Periodic integer-valued bilinear time series model

This paper deals with the study of some probabilistic and statistical properties of a periodic integer-valued diagonal bilinear model. The existence of a periodically strict stationary integer-valued process is shown. Sufficient conditions for the periodically stationary, both in the first and second orders, are established. The closed-forms of the mean and the second moment are obtained. The closed-form of the periodic autocovariance function is established. The Yule–Walker estimations of the underlying parameters are obtained. A simulation study is provided.     

Adaptive Test for Periodicity in Self-Exciting Threshold Autoregressive Models

This article is devoted to the study of the periodicity testing problem in a self-exciting threshold autoregressive (SETAR) model. The local asymptotic normality (LAN) property 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 . Journal of Multivariate Analysis 16 : 54 – 70 .[Crossref], [Web of Science ®] , [Google Scholar]). Moreover, the LAN of the central sequence is established. First, we consider the case where the innovation density is specified and we obtain a parametric local asymptotic test. Second, we construct an adaptive test in the case where this density is unspecified but symmetric. The performances of these established tests are shown via simulation studies.     

Periodic integer-valued GARCH(1, 1) model

This article deals with some probabilistic and statistical properties of a periodic integer-valued GARCH(1,1) model. Necessary and sufficient conditions for the periodical stationary, both in mean and second order, are established. The closed-forms of the mean and the second moment are, under these conditions, obtained. The condition of the existence of higher moment orders and their explicit formula in terms of the parameters are established. The autocovariance structure is studied, while providing the closed-form of the periodic autocorrelation function. The Yule–Walker and the likelihood estimations of the underlying parameters are obtained. A simulation study and an application on real dataset are provided.     

An On-Line Estimation Algorithm for Periodic Autoregressive Models

This paper develops an on-line estimation algorithm for periodic autoregressive models (PAR). Indeed, we provide an adaptation of the well known recursive least squares algorithm (RLS), which has been successfully applied to classical autoregressive models (AR), to deal with PAR models. The obtained estimators are shown to be asymptotically efficient under mild conditions. Moreover, the performance of the periodic least squares algorithm (PRLS) is assessed via an intensive simulation study.     

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.     

Predictive Density Order Selection of Periodic AR Models

This article considers the order selection problem of periodic autoregressive models. Our main goal is the adaptation of the Bayesian Predictive Density Criterion (PDC), established by Djuric' and Kay (1992 Djuric' , P. M. , Kay , S. M. ( 1992 ). Order selection of autoregressive models . IEEE Transactions on Signal Processing 40 : 2829 – 2833 . [Google Scholar]) for selecting the order of a stationary autoreg-ressive model, to deal with the order identification problem of a periodic autoregressive model. The performance of the established criterion, (P-PDC), is compared, via simulation studies, to the performances of some well-known existing criteria.     

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.     

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.     

Endogeneity: How Failure to Correct for it can Cause Wrong Inferences and Some Remedies

Although researchers in business and management are becoming increasingly aware of the importance of endogeneity affecting regression analysis, they frequently do not have the right methodological toolkit to adjust for this issue. In this paper we discuss such a toolkit. There are also areas in business and management research which to date seem to be mostly oblivious about the endogeneity issue. We highlight such an area, which studies the question of whether firms that are cross‐listed on a foreign stock exchange are charged premium fees by their auditors. When the same methodology (pooled ordinary least squares) as in the existing literature is used, the existence of an audit fee premium for cross‐listed firms seems to be confirmed. However, once methodologies are used which adjust for the various types of endogeneity (i.e. omitted variable bias, simultaneous and dynamic endogeneity) there is no longer support for the existence of such a generalized premium. Hence, not only do we illustrate that failure to adjust for endogeneity has severe consequences such as drawing the wrong inferences, but we also review various ways to control for the different types of endogeneity.