The previous article showed time series using autoregressive conditional hetroskedasticity (**ARCH)** model in STATA. The present article shows extensions of

**i.e.**

__ARCH,__**GARCH**model in STATA. Like

**model,**

__ARCH__**extensions like Generalised ARCH (**

__ARCH__**GARCH**) model also need squared residuals as determinants of the equation’s variance.

## Generalized ARCH (**GARCH)** model

In **GARCH** model, the conditional variance of error term at time ‘t’ depends on the following:

- Squared error term in the previous time period (ARCH1)
- Its conditional variance in the previous time period.

Follow this command for using **GARCH** model:

arch logRE_d1, arch(1) garch(1)

The interpretation of the syntax is as follows.

In the **ARCH** regression model, ‘logRE_d1’ is a dependent variable with no independent variables other than a constant. ‘arch(1)’ command adds a single lagged value of

*et*to the modelled variance in STATA. ‘garch(1)’ command adds a single lag of the variance,

*ht*, to the modelled variance.

## Results of **GARCH** model

The figure below shows the results of **GARCH **model. The estimate of a lagged value of error term is 0.491 whereas the coefficient estimate is 0.238. The p values are all significant and log likelihood is also highest in all the iterations.

Like **ARCH**, generate variances for

**GARCH**model using the same command:

predict GTgarch, variance

Here ‘GTgarch’ is the name for predicted series of variances. The results will not appear in ‘Result’ window, but in ‘data editor’ window of STATA. To examine the movement of GTgarch generates a time plot using this command:

**STATA Command: tsline ****GTgarch
**

The figure below shows the results.

The above graph shows that there is a lot more volatility towards the entire span of the sample considering the lagged values of variances.

## Threshold **GARCH** (TGARCH) model

The threshold **GARCH **model or ** TGARCH** is another generalization of the

**GARCH**model where positive and negative news are treated asymmetrically. This adds another option to the arch ‘Stock_RE_d1

**’**regression model in STATA. Use this command for

**model in STATA:**

*TGARCH*arch logRE_d1, arch(1) garch(1) tarch(1)

The figure below shows the results. The estimate of the lagged value of error term is 0.08 and the coefficient on the lagged variance is 0.919. The p values are all significant and log likelihood is also highest in all the iterations.

Further to generate variances for ** TGARCH** use this command:

predict HTgarch, variance

Here ‘HTgarch’ is the name for the predicted series of variances. The results do not appear in ‘Result’ window, but in ‘data editor’ window of STATA. To examine the movement of the variance of HTgarch, generate a time plot using this command:

tsline HTgarch

After analyzing ARIMA, VAR, VEC, ARCH and some extensions of the ARCH models, the next set of articles will focus upon some common diagnostics tests applied to time series analysis. These tests will pertain to normality, heteroskedasticity, autocorrelation, multicollinearity and stability.

### Divya Dhuria

#### Latest posts by Divya Dhuria (see all)

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