Seemingly unrelated regression on the autoregressive (Ar(p)) singular equation system

This paper studies the estimation of seemingly unrelated regressions (SUR) of singular equation systems with an autoregressive error process (AR(p)) for each equation.Parameter estimates of the autoregressive singular equation system are not generally invariant to the equation deleted. Under the model specification restriction on the autoregressive parameters, the invariance property is preserved, and this paper shows that a single equation generalized least squares (GLS) estimation for a general autoregressive error process is equivalent to the SURGLS estimation of the AR(p) singular equation system.     

Improved model selection criteria for SETAR time series models

The purpose of this paper is threefold. First, we obtain the asymptotic properties of the modified model selection criteria proposed by Hurvich et al. (1990. Improved estimators of Kullback-Leibler information for autoregressive model selection in small samples. Biometrika 77, 709–719) for autoregressive models. Second, we provide some highlights on the better performance of this modified criteria. Third, we extend the modification introduced by these authors to model selection criteria commonly used in the class of self-exciting threshold autoregressive (SETAR) time series models. We show the improvements of the modified criteria in their finite sample performance. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error (RMSE) of prediction improves for the efficient criteria. These results are illustrated via simulation with SETAR models in which we assume that the threshold and the parameters are unknown.     

GENERALIZED SIGNED-RANK ESTIMATORS FOR AUTOREGRESSION PARAMETERS

ABSTRACT

A new class of weighted signed-rank-based estimates for estimating the parameter vector of an autoregressive time series is considered. The Wilcoxon signed-rank estimate and the GR-estimates of Terpstra et al. (GR-Estimates for an Autoregressive Time Series. Statistics and Probability Letters 2001, 51, 165–172; Generalized Rank Estimates for an Autoregressive Time Series: A U-Statistic Approach. Statistical Inference for Stochastic Processes 2001, 4, 155–179) can be viewed as special cases of the so-called GSR-estimates. Asymptotic linearity properties are derived for the GSR-estimates. Based on these properties, and a symmetry assumption, the GSR-estimates are shown to be asymptotically normal at rate n ^1/2. The theory of U-Statistics along with a characterization of weak dependence that is inherent in stationary AR(p) models are the primary tools used to obtain the results. Tests of hypotheses as well as standard errors for confidence interval procedures can be based on such results. An efficiency study indicates that, for an appropriately chosen set of weights, the GSR-estimate is more efficient than the GR-estimate. Furthermore, the GSR-estimate has an added advantage in that an intercept term can be estimated simultaneously; unlike the GR-estimate. Two examples and a small simulation study are used to illustrate the computational and robust aspects of the GSR-estimates.     

Mixture inverse Gaussian for unobserved heterogeneity in the autoregressive conditional duration model

In this paper, we assume that the duration of a process has two different intrinsic components or phases which are independent. The first is the time it takes for a trade to be initiated in the market (for example, the time during which agents obtain knowledge about the market in which they are operating and accumulate information, which is coherent with Brownian motion) and the second is the subsequent time required for the trade to develop into a complete duration. Of course, if the first time is zero then the trade is initiated immediately and no initial knowledge is required. If we assume a specific compound Bernoulli distribution for the first time and an inverse Gaussian distribution for the second, the resulting convolution model has a mixture of an inverse Gaussian distribution with its reciprocal, which allows us to specify and test the unobserved heterogeneity in the autoregressive conditional duration (ACD) model.

Our proposals make it possible not only to capture various density shapes of the durations but also easily to accommodate the behaviour of the tail of the distribution and the non monotonic hazard function. The proposed model is easy to fit and characterizes the behaviour of the conditional durations reasonably well in terms of statistical criteria based on point and density forecasts.     

A Bayesian analysis of a change in the parameters of autoregressive time series

In this article, we consider a Bayesian analysis of a possible change in the parameters of autoregressive time series of known order p, AR(p). An unconditional Bayesian test based on highest posterior density (HPD) credible sets is determined. The test is useful to detect a change in any one of the parameters separately. Using the Gibbs sampler algorithm, we approximate the posterior densities of the change point and other parameters to calculate the p-values that define our test.     

Multiple Time Series Modeling and Extended Sample Cross-Correlations

This article provides an expository account of the multivariate autoregressive moving average models and proposes an extended sample cross-correlation approach for practical model identification. An iterative model building procedure for applying these models to real data is discussed and demonstrated by analyzing the 5-series U.S. Hog Data.     

Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary

Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies the asymptotic null distribution of the test statistics for testing p = 1 in the model Y_t = pY _t-1 + e _t – 0e _t-1 as 0 approaches 1. It is shown that the test statistics differ from one another in their asymptotic properties depending on the rate at which 0 converges to 1.     

Estimation and Prediction of Functional Autoregressive Processes

We present a generalization of some previous works (Bosq, Mourid, Pumo) about the functional forecast of a Banach autoregressive processes. We are mainly concerned with order p , p >1, autoregressive processes which appear to be a natural extension of the well-known R d -valued autoregressive processes to a functional framework. This modelization provides an new approach for estimating and for predicting a continuous time stochastic process over an entire time interval. Using results from [12] we prove asymptotic properties of estimators of the parameters and predictors which are based upon a principal component decomposition of a Hilbert-Schmidt operator with unknown eigenvectors.