Anon

216 The Basics of financial economeTrics

The key idea behind ARCH models is the following:

Unpredictable fluctuations of asset prices as well as of economic

time series do not have a constant average magnitude. Periods when

unpredictable fluctuations are large alternate with periods when

they are small.

This type of behavior of unpredictable fluctuations is almost universal in
financial and economic time series data.
ARCH modeling can be applied to a large class of financial and eco-
nomic variables. In order to gain an understanding of ARCH modeling,
we will consider asset returns. Let’s first assume that returns behave as a
sequence of independent and identically distributed random variables, com-
monly referred to as an i.i.d. sequence. As explained in Chapter 2, an i.i.d.
sequence is the simplest model of returns. It implies that returns are unpre-
dictable: the returns at any given time are random values independent from
previous returns; they are extracted from the same distribution.
Figure 11.1 represents the plot of simulated returns of a hypothetical asset.
Returns are assumed to be an i.i.d. sequence formed with 1,000 independent

0 200 400 600 800 1,000

−4

−3

−2

−1

0

1

2

3

4

Time Steps

Returns

FIGure 11.1 Plot of Simulated Returns as a Sequence of 1,000 i.i.d. Variables