following
terms.

6. Definition Of Certain Terms:
GDP (Gross Domestic Product):
It is defined as an aggregate measure of production equal to the sum of the gross values
added of all resident, institutional units engaged in production (plus any taxes, and minus
any subsidies, on products not included in the value of their outputs).
It is measured in three different approaches:
GDP
Product
Approach
Income
Approach
Expenditure
Approach
But we will use the Income Approach

7. • GDP:
Income Approach:
It is the sum of primary incomes distributed by resident producer units .It is measured as
GDP = compensation of employees + gross operating surplus + gross mixed income+ taxes less
subsidies on production and imports
Compensation of employees (COE) measures the total remuneration to employees for work done.
It includes wages and salaries, as well as employer contributions to social security and other such
programs.
Gross operating surplus (GOS) is the surplus due to owners of incorporated businesses. Often
called profits, although only a subset of total costs are subtracted from gross output to calculate
GOS.
Gross mixed income (GMI) is the same measure as GOS, but for unincorporated businesses. This
often includes most small businesses.
The sum of COE, GOS and GMI is called total factor income. Adding taxes less subsidies on
production and imports converts GDP at factor cost to GDP(I).
Total factor income is also sometimes expressed as:
Total factor income = employee compensation + corporate profits + proprietor's income + rental
income + net interest
Definition of certain terms

8. Definition of certain terms
NDP:
The full form of NDP is National Domestic Product. It is the gross domestic product (GDP)
minus depreciation on a country's capital goods.
Net domestic product accounts for capital that has been consumed over the year in the form of
housing, vehicle, or machinery deterioration. The depreciation accounted for is often referred to
as "capital consumption allowance" and represents the amount of capital that would be needed
to replace those depreciated assets.
If the country is not able to replace the capital stock lost through depreciation, then GDP will
fall. In addition, a growing gap between GDP and NDP indicates increasing obsolescence of
capital goods, while a narrowing gap means that the condition of capital stock in the country is
improving. It reduces the value of capital that is why it is separated from GDP to get NDP.
Factor Income Covariates:
It includes Agriculture ,Manufacturing ,forestry ,logging , mining &fishing, Construction
,Electricity ,gas & watersupply, Finance, Real Estate, Insurance & Business Services, Social
& Personal Services, Trade ,Hotels ,Transport & Communication.

9. Data:
Year Agriculture
forestry and logging
and fishing
Mining &
Quarrying Manufacturing
Electricity, gas
and water supply Construction
Trade,Hotels,Transp
ort&Communication
Finance,
Insurance, Real
Estate & Business
Services
Social & Personal
Services
Net Domestic
Product
1980 40056 4035 1474 18698 912 5771 18045 9264 12084 110339
1981 44971 4764 3020 21743 1012 6575 22213 10633 13825 128756
1982 47376 5404 3692 24100 1177 7598 25276 11852 16035 142510
1983 57806 5919 4021 28553 1417 8878 29635 12903 18362 167494
1984 61257 6462 4386 32159 1772 10479 34359 14484 21084 186442
1985 65387 6901 4823 35804 2116 12227 40061 16333 23910 207562
1986 69446 7586 5155 39447 2300 14426 45328 18170 28349 230207
1987 78065 8373 5184 45508 2458 16780 51903 20167 33072 261510
1988 97969 9370 6911 54991 2789 19690 61361 23151 38364 314596
1989 108387 10894 7469 65045 3301 22606 69814 28097 44644 360257
1990 131781 12309 11173 71335 5231 26831 55218 55547 62202 431627
1991 155246 13104 11893 75283 6243 30112 63265 67837 72040 495023
1992 173652 15026 13663 86822 8405 34349 74697 74878 83804 565296
1993 201528 17778 16098 101585 10383 37997 86914 90542 94217 657042
1994 231717 20848 17724 127434 13924 43690 101788 101931 105092 764148
1995 251674 22249 19518 160554 16369 51398 119665 121983 124432 887842
1996 304904 25150 21196 181486 16662 58588 140985 133931 148468 1031370
1997 319427 29715 26331 185017 20528 72945 170674 152588 173072 1150297
1998 369790 31497 27957 199460 27351 86464 201723 178239 213106 1335587
1999 390591 34361 33001 207186 24217 99364 227871 213443 246688 1476722
2000 439432 21176 45868 306296 48129 119897 252527 274940 317513 1825778
2001 467815 17265 48055 318496 49692 129390 399094 315689 341496 2086992
2002 429752 17802 62982 348534 56993 144894 490290 356089 371288 2278624
2003 476324 48058 64121 391190 59293 168386 623246 400056 411361 2642035
2004 501415 51007 84776 453603 59892 212807 706073 448952 452436 2970961
2005 512363 58509 94462 521669 69107 268634 846606 493102 505121 3369573
2006 585053 81312 106787 634828 76153 322429 998379 586595 573790 3965326
2007 609024 120242 124812 732720 83830 388908 1150044 691464 703895 4604939
2008 716276 136559 139828 818322 91070 451033 1310846 845368 883033 5392335
2009 806646 154928 159304 922151 113883 500458 1481623 964937 1015850 6119780
2010 928586 176169 204866 1072489 119560 571535 1779630 1165243 1154432 7172510
2011 1143517 198529 222716 1236182 135670 689797 2072272 1381524 1314734 8394941
2012 1300569 201135 222417 1320907 157132 759990 2324696 1617076 1522899 9426821
2013 1417468 211452 222652 1350039 203049 818431 2509908 1939482 1723458 10395939

