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B. Venkatesh

PROF Robert Engle, awarded the 2003 Nobel Prize for Economics, is well known for his work on Autoregressive Conditional Heteroskedasticity (ARCH). What is ARCH process?

Suppose you decide that the past prices of Satyam will help you forecast the future price of the stock. You, therefore, use autoregressive process of order 1, referred as AR (1). If you are using monthly prices, AR (1) process means that the stock price for the current month is dependent on the price of the previous month.

Now, there could be other variables also influencing the stock price, but not as important. You, therefore, add an error term to the AR (1) model to capture all the residual factors that may determine the stock price movement. The assumption in a time series model is that the variance of the error term is constant, or homoskedastic. This means that there is no systematic relationship between variable and the error term.

Often, there is some relationship between the error term and the variable-stock prices in our example. Statistically, the error term is said to be heteroskedastic. The forecast based on the AR (1) model that is heteroskedastic will be wrong.

Prof Engle first suggested a model to test for heteroskedasticity. The model itself is an AR (1) process, where the squared error term of one period is dependent on the squared error term of the previous period.

If the co-efficient of the error term in the model is statistically significant, we can say that the original time series, the stock price series above, contains ARCH (1) errors. You have to, therefore, use sophisticated models to correct for the heteroskedascity.

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