Use Log Returns as Inputs to a GARCH-BEKK Model

Summary

The document asks how to prepare two price series before estimating a GARCH-BEKK model to investigate volatility transmission. The questioner considers making the data stationary by first differencing prices and then fitting a bivariate model with a one-lag ARCH and GARCH specification in SAS. The response recommends using price returns rather than raw price differences.

Specifically, it describes the continuously compounded return as the natural logarithm of the ratio of the current price to the previous price. This is the only modeling guidance offered. The exchange does not explain how to specify or diagnose the BEKK system, test whether volatility transmission is significant, select lag orders, or handle other data issues. It therefore gives a useful input transformation but not a complete estimation workflow, and the recommendation should not be read as evidence that the model is correctly specified for every pair of series.

Key ideas

• The stated goal is to test volatility transmission between two price series with a GARCH-BEKK model.
• The response recommends modeling returns instead of price levels or raw price differences.
• Returns are defined as the natural logarithm of the ratio of consecutive prices.
• The exchange does not cover model diagnostics, lag selection, or inference on transmission.

Tags

# Fitting a GARCH BEKK model


# Fitting a GARCH BEKK model












I am trying to find whether there is significant volatility transmission between two price series (t=1000). A literature review learned me that the GARCH BEKK model is suitable for this.

The SAS package can estimate it, see user guide However, I am getting strange results. Now I am in doubt about whether I am doing this the right way. I thought I should just make sure the series are stationary by first differencing them and afterwards, I can directly put them into the GARCH BEKK model by SAS.

Like this:

```
proc varmax data=price-series;
model series1 series2; 
garch q=1 p=1 form=bekk;
run;
```

Which steps am I overlooking?

## Answer by MIAO ZHEN (score 2)

https://quant.stackexchange.com/a/9129

should be price returns, transforming your series as return=ln(Pt/Pt-1), in words, it means the natural logarithmic transformation of the ratio of price at time t to price at time t-1

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