10. Comparison of % Share of Different Economic
Factors in 2 years
Agriculture
14%
forestry and
logging and
fishing
2%
Mining &
Quarrying
2%
Manufacturin
g
13%
Electricity,
gas and
water
supply
2%
Construction
8%
Trade,Hotels,
Transport&Co
mmunication
24%
Finance,
Insurance,
Real Estate &
Business
Services
19%
Social &
Personal
Services
2013
We can see the impact of Agriculture and Manufacturing
Industry is more than other factors
We can see the impact of Other factors is more than
Agriculture and Manufacturing Industry.
Agriculture
36%
forestry and
logging and
fishing
4%
Mining &
Quarrying
1%
Manufacturin
g
17%
Electricity,
gas and water
supply
1%
Construction
5%
Trade,Hotels,
Transport&Co
mmunication
16%
Finance,
Insurance,
Real Estate &
Business
Services
9%
Social &
Personal
Services
1980

11. Data Representation in terms Of Time Series
Curves:
1980 1985 1990 1995 2000 2005 2010
0e+002e+064e+066e+068e+061e+07
time
NetdomesticProduct

12. 1980 1985 1990 1995 2000 2005 2010
152535
time
Agriculture%share
1980 1985 1990 1995 2000 2005 2010
1.02.03.0
time
Forestry&logging&fishing%share
1980 1985 1990 1995 2000 2005 2010
1.52.02.5
time
Mining&Quarrying%share
1980 1985 1990 1995 2000 2005 2010
131517
time
Manufacturing%share
1980 1985 1990 1995 2000 2005 2010
1.01.52.02.5
time
Electricity,gasandwatersupply%share
1980 1985 1990 1995 2000 2005 2010
5.06.07.08.0
time
Construction%share
1980 1985 1990 1995 2000 2005 2010
141822
time
Trade,Hotels,TransportandCommunication%share
1980 1985 1990 1995 2000 2005 2010
81216
time
,Finance,Insurance,RealEstateandBusinessServices%share
1980 1985 1990 1995 2000 2005 201011131517
time
dministration.and.Defence,socialandpersonalshares%share

13. From the diagram given above we have the following observations:
• Here the Agriculture share decreases and falls steeply from 1996 till 2007 after wards becomes
stable
• The Forestry, logging and fishing share decreases suddenly after 2000-2003 and after that again
rises.
• In case of Mining & Quarrying the share falls and rises quite frequently but it has an increasing
trend.
• The manufacturing industry has steep rise and falls in the end finally falls steeply after 2007.
• In case of Electricity, gas and water supply we see an increasing trend till 2000 and a decreasing
trend after 2000.
• In case of Construction the percentage share curve has a steep rise so we can say that construction
industry has an increasing impact on Indian Economy .
• Though there is a steep depression from the years 1990-2000 ,the trade ,hotels , transport and
communication industry has recovered from this phase and now has a great position.
• The Banking , Finance ,Insurance , Real Estate and Business Services percentage share here
increases and we can interpret it by saying people are using banks and are interested in financial
services which is a very good sign.
• In case of public administration , defence , social and personal services also we can see an upward
trend with a boom in the year 2000.
Interpretation from the diagrams:

14. Analysis Of The Data
As far as the analysis is concerned we shall firstly use the usual time series analysis.
We shall do it in the following steps:
Step-1
Test for
stationarity using
Augmented
Dickey Fueller
Test
Removing
Stationarity:We
shall remove
stationarity by
differencing
Step-2
Fitting ARMA
Model: We Shall
Fit ARMA model on
the data and check
the goodness of fit
by AIC.
We shall check
for the
volatility of the
residuals
Step-3 Check For
Volatility
If Volatility
presents we shall
go for trhe
GARCH modell
Step-4 Prediction
Using the given
time series predict
for the next 5
years.

15. Testing for Stationarity(Step-1)
Variables ADF Test p-Values No of differencing ADF Test p-Values
after differencing
Agriculture 0.9821 3 0.03591
Forestry,logging
&fishing
0.9677 3 <0.01
Mining & Quarrying >0.99 2 0.02759
Manufacturing >0.99 2 0.04569
Electricity,gas and
water supply
>0.99 3 0.01219
Construction >0.99 4 0.01296
Trade,Hotels,Transpo
rt and
Communication
>0.99 2 <0.01
Banking
,Finance,Insurance,Re
al Estate and Business
Services
>0.99 3 0.0125
Public.administration.
and.Defence,social
and personal Services
>0.99 3 <0.01
Net domestic Product >0.99 3 <0.01

16. Analysis of the Data:
Where 𝑌𝑡 is the observed value of the variable,
𝜇 𝑡 is the part of the time series variable explained by the
mean part with E(𝑋𝑡 )=0
𝑋𝑡 is the residual part .If the process has volatility 𝑋𝑡
becomes 𝜖 𝑡 ∗ 𝜎𝑡 and 𝜎𝑡 has a specific form whereas if 𝑋𝑡 = 𝜖 𝑡 (in both
cases 𝜖 𝑡 is a White Noise process).Thus in the former case we have to
go for ARCH or GARCH model.
𝜇 𝑡 is modelled using the ARMA ,ARIMA or SARIMA to get 𝜇.
Consider a given time series given over time t
Where 𝑋𝑡 evolves over time.𝒀 𝒕 = 𝝁 𝒕 + 𝑿 𝒕

