Modeling nonlinear dynamics of daily futures price changes
研究了四种期货（标普500、日元、德国马克、欧洲美元）每日价格变化中的线性和非线性序列依赖，发现所有序列都存在非线性，GARCH模型能解释其中三种的非线性来源，而阈值自回归和自回归波动模型能充分描述标普500序列的动态。
The purpose of this article is to characterize linear and nonlinear serial dependence in daily futures price changes. The daily prices of four futures are included in this study: (i) S&P 500; (ii) Japanese yen; (iii) Deutsche mark; and (iv) Eurodollar. Our major empirical findings are: (i) Based on the results of nonlinearity tests (that is, the BDS, the Q2, and the TAR-F tests), we found all futures price changes contain nonlinearity in the series; (ii) a GARCH model can explain the source of nonlinearity for three out of four series; (iii) a threshold autoregressive model and autoregressive volatility model can adequately represent nonlinear dynamics of S&P 500 series; and (iv) deterministic chaos is not evident in the scaled residuals from the nonlinear time series models. Hence we favor a statistical time series approach to represent the data-generating mechanism of futures price changes. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 325–351, 1999