A Monte Carlo study of new time series statistical tests and their application to the modeling of price dynamics in futures markets

Modeling price dynamics in financial markets has become an important research area in financial economics. In the past empirical studies of financial price movements were based on methods that were incapable of detecting or modeling nonlinear serial dependence that characterizes financial market data. Recently, advances in the study of nonlinear dynamics in the physical sciences have motivated researchers to apply nonlinear time-series models to the study of financial and economic data. This dissertation investigates three statistical tests which can detect nonlinear serial dependence, and applies these tests and two nonlinear time-series models to futures markets. In this dissertation, the finite sample properties of the BDS, TAR-F and Q$\sp2$ test are evaluated using Monte Carlo experiments. Monte Carlo findings show that the finite sample distribution of the tests under the data generating processes (DGPs) of the null hypothesis approximates their asymptotic counterpart quite closely. The power of the tests on DPGs of alternative hypotheses reaches unity at sample size of 1000 when the DGPs are not too close to the DGP of the null hypothesis. Based on findings of Monte Carlo investigation, the three tests and two nonlinear time-series models are applied to the study of price dynamics in futures markets. The futures studied are the S&P 500, Crude Oil, Japanese Yen, Deutsche Mark, and Eurodollar futures. The results show that the price changes of all five futures have nonlinear serial dependence, and that they can be modeled by nonlinear time-series models, either GARCH, or TAR, or combined TAR-GARCH model. The main conclusions to emerge from the findings of this dissertation are as follows. The three tests are reliable for detecting serial dependence, including nonlinear serial dependence. The tests work well when sample size equals 1000 or larger and the sample's departure from the null hypothesis is not too small. When analyzing futures prices, we have to acount for nonlinear serial dependence, use nonlinear models with conditional heteroskedasticity and conditional mean change.