17. Variable Notations:
For the model we take the following notations:
𝑌1𝑡:Incomes from Agriculture at time t
𝑌2𝑡:Incomes from Forestry & logging &fishing at time t
𝑌3𝑡: Incomes from Mining & Quarrying at time t
𝑌4𝑡: Incomes from Manufacturing at time t
𝑌5𝑡: Incomes from Electricity,gas and water supply at time t
𝑌6𝑡: Incomes from Construction at time t
𝑌7𝑡: Incomes from Trade,Hotels,Transport and Communication at time t
𝑌8𝑡: Incomes from Banking ,Finance,Insurance,Real Estate and Business
Services at time t
𝑌9𝑡: Incomes from Public administration and Defence,social and personal
services at time t
𝑌10𝑡:National Domestic Product values at time t
For the model we take the following notations:
𝑌1𝑡:Incomes from Agriculture at time t
𝑌2𝑡:Incomes from Forestry & logging &fishing at time t
𝑌3𝑡: Incomes from Mining & Quarrying at time t
𝑌4𝑡: Incomes from Manufacturing at time t
𝑌5𝑡: Incomes from Electricity,gas and water supply at time t
𝑌6𝑡: Incomes from Construction at time t
𝑌7𝑡: Incomes from Trade,Hotels,Transport and Communication at time t
𝑌8𝑡: Incomes from Banking ,Finance,Insurance,Real Estate and Business
Services at time t
𝑌9𝑡: Incomes from Public administration and Defence,social and personal
services at time t
𝑌10𝑡:National Domestic Product values at time t

18. ARMA ESTIMATION
For Agriculture:
ARMA(2,2) is the best model for the Agriculture stationary data with AIC=
742.01.Thus the model is given below:
𝒀 𝟏𝒕
= 𝟏. 𝟖𝟐𝟐𝟓 ∗ 𝒀 𝟏(𝒕−𝟏) −𝟎. 𝟏𝟎𝟖𝟑 ∗ 𝒀 𝟏 𝒕−𝟐 − 𝟎. 𝟔𝟏𝟎𝟏 ∗ 𝒀 𝟏 𝒕−𝟑 − 𝟎. 𝟕𝟒𝟒𝟗 ∗ 𝒀 𝟏 𝒕−𝟒 + 𝟎. 𝟔𝟒𝟎𝟖
∗ 𝒀 𝟏 𝒕−𝟓 + 𝑿 𝟏𝒕 + 𝟎. 𝟑𝟏𝟕𝟓 ∗ 𝑿 𝟏(𝒕−𝟏) + 𝟎. 𝟓𝟓𝟐𝟓 ∗ 𝑿 𝟏(𝒕−𝟐)
For Forestry ,Logging & Fishing :
ARMA(3,0) is the best model for the Forestry , Logging & Fishing stationary data with
AIC= 657.04.Thus the model is given below:
𝒀 𝟐𝒕
= 𝟏. 𝟗𝟗𝟓𝟔 ∗ 𝒀 𝟐(𝒕−𝟏) −𝟎. 𝟖𝟗𝟑𝟏 ∗ 𝒀 𝟐 𝒕−𝟐 − 𝟎. 𝟎𝟔𝟒𝟐 ∗ 𝒀 𝟐 𝒕−𝟑 + 𝟎. 𝟓𝟗𝟓𝟐 ∗ 𝒀 𝟐 𝒕−𝟒
+ 𝟏. 𝟒𝟎𝟑𝟒 ∗ 𝒀 𝟐 𝒕−𝟓 + 𝟎. 𝟕𝟔𝟗𝟗 ∗ 𝒀 𝟐 𝒕−𝟔 + 𝑿 𝟐𝒕
For Mining & Quarrying :
ARMA(0,1) is the best model for the Mining & Quarrying stationary data with AIC=
674.55.Thus the model is given below:
𝒀 𝟑𝒕 = 𝟐 ∗ 𝒀 𝟑(𝒕−𝟏) −𝒀 𝟑 𝒕−𝟐 + 𝝐 𝟑𝒕 + 𝟎. 𝟔𝟕𝟑𝟐 ∗ 𝑿 𝟑(𝒕−𝟏)
The ARMA model is given as :∅(𝑩)𝒀 𝒕 = 𝝋(𝑩)𝑿 𝒕,where ∅(𝑩) is the AR component and
𝝋(𝑩) is the MA Component of a Time Series.

19. For Manufacturing :
ARMA(0,0) is the best model for the Manufacturing stationary data with
AIC=756.08.Thus the model is given below:
𝒀 𝟒𝒕 = 𝟐 ∗ 𝒀 𝟒(𝒕−𝟏) −𝒀 𝟒 𝒕−𝟐 + 𝑿 𝟒𝒕
For Electricity,gas and water supply :
ARMA(1,1) is the best model for the Electricity,gas and water supply stationary data
with AIC= 652.81.Thus the model is given below:
𝒀 𝟓𝒕
= 𝟐. 𝟑𝟕𝟗𝟑 ∗ 𝒀 𝟓(𝒕−𝟏) −𝟏. 𝟏𝟑𝟕𝟗 ∗ 𝒀 𝟓 𝒕−𝟐 − 𝟎. 𝟖𝟔𝟐𝟏 ∗ 𝒀 𝟓 𝒕−𝟑 + 𝟎. 𝟔𝟐𝟎𝟕 ∗ 𝒀 𝟓 𝒕−𝟒
+ 𝑿 𝟓𝒕 + 𝟎. 𝟖𝟔𝟔𝟑 ∗ 𝑿 𝟓(𝒕−𝟏)
For Construction :
ARMA(0,2) is the best model for the Construction stationary data with AIC=
682.7.Thus the model is given below:
𝒀 𝟔𝒕
= 𝟒 ∗ 𝒀 𝟔(𝒕−𝟏) −𝟔 ∗ 𝒀 𝟔 𝒕−𝟐 + 𝟒 ∗ 𝒀 𝟔 𝒕−𝟑 − 𝒀 𝟔 𝒕−𝟒 + 𝑿 𝟔𝒕 + 𝟏. 𝟗𝟔𝟓𝟏 ∗ 𝑿 𝟔(𝒕−𝟏)
− 𝟎. 𝟗𝟖𝟒𝟐 ∗ 𝑿 𝟔(𝒕−𝟐)

