mfef final report.pdf

Modeling and Forecasting in Energy and

Financial Market

Submitted by:

Aravind Joni : NMP 08

Nikhil Padalia : EM 04

Prithwish Sinha : EM05

Rajesh Kumar : EM06

Table of Contents

1. Regression Analysis ............................................................................................................................... 4

1.1. Introduction ...................................................................................................................................... 4

1.2. Data description (data frequency, data span, source of data) ......................................................... 4

1.3. Model (brief theory, assumptions etc) ............................................................................................. 5

1.4. Empirical analysis .............................................................................................................................. 6

1.5. Conclusion ....................................................................................................................................... 11

2. DOW Effect and MOY Effect ............................................................................................................... 12

2.1. Introduction .................................................................................................................................... 12

2.2. DOW (Day of Week) effect .............................................................................................................. 13

2.2.1. Dummy Variables ........................................................................................................................ 14

2.2.2. Empirical Analysis ........................................................................................................................ 14

2.2.3. Regression Output ...................................................................................................................... 15

2.2.4. Conclusion ................................................................................................................................... 15

2.3. MOY (Month of Year) Effect ........................................................................................................... 16

2.3.1. Data ............................................................................................................................................. 16

2.3.2. Empirical Analysis ........................................................................................................................ 17

2.3.3. Regression Output ...................................................................................................................... 17

2.3.4. Conclusion ................................................................................................................................... 18

3. MSARIMA EGARCH MODEL ................................................................................................................. 19

3.1. Introduction .................................................................................................................................... 19

3.2. Data of Crude oil: ............................................................................................................................ 20

3.3. Analysis ........................................................................................................................................... 21

3.3.1. Graphical Representation of data: .............................................................................................. 21

3.3.2. Check Correlogram: .................................................................................................................... 22

3.3.3. Unit Root Test: ............................................................................................................................ 23

3.3.4. Detrend the series: ..................................................................................................................... 25

3.3.5. Deseasonalize the data: .............................................................................................................. 26

3.3.6. Estimation Stage ......................................................................................................................... 27

3.3.7. Residual Analysis stage(Diagnostic Checking): ........................................................................... 28

3.3.8. Forecasting Stage: ....................................................................................................................... 29

3.3.9. GARCH MODELLING: ................................................................................................................... 29

3.3.10. Static and Dynamic forecast ....................................................................................................... 32

3.4. Conclusion: ...................................................................................................................................... 33

4. VAR-Cointergration ............................................................................................................................. 34

4.1. Introduction .................................................................................................................................... 34

4.2. Objective ......................................................................................................................................... 34

4.3. Data Desciption ............................................................................................................................... 34

4.4. Empirical Analysis ............................................................................................................................ 35

4.5. Conclusion ....................................................................................................................................... 40

4.5.1. Long term relations ..................................................................................................................... 40

4.5.2. Short term relations .................................................................................................................... 40

1. Regression Analysis

1.1. Introduction

We have taken into account certain economic factors such as GDP (Gross Domestic

Product), Export, Installed Generation Capacity (MW), RBI credit to Government, WPI

(Wholesale Price Index).

As we all know that GDP is a function of Export, Installed Generation capacity, RBI credit to

Government and WPI. Therefore GDP is the dependent variable here. We have tried to find

out with the help of Regression model how the above mentioned economic factors affect

GDP.

1.2. Data description (data frequency, data span, source of data)

The data has been taken for our country. Data spans from June2004 to June2014, financial quarter wise.

