ARCH – only testing b2 not b1?

Question

Hello!

I just want to double check that if you are given a table of squared residuals and asked to check if ARCH is present, you should only look at the p-Value for the slope, not the intercept to see if there is significance? I ask because I've just come across a Schweser question testing against 5% sig and intercept p is 0.01 (sig) and the lag residual p is 0.31 (not sig).

I get that we are regressing the squared residuals from t-1 etc to see if the error variance equals the constant or not.

Thanks :)

Sophie Macon · Answer

Autoregressive conditional heteroskedasticity (ARCH) refers to a statistical model set up to analyze volatility across time, in order to better forecast future volatility.

It refers to an autoregressive equation in which the variance of the error terms (residuals) is heteroskedastic. In other words, when the error variance is not constant.

To test for ARCH:

Take the residuals from the original autoregressive model and square them.
 	Regress the squared residuals from this period against the squared residuals from the previous period:

&#949;t+12=&#945;0+&#945;1&#949;t2

The bit we're interested in is 𝝰1, i.e. the 'slope', and not the intercept (which basically indicates that εt+12 is non-zero). Presence of a non-zero 𝝰1 indicates that the error variance is not constant.

Sorry, got a bit lengthy in the end!