20. For Trade,Hotels,Transport and Communication :
ARMA(0,0) is the best model for the Trade,Hotels,Transport and Communication
stationary data with AIC= 769.83.Thus the model is given below:
𝒀 𝟕𝒕 = 𝟐 ∗ 𝒀 𝟕(𝒕−𝟏) −𝒀 𝟕 𝒕−𝟐 + 𝑿 𝟕𝒕
For Banking ,Finance,Insurance,Real Estate and Business Services :
ARMA(1,1) is the best model for the Banking ,Finance,Insurance,Real Estate and
Business Services stationary data with AIC= 713.53.Thus the model is given below:
𝒀 𝟖𝒕
= 𝟐. 𝟒𝟎𝟓𝟖 ∗ 𝒀 𝟖(𝒕−𝟏) −𝟏. 𝟐𝟏𝟕𝟒 ∗ 𝒀 𝟖 𝒕−𝟐 − 𝟎. 𝟕𝟖𝟐𝟔 ∗ 𝒀 𝟖 𝒕−𝟑 + 𝟎. 𝟓𝟗𝟒𝟐 ∗ 𝒀 𝟖 𝒕−𝟒
+ 𝑿 𝟖𝒕 − 𝟎. 𝟔𝟐𝟖𝟏 ∗ 𝑿 𝟖(𝒕−𝟏)
For Public administration and Defence,social and personal services :
ARMA(0,1) is the best model for the Public administration and
Defence,social and personal services stationary data with AIC= 714.43.Thus
the model is given below:
𝒀 𝟗𝒕 = 𝟑 ∗ 𝒀 𝟗(𝒕−𝟏) −𝟑 ∗ 𝒀 𝟗 𝒕−𝟐 + 𝒀 𝟗 𝒕−𝟑 + 𝑿 𝟗𝒕 + 𝟎. 𝟗𝟑𝟓𝟖 ∗ 𝑿 𝟗(𝒕−𝟏)

21. Variables X-Squared(Test
Statistic)
df P-Value
Agriculture 7.536 6 0.2741
Forestry,logging
&fishing
6.3936 7 0.4946
Mining & Quarrying 3.8832 9 0.9189
Manufacturing 7.0025 10 0.7252
Electricity,gas and
water supply
6.0192 8 0.6451
Construction 9.5938 8 0.2947
Trade,Hotels,Transpo
rt and
Communication
18.9396 10 0.4104
Banking
,Finance,Insurance,Re
al Estate and Business
Services
7.3738 8 0.4969
Public.administration.
and.Defence,social
and personal Services
13.2637 9 0.151
Diagnostic Testing (for the Goodness Of fit):Ljung-Box Test
Here we perform Ljung-box test on the residuals of the ARMA model.In this test the
null hypothesis is the independence of the error components .It is a type of
Portmanteau test.

22. time
Agriculture
1980 1985 1990 1995 2000 2005 2010
06000001400000
time
Forestry&logging&fishing
1980 1985 1990 1995 2000 2005 2010
0100000200000
time
Mining&Quarrying
1980 1985 1990 1995 2000 2005 2010
0100000
time
Manufacturing
1980 1985 1990 1995 2000 2005 2010
06000001400000
time
Electricity,gasandwatersupply
1980 1985 1990 1995 2000 2005 2010
0100000200000
time
Construction
1980 1985 1990 1995 2000 2005 2010
0e+004e+058e+05
time
Trade,Hotels,TransportandCommunication
1980 1985 1990 1995 2000 2005 2010
010000002500000
time
ing,Finance,Insurance,RealEstateandBusinessServices
1980 1985 1990 1995 2000 2005 2010
01000000
time
icadministrationandDefence,socialandpersonalservices
1980 1985 1990 1995 2000 2005 201001000000
Fitting of the ARMA model on the dataset
Here some points are missing the line

23. time
Agriculture
1980 1985 1990 1995 2000 2005 2010
-50000050000
time
Forestry&logging&fishing
1980 1985 1990 1995 2000 2005 2010
-1000020000
time
Mining&Quarrying
1980 1985 1990 1995 2000 2005 2010
-20000020000
time
Manufacturing
1980 1985 1990 1995 2000 2005 2010
-5000050000
time
Electricity,gasandwatersupply
1980 1985 1990 1995 2000 2005 2010
-20000020000
time
Construction
1980 1985 1990 1995 2000 2005 2010
-60000040000time
Trade,Hotels,TransportandCommunication
1980 1985 1990 1995 2000 2005 2010
-5000050000
time
Banking,Finance,Insurance,RealEstateandBusinessServices
1980 1985 1990 1995 2000 2005 2010
-40000040000
time
PublicadministrationandDefence,socialandpersonalservices
1980 1985 1990 1995 2000 2005 2010
-60000040000
Now we study the residuals:
Thus we can see that there exists volatility in the data.

