Time-Varying Volatility and ARCH Models: Introduction to Financial Econometrics

In this chapter we’ll estimate several models in which the variance of the dependent variable changes over time. These are broadly referred to as ARCH (autoregressive conditional heteroskedas – ticity) models and there are many variations upon the theme.

The first thing to do is illustrate the problem graphically using data on stock returns. The data are stored in the gretl dataset returns. gdt. The data contain four monthly stock price indices: U. S. Nasdaq (nasdaq), the Australian All Ordinaries (allords), the Japanese Nikkei (nikkei) and the U. K. FTSE (ftse). The data are recorded monthly beginning in 1988:01 and ending in 2009:07. Notice that with monthly data, the suffix is two digits, that is 1988:01 is January (01) in the year 1988.

Simple scatter plots appear below. They can be generated using the GUI as described on page 278, or using the scatters command. [79] [80]

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