Nonlinear Serial Dependence Research Articles

Modeling nonlinear dynamics of daily futures price changes

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) SP (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 Q-super-2, 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 SP 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

A multiple distribution Markovian model for annual hydrologic time series

Nonlinear serial dependence and skewness of annual hydrologic time series {X t } have been challenging the classical theory of Gaussian stochastic processes, particularly if the study of extremes (dry or wet years) is required as it is often the case. In this paper, a new and general model is proposed assuming that the geophysical system which is responsible forX t can take different states and that this state process is modeled by a Markov chain. At each time,X t is generated from a statistical distribution which depends on the state that has occurred. This model can preserve non-linear structures of serial dependence and it can produce a skewed marginal distribution ofX t without any transformation. A successful application of this model to the study of annual rainfall at Fortaleza (Northeast of Brazil) is also presented.

A DIAGNOSTIC TEST FOR NONLINEAR SERIAL DEPENDENCE IN TIME SERIES FITTING ERRORS

Abstract. Time series analysts have begun to consider the applicability of nonlinear models. In order for nonlinear models to be accepted by practitioners, practicai tests must be avilable to test for the presence of nonlinearity in both raw time series and in the residuals from fitted models. A diagnostic test, based on the bispectrum, for the presence of nonlinear serial dependence in these time series is investigated here using artificial data. Detection of such nonlinear dependence is taken to indicate that nonlinear modelling methods are necessary. The theory behind the test is reviewed and simulations driven by pseudorandom numbers are presented for a variety of models and sample sizes. The simulations indicate that the test has substantial power for many models. In addition, theoretical and empirical results are presented which show that the bispectral diagnostic test is equally powerful for both the source series and for the fitting errors from a line& model. Thus, while the test is suitable for use as a diagnostic test on the fitting errors of linear time series models, prior linear modeling of the time series is not required.