24. GARCH MODEL
The Garch model is given as where (𝝈 𝒕 ) 𝟐
= 𝒊=𝟎
𝒑
𝜹𝒊 ∗ 𝑿 𝒕−𝒊 +
𝒊=𝟏
𝒒
𝜽𝒊 ∗ (𝝈 𝒕−𝒊) 𝟐
𝑿 𝒕 = 𝝈 𝒕 ∗ 𝝐𝒕
For Agriculture:
GARCH(1,1) is the best model for the Agriculture stationary data . Thus the model is
given below:
(𝝈 𝟏𝒕) 𝟐
= 𝟕𝟕𝟒𝟐𝟕𝟑𝟐𝟎𝟎 + 𝟎. 𝟑𝟓𝟕𝟎𝟐𝟒𝟐 ∗ 𝑿 𝟏 𝒕−𝟏
𝟐
+ 𝟎. 𝟏𝟑𝟏𝟏𝟎𝟑𝟒 ∗ 𝝈 𝟏 𝒕−𝟏
𝟐
For Forestry ,Logging & Fishing :
GARCH(1,1) is the best model for the Forestry ,Logging & Fishing stationary data .
Thus the model is given below:
(𝝈 𝟐𝒕) 𝟐
= 𝟓𝟓𝟎𝟏𝟏𝟖𝟎𝟎 + 𝟎. 𝟐𝟏𝟒𝟓𝟒𝟐𝟑 ∗ 𝑿 𝟐 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎𝟑𝟑𝟑𝟓𝟒𝟑𝟕 ∗ 𝝈 𝟐 𝒕−𝟏
𝟐
For Mining & Quarrying :
GARCH(1,1) is the best model for the Mining & Quarrying stationary data . Thus
the model is given below:
(𝝈 𝟑𝒕) 𝟐
= 𝟔𝟐𝟓𝟓𝟔𝟐𝟐𝟎 + 𝟏. 𝟓𝟏𝟔𝟏𝟖𝟖 ∗ 𝑿 𝟑 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟒𝟕𝟒𝟓𝟎𝟐𝟖 ∗ 𝝈 𝟑 𝒕−𝟏
𝟐

25. For Manufacturing :
GARCH(1,1) is the best model for the Manufacturing stationary data . Thus the
model is given below:
(𝝈 𝟒𝒕) 𝟐
= 𝟖𝟕𝟓𝟓𝟔𝟗𝟕𝟎𝟎 + 𝟎. 𝟏𝟖𝟐𝟕𝟎𝟎𝟗 ∗ 𝑿 𝟒 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟏𝟕𝟗𝟒𝟑𝟗𝟑 ∗ 𝝈 𝟒 𝒕−𝟏
𝟐
For Electricity,gas and water supply :
GARCH(1,1) is the best model for the Electricity,gas and water supply stationary
data . Thus the model is given below:
(𝝈 𝟓𝒕) 𝟐
= 𝟓𝟎𝟕𝟔𝟐𝟖𝟖𝟎𝟎 + 𝟏. 𝟎𝟒𝟖𝟗𝟒𝟐 ∗ 𝑿 𝟓 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟎𝟑𝟔𝟑𝟕𝟔𝟑𝟗 ∗ 𝝈 𝟓 𝒕−𝟏
𝟐
For Construction :
GARCH(1,1) is the best model for the Construction stationary data . Thus the model
is given below:
(𝝈 𝟔𝒕) 𝟐
= 𝟏𝟖𝟏𝟏𝟗𝟐𝟖𝟎𝟎 + 𝟎. 𝟐𝟏𝟑𝟗𝟎𝟑𝟕 ∗ 𝑿 𝟔 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟑𝟎𝟒𝟎𝟐𝟓𝟏 ∗ 𝝈 𝟔 𝒕−𝟏
𝟐
For Trade,Hotels,Transport and Communication :
GARCH(1,1) is the best model for the Trade,Hotels,Transport and Communication
stationary data . Thus the model is given below:
(𝝈 𝟕𝒕) 𝟐
= 𝟏𝟑𝟐𝟎𝟐𝟒𝟒𝟎𝟎𝟎 + 𝟎. 𝟎𝟎𝟓 ∗ 𝑿 𝟕 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟓 ∗ 𝝈 𝟕 𝒕−𝟏
𝟐

26. For Banking ,Finance,Insurance,Real Estate and Business Services :
GARCH(1,1) is the best model for the Banking ,Finance,Insurance,Real Estate and Business
Services stationary data . Thus the model is given below:
(𝝈 𝟖𝒕) 𝟐
= 𝟑𝟔𝟐𝟐𝟔𝟎𝟒𝟎𝟎 + 𝟏. 𝟎𝟐𝟔𝟔𝟗𝟖 ∗ 𝑿 𝟖 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟏𝟒𝟏𝟖𝟕𝟗𝟗 ∗ 𝝈 𝟖 𝒕−𝟏
𝟐
For Public administration and Defence,social and personal services :
GARCH(1,1) is the best model for the Public administration and Defence,social and
personal services stationary data . Thus the model is given below:
(𝝈 𝟗𝒕) 𝟐
= 𝟒𝟎𝟒𝟓𝟎𝟓𝟕𝟎𝟎 + 𝟏. 𝟎𝟒𝟖𝟕𝟓𝟔 ∗ 𝑿 𝟗 𝒕−𝟏
𝟐
+ 𝟎. 𝟎𝟎𝟎𝟎𝟎𝟐𝟎𝟒𝟒𝟎𝟐𝟗 ∗ 𝝈 𝟗 𝒕−𝟏
𝟐

