ARCH and GARCH modelling Basics Part 1 (Applied Econometrics)

● Basics of ARCH and GARCH modelling.

Previously the modelling was only concerned to the modelling the mean term only.

We did not consider to model the variance of Y. This is the concern of modelling the variance.

This also refers to the modelling the attitude of the investors. Modelling variance in the Financial Econometrics is what the central idea is all about.

Its about the volatality of the risk. The models capable of modelling volatality or variance of the series.

Our concern is not the Ecpected value here but the risk (variance). The heteroscedasticity is encountered in cross section data (unequal variance), due to the heterogeneous nature of the individuals and entities.

Say there is the time series data involving asset returns, such as stock return on Foreign Exchange, we observe the autocorrelated heteroscedasticity i.e. heteroscedasticity observed over different periods and such a phenomena is called as ARCH (Autoregressive Conditional Heteroscedasticity).

Suppose, for modelling of the Financial time series, 

If we have NEPSE index and if we take:

dlog (NEPSE) = dlog (Price) = dP/P × 100 %

Then we will get daily returns.

There is considerable variability in the daily returns.

The Finacial data exhibits a phenomena called as the volatality clustering.

VOLATALITY CLUSTERING: The periods of turbulence in which the price is widely distributed and periods of tranquility (wild and calm periods).

The mean of the process remains constant but the conditional variance changes over time.

However, the asset prices are non stationary (for eg, NEPSEs price) but the returns are stationary, it is also volatile.

Suppose we calculate the daily return of NEPSE i.e. rt,

Sigma [(rt - r') ^2] / n - 1 = Variance; r' = average return.

This variance will not capture volatality clustering, the reason is that it's unconditional variance. This is also the long run variance. This won't consider the past history of accounts. This won't consider time varying volatality in returns. Conditional on past volatality. Such value is depicted as ARCH.

We suppose,we purchase an asset a share at time period t, suppose now we want to sell it at  t+1 and for this a investor,  a forecast of the t+1 is important but that's not enough, becauee the variance of the returns may play an important role.

If ee purchase an asset today and plan to sell on t+1 then if the value of t+1 is low we'll loose, but if the vlaue o t+1, is high we'll gain a lot.

So, the variance of the returns is required during the holding period.

Thus, the unconditional variance is not useful. Conditional variance (daily basis) is only significant.

To be contd...

Thank you

Aditya Pokhrel

MBA, MA Economics, MPA.