Data Sample

GDP Export

Installed Gen Capacity

(MW)

RBI Credit to

Govt WPI

Jun-04 68,15,520.00 7,85,265.00 1,09,852.90 75,16,790.00 97.9

Sep-04 69,26,820.00 8,48,027.90 1,11,560.50 74,04,880.00 100.1

Dec-04 78,77,230.00 9,17,523.30 1,14,739.80 73,28,240.00 100.9

Mar-05 80,95,070.00 11,40,289.50 1,18,419.10 75,24,360.00 101.2

Jun-05 77,63,780.00 10,28,953.20 1,21,175.00 75,92,100.00 102.7

Sep-05 78,26,590.00 10,70,639.80 1,23,014.80 75,45,890.00 104.3

Dec-05 90,21,210.00 11,35,718.70 1,23,667.80 74,90,340.00 105.3

Mar-06 92,93,440.00 13,22,705.30 1,24,287.20 75,94,160.00 105.6

Jun-06 89,92,100.00 13,21,345.40 1,26,089.00 78,36,370.00 108.8

Sep-06 91,48,490.00 14,80,695.30 1,27,423.00 79,74,930.00 111.5

Dec-06 105,16,360.00 13,59,003.10 1,27,752.50 78,42,430.00 112.5

Mar-07 108,75,810.00 15,14,685.40 1,32,329.20 82,76,260.00 112.6

Jun-07 105,55,130.00 14,43,577.10 1,34,716.60 85,52,710.00 114.7

Sep-07 105,48,580.00 15,20,652.30 1,35,781.60 87,13,660.00 115.9

Dec-07 121,24,140.00 15,85,730.40 1,40,301.80 83,54,290.00 116.6

Mar-08 125,93,000.00 18,76,387.40 1,43,061.00 89,95,180.00 119.3

Jun-08 126,70,290.00 23,47,333.10 1,44,913.00 93,56,420.00 125

Sep-08 127,02,820.00 22,97,170.70 1,45,555.00 96,72,960.00 128.7

Dec-08 139,68,400.00 18,84,692.30 1,47,402.80 109,66,310.00 126.7

Mar-09 136,94,170.00 18,78,355.10 1,47,965.40 127,73,330.00 123.7

Jun-09 137,37,440.00 18,72,260.00 1,50,323.40 139,81,490.00 125.9

1.3. Model (brief theory, assumptions etc)

With the help of Regression model, we have tried to analyze how the dependent

variable, GDP is related to the independent variables, Export, Installed Generation

capacity, RBI credit to Government and WPI.

Regression analysis explains the relationship between two variables. The purpose of

this model is to test a theory or hypothesis.

From Regression equation, Y= 0 + 1X1 + 2X2 + 3X3 + 4X4 + e

X1 is Export

X2 is Installed Generation capacity

X3 is RBI credit to Government and

X4 is WPI.

Apart from X, there might be other variables which are unknown, but might have an

influence on Y. We capture this influence by error,

Actual value = Systematic part + random error

is randomly distributed

Econometric model = Mathematical model + Error term ()

Our objective is to create a best fitted line among the scattered plot. The OLS (Ordinary

Least Squares Method) is to create the best fitted line

Assumptions:-

We then check for the validity of the four important assumptions of a multiple

regression model.

The errors are normally distributed Normality

The mean of the errors is zero

Errors have a constant variance No heteroskedasticity

1.4. Empirical analysis

Step 1: First, we have done t

statistic of all the independent variables (which should be ideally greater than 2), we can

observe that only WPI is significant.

Only Probability value of WPI is

insignificant.

The Durbin Watson stat value is 1.8(tending to 2) which means that we can say there is no

auto correlation. Same cannot be confirmed now.

Probability value of F statistic is 0 which is

Empirical analysis

First, we have done the LS (Least Squares) test. We check the mod value of t

statistic of all the independent variables (which should be ideally greater than 2), we can

observe that only WPI is significant.

Only Probability value of WPI is significant (

Step 2: Next we have done the pair wise correlation test between independent variables. If pair

wise correlation is

Step 4: Now we have removed the Credit to Government variable in the LS test. We can

observe that except WPI, remaining variables are insignificant (

Step 5: Now we have removed the Credit to Government variable and Exchange rate variable in

the LS test. We can observe that except WPI, remaining variables are insignificant (

Step 6: Now we have done the LM test which is the confirmatory test.