27. Residuals before Garch Estimation
time
Agriculture
1980 1985 1990 1995 2000 2005 2010
-50000050000
Residuals after Garch Estimation
time
Agriculture
1980 1985 1990 1995 2000 2005 2010
-2-1012

28. Residuals before Garch Estimation
time
Forestry&logging&fishing
1980 1985 1990 1995 2000 2005 2010
-100000100002000030000
Residuals after Garch Estimation
time
Forestry&logging&fishing
1980 1985 1990 1995 2000 2005 2010
-2-10123

29. Residuals before Garch Estimation
time
Mining&Quarrying
1980 1985 1990 1995 2000 2005 2010
-20000-100000100002000030000
Residuals after Garch Estimation
time
Mining&Quarrying
1980 1985 1990 1995 2000 2005 2010
-2-10123

30. Residuals before Garch Estimation
time
Manufacturing
1980 1985 1990 1995 2000 2005 2010
-50000050000
Residuals after Garch Estimation
time
Manufacturing
1980 1985 1990 1995 2000 2005 2010
-2-10123

31. Residuals before Garch Estimation
time
Construction
1980 1985 1990 1995 2000 2005 2010
-60000-40000-2000002000040000 Residuals after Garch Estimation
time
Construction
1980 1985 1990 1995 2000 2005 2010
-2-1012

32. Residuals before Garch Estimation
time
Electricity,gasandwatersupply
1980 1985 1990 1995 2000 2005 2010
-10000-50000500010000150002000025000
Residuals before Garch Estimation
time
Electricity,gasandwatersupply
1980 1985 1990 1995 2000 2005 2010
-1.0-0.50.00.51.01.52.0

33. Residuals before Garch Estimation
time
Trade,Hotels,TransportandCommunication
1980 1985 1990 1995 2000 2005 2010
-50000050000100000
Residuals before Garch Estimation
time
Trade,Hotels,TransportandCommunication
1980 1985 1990 1995 2000 2005 2010
-10123

34. Residuals before Garch Estimation
time
Banking,Finance,Insurance,RealEstateandBusinessServices
1980 1985 1990 1995 2000 2005 2010
-40000-200000200004000060000
Residuals after Garch Estimation
time
Banking,Finance,Insurance,RealEstateandBusinessServices
1980 1985 1990 1995 2000 2005 2010
-1.0-0.50.00.51.01.52.0

35. Residuals before Garch Estimation
time
PublicadministrationandDefence,socialandpersonalservices
1980 1985 1990 1995 2000 2005 2010
-60000-40000-200000200004000060000
Residuals after Garch Estimation
time
PublicadministrationandDefence,socialandpersonalservices
1980 1985 1990 1995 2000 2005 2010
-1012

36. A Multivariate Approach to the Analysis
A multivariate analogue to our current analysis is to use the VAR model.The usual
Vector Autoregressive model (VAR) of order p is given below:
𝑿 𝒕 = 𝑨 𝟏 ∗ 𝑿 𝒕−𝟏 + 𝑨 𝟐 ∗ 𝑿 𝒕−𝟐 + ⋯ + 𝑨 𝒑 ∗ 𝑿 𝒕−𝒑 +∈ 𝒕
Where 𝑿 𝒕 is the vector of time series variables and 𝑨𝒊’s are coefficient matrices.
A Second form of the model is the Error Correction Model which is given below:
∆𝑿 𝒕= 𝜹 + 𝝅 ∗ 𝑿 𝒕−𝟏 + 𝑨 𝟏′ ∗ ∆𝑿 𝒕−𝟏 + 𝑨 𝟐′ ∗
∆𝑿 𝒕−𝟐 + ⋯ + 𝑨 𝒑′ ∗ ∆𝑿(𝒕−𝒑)+∈ 𝒕
Where π=G*H′ and H′ is the cointegrating matrix

37. Cointegration and VAR model fitting
Here we perform Johansen’s Test which gives the following results:
test 10pct 5pct 1pct
r<=8 | 2.48 10.49 12.25 16.26
r<=7 | 18.79 16.85 18.96 23.65
r<=6 | 26.6 23.11 25.54 30.34
r<=5 | 60.41 29.12 31.46 36.65
r<=4 | 61.96 34.75 37.52 42.36
r<=3 | 98.59 40.91 43.97 49.51
r<=2 | 128.19 46.32 49.42 54.71
r<=1 | 139.6 52.16 55.5 62.46
r<=0 | 203.03 57.87 61.29 67.88
Eigenvalues (lambda):
9.982438e-01 9.872533e-01 9.817916e-01 9.540891e-01 8.557612e-01
8.486086e-01 5.645060e-01 4.441629e-01 7.448209e-02 -2.081668e-16
Values of test statistic and critical values of test:
Since the rank of π is 8 <10 we can say that the model has unit roots and we have to fit an
EC Model with Co integrating Matrix.

