Statistics for Finance

Chapter 5

Nonlinear time series models

5.1 Introduction

The linear models have some characteristics, which have been discussed in Chapter 4, and which clearly might be a serious limitation. Some of the most important characteristics and limitations of the linear models are that the dynamics is constant for all values of the process and for all time. Furthermore, the variance of any forecast is constant. It is, however, well known that financial data tends to display heteroscedasticity (Section 1.3), which means that the (conditional) variance changes over time and typically depends on the past observations. In finance the variance is an expression of the risk or the volatility, and it is often found that large values of, for instance, interest ...