Here the hypothesis is:-

Ho: There is no auto correlation

H1: There is auto correlation

From the above table we can observe that the Probability value is 0.58. Therefore we can say

that there is 58% chance of no auto correlation.

Now we have done the LM test which is the confirmatory test.


that there is 58% chance of no auto correlation.


1.5. Conclusion

From the above results, we can conclude that only the independent variable WPI (Wholesale

Price Index) has an impact on the GDP in the data period which we have taken.

2. DOW Effect and MOY Effect

2.1. Introduction

The efficient market hypothesis (EMH) postulates that stock prices must efficiently reflect all

available information about their intrinsic value. According to the EMH, stocks always trade at

their fair value on stock exchanges, making it impossible for investors to either purchase

undervalued stocks or sell stocks for inflated prices.

As such, it should be impossible to outperform the overall market through expert stock

selection or market timing, and that the only way an investor can possibly obtain higher returns

is by purchasing riskier investments. The opponents of efficient market theory asserts that

stock prices are largely determined based on investor expectation, and that price movements

will follow any patterns or trends and that past price movements can be used to predict future

price movements.

Besides, the efficient market hypothesis was contradicted by anomalies such as calendar

anomalies, fundamental anomalies and technical anomalies. Calendar anomalies refer to the

tendency of securities to behave differently on a particular day-of-the-week, or month-of-the-

year. Among such anomalies, the day-of-the-week effect has been seen as one of the most

important patterns and it has been found in several emerging stock markets (French, 1980;

Jaffe and Westerfield, 1985; Balaban, 1995; Lian and Chen,2004).

The day-of-the-week effect indicates that returns are abnormally higher on some days of the

week than on other days. Specifically, results derived from many empirical studies have

documented that the average return on Friday is abnormally high, and the average return on

Monday is abnormally low.

Besides, the rational investor should consider the risk or volatility of returns while making of

investment decisions. It is expected that there exist significant differences in volatility across

day of the week in stock markets. The day-of-the-week effects have been significantly

documented in the financial literature in the context of both developed and emerging stock-

markets.

Examination of day-of-the week effects is immense helpful for rational decision-makers to be

sentient of variation in the volatility of stock returns dependent on the day-of-the week and

whether high or low returns are associated with a correspondingly high or low volatility for a

given day.

If investors can identify a certain pattern of volatility, it is easier to make investment decisions

based on both the projected returns and the risks associated with the particular security.

Besides, the investigation of anomalous patterns may reveal evidence about the extent of

market efficiency.

2.2. DOW (Day of Week) effect

The data is Return on Sensex for 5 days viz Monday, Tuesday, Wednesday, Thursday and Friday.

The data has 1259 observations from Wednesday, September 10, 2014 to Friday, August 21,

2009.

A sample of that data is shown below

Date Sensex Return Monday Tuesday Wednesday Thursday Friday Wednesday,September10,2014 27057.41 -0.762543774 0 0 1 0 0

