Nonlinear Autocorrelograms: an Application to Inter-Trade Durations

The paper presents a study of temporal dependence in nonlinear transformations of time series. We examine the effects of parametric transformations on autocorrelation values and the persistence range with special emphasis on long memory processes. We derive an invariance property for the order of fractional integration of transformed normal processes and propose a related specification test. Within the class of nonlinear time series transforms, we identify those which maximize autocorrelations at selected lags. This procedure is based on nonlinear canonical correlations analysis adapted to serially correlated data. The methods proposed in this paper may be applied to various financial time series that usually are transformed prior to estimation, like returns, volumes or inter-trade durations. In examples illustrating our approach, we use series of durations between trades of the Alcatel stock on the Paris Bourse.     

First-Order Autoregressive Processes with Heterogeneous Persistence

Abstract. We propose a semi-nonparametric method of identification and estimation for Gaussian autoregressive processes with stochastic autoregressive coefficients. The autoregressive coefficient is considered as a latent process with either a moving average or regime switching representation. We develop a consistent estimator of the distribution of the autoregressive coefficient based on nonlinear canonical decomposition of the observed process. The approach is illustrated by simulations.