38. 𝜹=(-3.238e+03 ,5.687e+02 ,-7.172e+01 ,1.524e+03 , 5.683e+02 ,-5.766e+02 ,-5.648e+02 ,5.690e+02 ,1.778e+03)′
𝑨 𝟏
′
= -0.0107 1.711 2.26 0.6542 -3.788 -3.025 0.4509 0.0499 0.8652
0.1137 0.54 2.19 -0.0962 0.488 -1.164 -0.0757 -0.1508 -0.1776
0.0236 0.317 0.687 0.0603 0.143 -0.194 -0.1418 -0.3362 0.0032
-0.4633 0.687 1.861 1.3537 -3.689 -1.483 -0.5694 -1.1127 0.2657
-0.0479 -0.375 -0.442 0.0972 -0.817 0.19 -0.0698 -0.0466 0.1946
0.1601 0.432 1.368 -0.0214 0.16 0.365 0.2542 -0.3114 -0.0951
-0.0635 -0.656 3.048 0.407 2.581 0.51 0.3938 -0.7854 -0.0378
-0.1771 0.719 -1.082 0.1728 -1.43 0.561 0.3848 0.7461 -0.0203
-0.2172 1.201 -1.889 0.303 -1.936 2.504 -0.2558 0.2963 0.5503
𝑨 𝟐
′
=
1.4186 0.00348 5.302 -0.6288 -5.11 0.4663 -0.1388 -0.8322 -0.0128
-0.0707 -0.11726 1.016 0.2962 -0.804 1.2232 0.1243 -0.1032 -0.1797
-0.0674 -0.03084 0.624 -0.1106 1.088 0.4343 0.0926 -0.0119 0.2639
0.6912 0.74337 7.535 -1.4054 5.047 2.0921 0.403 -0.581 0.7703
0.1196 -0.02824 0.322 -0.207 1.006 0.0885 0.0641 -0.0165 -0.0137
0.0243 0.23226 -0.881 -0.2746 0.651 0.6107 -0.0236 0.0805 -0.0758
-0.4014 -0.3115 -1.818 0.0164 -0.121 0.1251 0.1219 0.6366 0.6204
0.5338 -1.25299 -1.675 -0.5942 -2.267 0.8548 -0.2309 0.1949 0.341
0.3126 -2.0733 -2.391 -0.2038 0.952 -0.4908 0.0262 -0.2423 0.6013
Estimated Values of the VAR Coefficients:

39. G=
-2.51E+00 -1.41E-01 -5.91E-02 -2.19E-01 1.44E-01 -3.06E+00 -4.63E-01 -1.37E-01 6.20E-02 4.55E-01
1.78E+00 -1.51E+00 4.29E-01 4.46E-01 -3.99E-01 9.34E-01 -9.27E-01 1.03E-01 -2.81E+00 -1.44E+00
4.91E+00 -3.65E-01 8.77E-02 2.57E+00 -1.24E+00 7.87E+00 -6.57E-01 -3.80E-01 1.34E+00 -3.34E+00
5.72E-01 1.07E-01 1.63E-01 -4.55E-01 -1.38E-01 -6.66E-01 5.06E-01 -8.49E-02 -2.30E+00 -4.22E-01
-1.83E+00 3.25E-01 -2.58E-01 -4.07E+00 -2.66E+00 -1.61E+00 -6.10E-01 2.29E-01 -5.77E+00 -4.55E+00
2.94E-01 -5.96E-01 2.59E-02 1.27E-01 1.49E-01 1.18E+00 -7.84E-01 2.80E-01 9.42E-01 3.82E-01
-3.33E-01 -2.91E-02 -6.25E-02 3.49E-01 4.48E-01 6.98E-02 -1.92E-01 1.02E-01 6.43E-01 2.81E-01
-5.77E-01 2.52E-01 -2.91E-01 2.40E-01 4.69E-01 -1.39E+00 4.38E-01 -4.06E-01 3.57E-01 6.41E-01
1.06E+00 -8.06E-01 8.45E-02 8.39E-01 3.29E-01 2.70E+00 -1.32E+00 5.90E-01 2.40E+00 4.97E-01
H′=
-3.06E+00 -4.63E-01 -1.37E-01 6.20E-02 4.55E-01 -3.18E-02 -3.00E-01 4.42E-01 3.39E-01
9.34E-01 -9.27E-01 1.03E-01 -2.81E+00 -1.44E+00 -4.07E-02 -3.36E-01 -2.50E+00 6.68E-01
7.87E+00 -6.57E-01 -3.80E-01 1.34E+00 -3.34E+00 -1.89E+00 2.29E+00 -2.96E+00 -4.93E-01
-6.66E-01 5.06E-01 -8.49E-02 -2.30E+00 -4.22E-01 -4.71E-01 5.51E-01 -8.40E-01 7.69E-02
-1.61E+00 -6.10E-01 2.29E-01 -5.77E+00 -4.55E+00 -6.53E-04 1.86E+00 5.11E-01 -3.07E+00
1.18E+00 -7.84E-01 2.80E-01 9.42E-01 3.82E-01 -1.75E+00 1.87E-01 4.79E-01 -6.01E-01
6.98E-02 -1.92E-01 1.02E-01 6.43E-01 2.81E-01 3.41E-01 -4.37E-01 7.18E-01 -1.73E-01
-1.39E+00 4.38E-01 -4.06E-01 3.57E-01 6.41E-01 -1.17E-01 -8.80E-02 -1.44E+00 9.57E-01
2.70E+00 -1.32E+00 5.90E-01 2.40E+00 4.97E-01 4.48E-01 1.47E-01 1.06E+00 -2.00E+00