Tuesday, September 09, 2014 27265.32 -0.19959846 0 1 0 0 0

Monday, September 08, 2014 27319.85 1.084668124 1 0 0 0 0

Friday, September 05, 2014 27026.7 -0.218674419 0 0 0 0 1

Thursday, September 04, 2014 27085.93 -0.199005598 0 0 0 1 0

Wednesday,September03,2014 27139.94 0.446161072 0 0 1 0 0

Tuesday, September 02, 2014 27019.39 0.565142709 0 1 0 0 0

Monday, September 01, 2014 26867.55 0.861322369 1 0 0 0 0

Thursday, August 28, 2014 26638.11 0.293522439 0 0 0 1 0

Wednesday, August 27, 2014 26560.15 0.443750116 0 0 1 0 0

Tuesday, August 26, 2014 26442.81 0.021901107 0 1 0 0 0

Monday, August 25, 2014 26437.02 0.066125275 1 0 0 0 0

Friday, August 22, 2014 26419.55 0.22549223 0 0 0 0 1

Thursday, August 21, 2014 26360.11 0.174125922 0 0 0 1 0

Wednesday, August 20, 2014 26314.29 -0.402639297 0 0 1 0 0

Tuesday, August 19, 2014 26420.67 0.112576428 0 1 0 0 0

Monday, August 18, 2014 26390.96 1.102277381 1 0 0 0 0

Thursday, August 14, 2014 26103.23 0.710985592 0 0 0 1 0

2.2.1. Dummy Variables

In statistics and econometrics, particularly in regression analysis, a dummy variable (also known

as an indicator variable, design variable, Boolean indicator, categorical variable, binary variable,

or qualitative variable is one that takes the value 0 or 1 to indicate the absence or presence of

some categorical effect that may be expected to shift the outcome.

Dummy variables are "proxy" variables or numeric stand-ins for qualitative facts in a regression

model. In regression analysis, the dependent variables may be influenced not only by

quantitative variables (income, output, prices, etc.), but also by qualitative variables (gender,

religion, geographic region, etc.).

A dummy independent variable (also called a dummy explanatory variable) which for some

observation has a value of 0 will cause that variable's coefficient to have no role in influencing

the dependent variable, while when the dummy takes on a value 1 its coefficient acts to alter

the intercept.

For example, suppose Gender is one of the qualitative variables relevant to a regression. Then,

female and male would be the categories included under the Gender variable. If female is

arbitrarily assigned the value of 1, then male would get the value 0. Then the intercept (the

value of the dependent variable if all other explanatory variables hypothetically took on the

value zero) would be the constant term for males but would be the constant term plus the

coefficient of the gender dummy in the case of females.

Dummy variables are used frequently in time series analysis with regime switching, seasonal

analysis and qualitative data applications.

2.2.2. Empirical Analysis

OLS Technique is used for Empirical Analysis of Time Series data. Regression is performed and

then significance of variables is checked. If Monday comes out to be significant then it is

removed and again OLS is performed to check any other day significant or not.

Based on that inference is evaluated. The output of Regression is shown below

2.2.3. Regression Output

Here Return on Sensex is dependent variable and rest are independent variable.

The confidence interval is 95% so as we can see all variables are in significant with p value >0.05

and variability of model is also poor at 2.3%.

Dependent Variable: RETURN

Method: Least Squares

Date: 10/21/14 Time: 03:36

Sample (adjusted): 8/24/2009 9/10/2014

Included observations: 1259 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 0.114682 0.066743 1.718263 0.086

MON -0.007397 0.094953 -0.0779 0.9379

TUE -0.061726 0.094481 -0.65332 0.5137

THR -0.129488 0.094858 -1.36508 0.1725

FRI -0.120317 0.095245 -1.26324 0.2067

R-squared 0.002588 Mean dependent var 0.051291

Adjusted R-squared -0.000594 S.D. dependent var 1.067568

S.E. of regression 1.067885 Akaike info criterion 2.973201

Sum squared resid 1430.035 Schwarz criterion 2.993607

Log likelihood -1866.63 F-statistic 0.813382

Durbin-Watson stat 1.861889 Prob(F-statistic) 0.516589

2.2.4. Conclusion

Now we remove independent variable Wednesday and use C and calculate OLS. We find that all

variables are insignificant and variability explained by model is also low at 2.5% . Also overall

explanatory power of the model explained by F statistic is also insignificant so we can conclude

that there is no DOW week in Sensex return.

2.3. MOY (Month of Year) Effect

In the context of financial markets, calendar effects, that contradict the EMH, have been

documented over several years. These calendar effects are trends seen in stock returns, where

the returns tend to rise or fall on a particular day or month as compared to the mean.

