Financial Modeling with Crystal Ball and Excel, + Website, 2nd Edition

CHAPTER 11

Simulating Financial Time Series

In financial modeling, we encounter two main types of time-series data:

1. Observations that appear to be independent and identically distributed (IID); and

2. Observations that do not appear to be IID because they follow a trend or some other pattern over time.

Financial theory provides a compelling argument–the efficient markets hypothesis–that returns on investments must be independent over time because no one has access to information not already available to someone else. If returns are independent however, prices will be dependent over time and we will require a way to model that dependence. In this chapter we will see some models that can be used for projecting future returns, asset prices, and other financial time series in simulation models for risk analysis.

11.1 WHITE NOISE

A white noise process is defined as one that generates data appearing to be IID. It takes its name from the fact that no specific frequency or pattern dominates in a spectral analysis of the observations, similar to white light, or the noise of static emitted from an AM radio that is not tuned into a station.

The model for a white noise process is

(11.1)

where μ is a constant, and εt is a sequence of uncorrelated random variables identically distributed with mean zero and finite variance for t = 1, ... , T. The probability distribution of εt is not necessarily ...