Correlogram

Quick Series Statistics- Correlogram.

Put the series name.

Select Level Put number of lags

Press OK

Test the joint significance of autocorrelation up to the given lag-order.

Correlogram of a Non-Stationary /Unit-Root Process

Unit Root Test: Step by Step

Open : Quick Series Statistics-Unit Root Test.

-Enter the variable

Name of the test

1) Lag Selection

First select at Level

First select only intercept

If a series is trend stationary detrend it, or explicitly include trend in your model.

If a series is difference stationary, difference it to make it stationary.

Read t-statistics and p-value;

If p

Granger Causality Test

Quick- Group Statistics-Granger Causality Test

Name Two Series

Select Lag Order

Read F-Statistics and p-value

If p is less than 0.05, null hypothesis is rejected.

VAR Model

Enter at least two variables

Select unrestricted VAR

Select lag order

Lag Length Selection: Go to

View-lag structure-lag length criteria

Select the lag based on the criteria of your choice, where the value of the criteria is minimum.

Granger Causality (Block Exogenity Test)

View-lag structure Granger causality/Block Exogenity Test

Read chi-square and its p-value. Here the null hypothesis of exclusion is rejected, hence US returns cause Indian returns

Here the null hypothesis of exclusion is not rejected; hence Indian returns do not causeUS returns

Impulse Response

View Impulse Response

Define the impulse. Cholesky decomposition is most frequently used.

If Cholesky decomposition is used the sequence of the variable becomes important

Co integration Test

Here select the appropriate model.

If you are not sure you can get summary of the models (Option 6)

In this case use Panetula Principle and select the first model showing cointegration

Results of the first model

If Variables are cointegrated fit a Error correction Model

-Open VAR

-Select Error Correction Model

-Open Cointegration window and select model 1

Ho r=0 rejected

H0 r=1 not rejected

Variables are cointegrated

Results

Cointegration equation normalized to LOGSPOT

Error Correction , since both are significant, there is two way adjustment/causality

Short run VAR,

You may conduct a Granger causality test for this.

Granger Causality Test

Both the hypotheses are rejected, there is two w ay short-run causality

ARCH-GARCH Models

Testing ARCH Effect:

We will estimate AR(1) Model of stock market returns in India (ind) and then we will test the presence of ARCH effect:

Open Quick - Estimate Equation

Get results

AR(1) model

Method of Estimation OLS/ARMA

Go to:

View- Residual Test - ARCH-ML test

Select lag-order (say 1)

Null hypothesis that there is no ARCH effect is strongly rejected, So now estimate ARCH or GARCH model

Estimating ARCH Model

Open-Quick-Estimate Equation

The following dialog box will appear

Enter the variable also the mean equation

Select ARCH from drop-down box

The following dialog Box will appear

If you have to estimate ARCH(1) model make it zero

If you have to estimate ARCH (p) p=1,2,; change this accordingly

Test is there further ARCH Effect in residuals using the procedure discussed earlier. Generally you will observe ARCH effect at higher lag orders as volatility is known to be highly persistent. Therefore it is better to estimate a GARCH model than an ARCH model.

This is the ARCH (1) coefficient

And this is statistically significant.

Estimation of GARCH (1, 1) Model

Results:

ARCH Coefficient

GARCH Coefficient

Test for Residual ARCH effect (selected lag order 10):

If you have to get the estimated conditional volatility graphically; go to

View Conditional SD Graph

You obtain the following graph.

To save the graph in word file go to

Edit - copy

Now ARCH effect is not there in the residuals

To obtain the conditional Volatility as a variable

Go to

Proc Make a GARCH Variance Series

Estimating TRARCH Model

Estimating EGARCH Model:

Change this to 1

Change the model to EARCH using drop down Box

GARCH-X Model

If you want to include some additional variables in volatility equation you can do it by putting the name of the variable in appropriate box. But make sure that the variable should not contain negative values. For example if you have to study the day-of-the week effect in volatility (say Monday effect), make a Monday dummy and put the dummy in the box.

Put additional variable here.