They are called anomalies because they cannot be explained by traditional asset pricing models

and they violate the weak-form of market efficiency (i.e. asset prices fully reflect all past

information).

Examples of such patterns include the Month-of-the-year effect, Day-of-the-week effect, Intra-

month effect, Turn-of-the-month effect, Holiday effect, Halloween effect, and Daylight savings

effect.

As the name suggests, the month-of-the-year effectis a seasonal phenomenon where exchange

traded equities tend to produce abnormal returns during particular months of the year. This

effect is sometimes identified as the 'January effect' since most developed countries tend to

produce abnormal returns in January.

2.3.1. Data

The observations are from October 1, 2014 to August 12, 2002.

Return is the dependent variable and Months from January to December are independent

variable. A sample of data is shown below

Date return JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

October 1, 2014 -2.51 0 0 0 0 0 0 0 0 0 1 0 0

September 1, 2014 -10.54 0 0 0 0 0 0 0 0 1 0 0 0

August 1, 2014 -7.27 0 0 0 0 0 0 0 1 0 0 0 0

July 1, 2014 4.73 0 0 0 0 0 0 1 0 0 0 0 0

June 2, 2014 11.22 0 0 0 0 0 1 0 0 0 0 0 0

May 1, 2014 18.58 0 0 0 0 1 0 0 0 0 0 0 0

April 1, 2014 1.70 0 0 0 1 0 0 0 0 0 0 0 0

March 3, 2014 14.59 0 0 1 0 0 0 0 0 0 0 0 0

February 3, 2014 -3.44 0 1 0 0 0 0 0 0 0 0 0 0

January 1, 2014 -16.07 1 0 0 0 0 0 0 0 0 0 0 0

2.3.2. Empirical Analysis

OLS method is used on E Views software to establish significance of the Variables.

2.3.3. Regression Output



Date: 10/21/14 Time: 03:47

Sample (adjusted): 2002M09 2014M10



JAN -3.494242 4.428802

-

0.788981 0.4315

FEB -0.030156 4.428802

-

0.006809 0.9946

MAR 1.99687 4.428802 0.450883 0.6528

APR 3.783424 4.428802 0.854277 0.3945

MAY 5.687706 4.428802 1.284254 0.2013

JUN -1.092606 4.428802

-

0.246705 0.8055

JUL 4.406515 4.428802 0.994968 0.3215

AUG -2.713964 4.428802

-

0.612799 0.541

SEP 4.605324 4.255055 1.082318 0.2811

OCT -0.917103 4.255055

-

0.215533 0.8297

NOV -0.017103 4.428802

-

0.003862 0.9969

DEC 12.33089 4.428802 2.784251 0.0061


Adjusted R-squared 0.000089 S.D. dependent var 15.3425



Log likelihood -599.5691 Durbin-Watson stat 1.866882

According to regression output only DEC is significant and variability explained by model is 7.5%

Next Regression output



Date: 10/21/14 Time: 03:48

Sample (adjusted): 2002M09 2014M10



C 12.33089 4.428802 2.784251 0.0061

JAN -15.82514 6.263271

-

2.526657 0.0127

FEB -12.36105 6.263271

-

1.973577 0.0505

MAR -10.33402 6.263271 -1.64994 0.1013

APR -8.547469 6.263271

-

1.364697 0.1746

MAY -6.643188 6.263271

-

1.060658 0.2908

JUN -13.4235 6.263271

-

2.143209 0.0339

JUL -7.924378 6.263271

-

1.265214 0.208

AUG -15.04486 6.263271

-

2.402077 0.0177

SEP -7.72557 6.141643 -1.2579 0.2106

OCT -13.248 6.141643

-

2.157077 0.0328

NOV -12.348 6.263271

-

1.971493 0.0507


Adjusted R-squared 0.000089 S.D. dependent var 15.3425



Log likelihood -599.5691 F-statistic 1.001176

Durbin-Watson stat 1.866882 Prob(F-statistic) 0.448805

2.3.4. Conclusion Now DEC is removed and C is added and now Jan is significant .Overall model is insignificant

because F statistic is insignificant. So we can conclude there is no MOY effect and DOW effect.

