Analysis of Financial Time Series, Third Edition

4.3 Modeling

Nonlinear time series modeling necessarily involves subjective judgment. However, there are some general guidelines to follow. It starts with building an adequate linear model on which nonlinearity tests are based. For financial time series, the Ljung–Box statistics and Engle's test are commonly used to detect conditional heteroscedasticity. For general series, other tests of Section 4.2 apply. If nonlinearity is statistically significant, then one chooses a class of nonlinear models to entertain. The selection here may depend on the experience of the analyst and the substantive matter of the problem under study. For volatility models, the order of an ARCH process can often be determined by checking the partial autocorrelation function of the squared series. For GARCH and EGARCH models, only lower orders such as (1,1), (1,2), and (2,1) are considered in most applications. Higher order models are hard to estimate and understand. For TAR models, one may use the procedures given in Tong (1990) and Tsay (1989, 1998) to build an adequate model. When the sample size is sufficiently large, one may apply nonparametric techniques to explore the nonlinear feature of the data and choose a proper nonlinear model accordingly; see Chen and Tsay (1993a) and Cai, Fan, and Yao (2000). The MARS procedure of Lewis and Stevens (1991) can also be used to explore the dynamic structure of the data. Finally, information criteria such as the Akaike information criterion (Akaike, 1974) and ...