40. Prediction
Here we have a five year prediction based on the time series model that we have
obtained. These values are given below:
2014 2015 2016 2017 2018
Agriculture 1593810 1745342 1907452 2092458 2263180
Forestry,Logging & Fishing 222161.1 231791.4 227308.5 228772.1 228979.8
Minning &Qyarrying 233073.7 243495.3 253917 264338.6 274760.3
Manufacturing 1379171 1408303 1437435 1466567 1495699
Trade,Hotels,Transport & Communication 2695120 2880332 3065544 3250756 3435968
Public.administration.and.Defence,social and personal services 1932909 2151252 2378487 2614613 2859632
Electricity,gas and water supply 239603.8 287786.8 334569.2 388037.9 443173.5
Construction 882073.2 950550.6 1023497 1100547 1181333
Banking ,Finance,Insurance,Real Estate and Business Services 2271865 2659905 3076458 3537654 4033909

41. Comparison Of Contribution of Factor Incomes
to NDP
The predicted value also shows that the effect of
agriculture becomes insignificant
The other factors are rising but still very
slowly
Agriculture
14%
Forestry,Logg
ing & Fishing
2%
Minning
&Qyarrying
2%
Manufacturin
g
12%Trade,Hotels,
Transport &
Communicati
on
23%
Public.adminis
tration.and.D
efence,social
and personal
services
17%
Electricity,gas
and water
supply
2%
Construction
8%
Banking
,Finance,Insur
ance,Real
Estate and
Business
Services
20%
Factor Incomes in 2014
Agriculture
14%
Forestry,Logg
ing & Fishing
1% Minning
&Qyarrying
2%
Manufacturin
g
9%
Trade,Hotels,
Transport &
Communicati
on
21%
Public.adminis
tration.and.D
efence,social
and personal
services
18%
Electricity,gas
and water
supply
3%
Construction
7%
Banking
,Finance,Insur
ance,Real
Estate and
Business
Services
25%
Factor Incomes on 2018

42. 2014 2015 2016 2017 2018
13.9013.9413.98
time
Agriculture%share
2014 2015 2016 2017 2018
1.41.61.8
time
Forestry&logging&fishing%share
2014 2015 2016 2017 2018
1.701.852.00
time
Mining&Quarrying%share
2014 2015 2016 2017 2018
9.510.511.5
time
Manufacturing%share
2014 2015 2016 2017 2018
2.12.32.52.7
time
Electricity,gasandwatersupply%share
2014 2015 2016 2017 2018
7.37.57.7
time
Construction%share
2014 2015 2016 2017 2018
21.522.523.5
time
de,Hotels,TransportandCommunication%share
2014 2015 2016 2017 2018
202224
time
nce,Insurance,RealEstateandBusinessServices%share
2014 2015 2016 2017 2018
17.017.4
time
istration.and.Defence,socialandpersonalshares%share
Forecasted percentage shares

43. • We can see that the share in the Agriculture decreases till 2015 ,rises from there
and attains maximum in 2017 after which it again decreases.
• We see that Mining ,Forestry ,Manufacturing , Construction ,Trade &
Hotels & Transport industry have a decreasing percentage shares and the
government should look upon it in future
• We also find out that Financial Services and Electricity, Gas and
water supply has an increasing percentage share and government
should invest upon these factors as they provide them more incomes.
Findings from the forcasted figures:

44. • Here we have data on factor incomes like Agriculture , Forestry & logging & fishing , Mining & Quarrying
,Manufacturing Electricity , gas and water supply ,Construction ,Trade,Hotels,Transport ,Banking ,Finance
,Insurance , Real Estate and Business Services Public administration and Defence,social and personal
services and we have to study its effects on NDP and see how these are effecting NDP in future
• Here we see though Agriculture was the main determinant of Income at the first few years but later
we find that other factors have more effect at the succeeding years and these play important roles in
future.
• We see that Public administration and Defence , social and personal services , Banking , Finance ,
Insurance, Real Estate and Business Services, Construction ,Mining & Quarrying , Electricity , gas and
water supply has an increasing trend though they are harmonic rising in some years and falling in some
years
• We see the remaining factors have a decreasing percentage share of incomes.
• We have fitted ARMA Models on the entire data see that the fitting is good except for some points
• We have tested for Volatility factor and find that we have to fit GARCH Model on the data
• Here the most appropriate model is the GARCH (1,1) model and see that the residuals after
fitting is not volatile

45. • We have used Augmented Dickey Fuller test before ARMA fitting to remove trend component by finding
the no of unit roots, Portmanteau tests for diagnostic checking (goodness of fit of the ARMA
model),Lagrange's test for the volatility checking.
• In case of ADF test we found the presence of unit roots in all the covariates and have to difference to
remove trend .
• We have also fitted a Multivariate model to see the effects of the covariates at the same time on
different years. Since Johansen’s Test suggests the presence of cointegrating effects we used Error
Correction Model form of the usual VAR model having cointegrated effects(i.e Cointegrating
matrix)
• Now we get predictions from the fitted model and can infer that under the continuing conditions the
share in the Agriculture decreases till 2015 ,rises from there and attains maximum in 2017 after
which it again decreases. Mining ,Forestry ,Manufacturing , Construction ,Trade & Hotels &
Transport industry have a decreasing percentage shares and Financial Services and Electricity,
Gas and water supply has an increasing percentage share.

46. Theory Sources:
• Economics: Paul & Samuelson , William D Nordhaus
• Chris Chatfield: Analysis of Time Series: An Introduction.
• Use R : Time Series And Cointegration **Springer
Statistical Softwares:
• R Statistical Software
• Minitab
Other Softwares:
• Ms-Excel
• MS-Word(For Documentation)
• MS-Powepoint(ForPresentation)

47. Project submitted by
Subhodeep Mukherjee
Roll No: 91/STS/131032 Reg No: A03-1112-
0103-10
University Of Calcutta
Department Of Statistics