3. MSARIMA EGARCH MODEL

3.1. Introduction

The world oil market is a capital-intensive environment characterized by complex

interactions deriving from the wide variety of products, transportation/ storage issues and

stringent environmental regulation.

Worldwide consumption of oil exceeds $500 billion, roughly 10% of the US GDP. Crude oil is

also the worlds most actively traded commodity, accounting for about 10% of total world

trade.

The economic importance of oil derives not only from the sheer size of the market, but also

from the crucial, almost strategic, role it plays in the economies of oil-exporting and oil-

consuming countries. Oil prices drive revenues to oil-exporting countries in a large number

of which, oil exports comprise over 20% of the GDP. On the other hand, costs of oil imports

(typically over 20% of the total import bill) have a substantial impact on growth initiatives in

developing countries. Energy price shocks have often been cited as causing adverse

macroeconomic impacts on aggregate output and employment, in countries across the

world.

Oil price generally shows Non-stationarity, Seasonality,Time-varying volatility, Regime

switching properties among others,Hence Forecasting volatility is fundamental to the risk

management process in order to price derivatives, devise hedging strategies and estimate

the financial risk of a firms portfolio of positions. In recent years, Autoregressive

Conditional Heteroscedasticity (ARCH) type models have become popular as a means of

capturing observed characteristics of financial returns like thick tails and volatility clustering.

This study forecasts day-ahead Crude Oil price using of multiplicative seasonal

autoregressive integrated moving average (MSARIMA) model and compares MSARIMA

forecasting performance with that of MSARIMA-exponential generalized autoregressive

conditional heteroskedasticity (EGARCH) model with an additional objective of modeling

time-varying volatility present in the time series data.

3.2. Data of Crude oil:

No of data points :501

Data span: 2-Jan-2013 to 5-Dec-2014

Data Frequency: Daily(5 working days / week)

