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). 2. Observations that do not appear to be IID because they follow a trend or some other pattern over time. | 11 Simulating Financial Time Series I n financial modeling we encounter two main types of time-series data 1. Observations that appear to be independent and identically distributed IID . 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. This chapter presents some models that can be used for projecting future returns asset prices and other financial times series in simulation models for risk analysis. WHITE NOISE A white noise process is defined to be 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 in to a station. The model for a white noise process is Wt p et where p is a constant and et is a sequence of uncorrelated random variables identically distributed with mean zero and finite variance for t 1 . T. The probability distribution of et is not necessarily normal but if it is the process is said to be Gaussian white noise named after the eighteenth-century mathematician Carl F. Gauss who studied the properties of the normal distribution. For example we can simulate observations from a Gaussian white noise process with Crystal Ball by placing several uncorrelated Normal 0 10 assumptions in a column adding a constant say p 200 and plotting the results as was done in the file . Figure shows the model. In cells B6 B35 are Crystal Ball 147 148 FINANCIAL MODELING WITH CRYSTAL BALL AND EXCEL FIGURE Model to compare a white noise process to a .
