Order choice in semiparametric GARCH models

Most previous studies that develop parametric tests of the lag structure in models with generalized autoregressive conditional heteroscedasticity (GARCH) are derived assuming the underlying conditional distribution of the errors is normal. The conditional normality assumption may be incorrect in many financial applications. Estimated moments of many financial time series exceed the moments predicted by a GARCH model with a normal density. In Chapter I, I develop a one-sided semiparametric test of the lag order that relaxes the assumption that the conditional density is normal and uses a nonparametric density estimator. The limiting distribution of the test statistic is derived using functional central limit theory and stochastic equicontinuity.;Chapter II presents monte carlo investigations into size and size-adjusted power of semiparametric tests of generalized ARCH processes. Tests applied included a semiparametric Lagrange multiplier and one-sided semiparametric test. The null and alternative hypotheses include models estimated by empirical researchers. Multiparameter hypotheses are also explored. A monte carlo simulation compares the size and power of parametric tests to semiparametric tests. For a sample size of 100 and 500 observations, I show that the semiparametric test provides as much as a 50 percent gain in size adjusted power over the parametric test.;Chapter III applies the semiparametric estimation techniques and testing results to a model of a hedged portfolio containing spot and futures exchange. The univariate behavior of spot and futures exchange rates are examined, building up a GARCH model for the variances. The results are extended to examine the joint distribution of currency spot exchange rates and currency futures, and to estimate the optimal futures hedge. I compare three models of a hedge portfolio: a constant hedge, GARCH variance under the assumption of normality, and GARCH variances with a nonparametric density estimator. Performance of the hedge is based on the average reduction in variance from a no-hedge position. I find that including a nonparametric density estimator improves the relative performance of the hedge portfolio by as much as 9 percent, compared to the hedge constructed under the assumption of normality.