Date Oil price Date Oil price Date Oil price Date Oil price

5-Dec-14 65.84 27-Oct-14 81 11-Sep-14 91.86 29-Jul-14 100.97

4-Dec-14 66.81 24-Oct-14 81.01 10-Sep-14 90.84 28-Jul-14 101.67

3-Dec-14 67.38 23-Oct-14 82.09 9-Sep-14 91.89 25-Jul-14 102.09

2-Dec-14 66.88 22-Oct-14 80.52 8-Sep-14 92.05 24-Jul-14 102.07

1-Dec-14 69 21-Oct-14 82.49 5-Sep-14 93.29 23-Jul-14 103.12

30-Nov-14 64.31 20-Oct-14 81.91 4-Sep-14 94.45 22-Jul-14 102.39

28-Nov-14 66.15 17-Oct-14 82.06 3-Sep-14 95.54 21-Jul-14 102.86

27-Nov-14 68.55 16-Oct-14 81.95 2-Sep-14 92.88 18-Jul-14 101.95

26-Nov-14 73.69 15-Oct-14 80.94 1-Sep-14 95.83 17-Jul-14 102.2

25-Nov-14 74.09 14-Oct-14 81.2 29-Aug-14 95.96 16-Jul-14 100.6

24-Nov-14 75.78 13-Oct-14 84.98 28-Aug-14 94.55 15-Jul-14 99.53

23-Nov-14 76.56 10-Oct-14 85.82 27-Aug-14 93.88 14-Jul-14 100.48

21-Nov-14 76.51 9-Oct-14 85.77 26-Aug-14 93.86 11-Jul-14 100.83

20-Nov-14 75.85 8-Oct-14 87.31 25-Aug-14 93.35 10-Jul-14 102.93

19-Nov-14 74.5 7-Oct-14 88.85 22-Aug-14 93.65 9-Jul-14 102.29

18-Nov-14 74.64 6-Oct-14 90.34 21-Aug-14 93.96 8-Jul-14 103.4

17-Nov-14 75.66 3-Oct-14 89.74 20-Aug-14 93.45 7-Jul-14 103.53

16-Nov-14 75.61 2-Oct-14 91.01 19-Aug-14 92.86 4-Jul-14 103.76

14-Nov-14 75.82 1-Oct-14 90.73 18-Aug-14 93.75 3-Jul-14 104.06

13-Nov-14 74.16 30-Sep-14 91.16 15-Aug-14 95.32 2-Jul-14 104.48

12-Nov-14 77.15 29-Sep-14 94.57 14-Aug-14 94.08 1-Jul-14 105.34

11-Nov-14 77.87 26-Sep-14 93.54 13-Aug-14 96.74 30-Jun-14 105.37

10-Nov-14 77.38 25-Sep-14 92.53 12-Aug-14 96.48 27-Jun-14 105.74

7-Nov-14 78.65 24-Sep-14 92.8 11-Aug-14 97.21 26-Jun-14 105.84

6-Nov-14 77.91 23-Sep-14 91.56 8-Aug-14 97.65 25-Jun-14 106.5

5-Nov-14 78.68 22-Sep-14 90.87 7-Aug-14 97.34 24-Jun-14 106.03

4-Nov-14 77.19 19-Sep-14 91.65 6-Aug-14 96.92 23-Jun-14 106.17

3-Nov-14 78.78 18-Sep-14 91.98 5-Aug-14 97.38 20-Jun-14 106.83

31-Oct-14 80.54 17-Sep-14 93.2 4-Aug-14 98.29 19-Jun-14 106.05

30-Oct-14 81.12 16-Sep-14 93.81 1-Aug-14 97.88

29-Oct-14 82.2 15-Sep-14 91.99 31-Jul-14 98.17

28-Oct-14 81.42 12-Sep-14 91.37 30-Jul-14 100.27

3.3. Analysis

3.3.1. Graphical Representation of data:

Note that from above graph we are not sure about the trend and seasonality present in the

data.

3.3.2. Check Correlogram:

ACF graph indicates that there is a Trend in the data with decay and a pattern of AR(1) as per

PACF, hence both tend and seasonality present. Also, it looks like that the data is Stationary.

3.3.3. Unit Root Test:

Null Hypothesis: The data has unit root and the data is not stationary.

Alternate hypothesis: data has no root and the data is stationary.

Check the data at Level Difference & observed that the Null Hypothesis accepted at 5% level of

significance, hence there is unit root and the data series is not stationary.

Hence we have to check the data at 1st difference.

Null Hypothesis Rejected at 5% level of signifiance, There is no unit root.

Thus, the data series is Stationary. Hence we need differencing to make the series stationary

3.3.4. Detrend the series:

Let us detrend the series with the equation series dd=d(price,1,0) and check correlogram

Inference: Dead end is reached. From correlogram it is difficult to identify AR, MA patterns.

Let us de-seasonalize the series & check correlogram

3.3.5. Deseasonalize the data:

Deseasonalize the series with the equation series dd=d(price,0,5)

From the correlogram, AR(1) SAR(5) signatures observed.

3.3.6. Estimation Stage

All the variables are statistically significant and < 1 Hence Stationarity & invertibility

conditions satisfied

Next, check if the residual series reach White Noise

3.3.7. Residual Analysis stage(Diagnostic Checking):

Inference: - White noise has been reached as alll prob value more than 0.05 as per the

correlogram.

3.3.8. Forecasting Stage:

Inference: - MAE error is 1.75 using static forecast processes and so we can go ahead with the

dynamic forecast process.

