Adaptive Test for Periodicity in Autoregressive Conditional Heteroskedastic Processes

This article is concerned with the periodicity testing problem in Autoregressive Conditional Heteroskedastic (ARCH) process. Adaptive locally asymptotically optimal test is derived, when the innovation density is unspecified but symmetric satisfying only some general technical assumptions, for the null hypothesis of classical ARCH process against an alternative of periodically correlated ARCH dependence. The main technical tool is LeCam's (1960 LeCam , L. ( 1960 ). Locally Asymptotically Normal Families of Distributions . University California Publ. Statistics 3:27–98 . [Google Scholar]) Local Asymptotic Normality (LAN) property. The LAN property of the central sequence is shown via the adapted sufficient Swensen's conditions (1985 Swensen , A. R. ( 1985 ). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend . Journal of Multivariate Analysis 16 : 54 – 70 .[Crossref], [Web of Science ®] , [Google Scholar]). The performance of the established test is shown via simulation studies.     

Adaptive Estimation of Periodic First-Order Threshold Autoregressive Model

This paper focuses on the adaptive estimation problem of a Periodic Self-Exciting Threshold Autoregressive (PSETAR) model. The adapted sufficient conditions of Swensen (1985 Swensen, A. R. 1985. The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis, 16: 54–70. [Crossref], [Web of Science ®] , [Google Scholar]) to our model, are verified and then explored to establish the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ) and the Local Asymptotic properties satisfied by its central sequence. Using these results, we construct adaptive estimators for the parameter model where the innovation density is unspecified but symmetric, while satisfying only some general conditions. The performances of these adaptive estimations are shown via simulation studies and an application on the modeling of the Fraser River data.     

Test for periodicity in restrictive EXPAR models

Abstract

This article is devoted to study the problem of test of periodicity in the restricted exponential autoregressive (EXPAR) model. The local asymptotic normality property, of this model, is shown via the adapted sufficient conditions due to Swensen (1985 Swensen, A.R. (1985). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. J. Multivariate Anal. 16:54–70.[Crossref], [Web of Science ®] , [Google Scholar]). Using this result, in the case where the innovation density is specified, we obtain a parametric local asymptotic “most stringent” test.     

Moments of Mixture Periodic Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated autoregressive (MPAR _S ) time series model, which extends the mixture time invariant parameter autoregressive (MAR) model, that has recently received a considerable interest from many economic time series analysts, to mixture periodic parameter autoregressive model. The aim behind this extension is to make the model able to capture, in addition to all features captured by the classical MAR model, the periodicity feature exhibited by the autocovariance structure of many encountered financial and environmental time series with eventual multimodal distributions. Our main contribution here is obtaining of the second moment periodically stationary condition for a MPAR _S (K; 2,…, 2) model, furthermore the closed-form of the second moment is obtained.     

On Mixture Periodic Vector Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007 Fong, P.W., Li, W.K., Yau, C.W., Wong, C.S. (2007). On a mixture vector autoregressive model. The Canadian Journal of Statistics 35:135–150.[Crossref], [Web of Science ®] , [Google Scholar]). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVAR_S(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.     

Adaptive Estimation of Causal Periodic Autoregressive Model

This article deals with the adaptive estimation of a periodic autoregressive model, with unspecified innovation density satisfying only some general technical assumptions. We first establish, while verifying the adapted sufficient conditions of Swensen (1985 Swensen , A. R. ( 1985 ). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend . Journal of Multivariate Analysis 16 : 54 – 70 .[Crossref], [Web of Science ®] , [Google Scholar]) to our model, the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ), and the Local Asymptotic properties satisfied by its central sequence. Secondly, the Locally Asymptotically Minimax (LAM) estimators are constructed. Using these results, we construct the adaptive estimators of the unknown autoregressive parameters. The performances of the established estimators are shown, via simulation studies.