3.3.9. GARCH MODELLING:

Residuals graph after achieving white noise through ARIMA modelling

Results Of Arch Test@Lag1 For Conforming Volatility

Inferences Null Hypothesis for ARCH TEST is ARCH effect does not exist.

Here, the Null Hypothesis is rejected at approximately 95% confidence interval

Hence we can say that the model has an ARCH effect @ Lag 1

Variance Equation Will Be Generated By Using Garch Model At Lag 1

Inference: Coefficients of Constant value, size effect (coeff C5) and perseverance (coeff C7) are

significant and sign effect(Coeff C6) is insignificant at 95% confidence interval.

Result Of Arch Lm Test@ Lag 1 To Confirm Absence Of Arch Effect Now

Inference The variance equation is generated after the arch effect at lag 1 is taken into

consideration and further the arch effect is not present after that.

3.3.10. Static and Dynamic forecast

3.4. Conclusion:

By using ARIMA time series modeling we forecasted crude oil prices using Eviews software and

further to improve the accuracy of forecast by including the variance effect, we used ARIMA-

GARCH model. From the result it is observed that all the coefficients in the mean equation are

statistically significant and size effect, , is negative and statistically significant 5% level with

coefficient estimate of -0.153 indicating that a shock to crude oil prices has the impact on

volatility with respective of the direction of shock. The sign effect, , is statistically insignificant

indicating the presence of symmetric effects. i.e. negative shocks and positive shocks give rise

to similar volatility of prices. The volatility persistence term, , is statistically significant at 5 %

level, however, the coefficient is large indicating that the shocks effect will stay for a longer

time.

4. VAR-Cointergration

4.1. Introduction Co-integration is a statistical property of time series variables. Two or more time series are

co-integrated if they share a common stochastic drift. Vector auto regression (VAR) is an

econometric model used to capture the linear interdependencies among multiple time

series.

VAR models generalize the univariate auto regression (AR) models by allowing for more

than one evolving variable. A VAR model describes the evolution of a set of k variables

(called endogenous variables) over the same sample period (t = 1... T) as a linear function of

only their past values.

4.2. Objective We have taken major stock exchange index: BSE SENSEX -BSE, NYSE COMPOSITE -NYSE,

FTSE 100 -FTSE.

Through this analysis we intend to understand the relationship between these series in

terms of how they impact each other and how the return on each stock exchange is related

to each other.

4.3. Data Desciption BSE SENSEX -BSE, NYSE COMPOSITE -NYSE, FTSE 100 FTSE rates have been taken for 5

years (from 19/Dec/2014 to 4/Jan/2010) from Yahoo Finance.

Sample Data

Date BSE NYSE FTSE

12/19/2014 27371.84 4765 6545.3

12/18/2014 27126.57 4748 6466

12/17/2014 26710.13 4644 6336.5

12/16/2014 26781.44 4548 6331.8

12/15/2014 27319.56 4605 6182.7

12/12/2014 27350.68 4654 6300.6

12/11/2014 27602.01 4708 6461.7

12/10/2014 27831.1 4684 6500

12/9/2014 27797.01 4766 6529.5

12/8/2014 28119.4 4741 6672.2

12/5/2014 28458.1 4781 6742.8

4.4. Empirical Analysis We conducted tests to determine the nature of each of the series.

We found Each series is non stationary as per ADF unit root test. Each of the series is I (1)

in nature.

Figure 1- Return on stock exchange

Figure

Figure 2- Estimation of lag of VAR

Figure

Figure 3- Cointegration Testing

Figure

Figure 4- Error Correction Estimate

Figure 5

5-Granger Causlity Test (Short Run)

4.5. Conclusion

4.5.1. Long term relations

FTSE has long term relation with lag of order 1 and 2 with NYSE, NYSE has long term relation of

lag order 1 and 2 with FTSE, and BSE has long term relation of lag order 1 with NYSE.

4.5.2. Short term relations

BSE has short term relation with NYSE. NYSE & FTSE has mutual short term relationship.

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