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We consider a parameter-driven regression model for binary time series, where serial dependence is introduced by an autocorrelated latent process incorporated into the logit link function. Unlike in the case of parameter-driven Poisson log-linear or negative binomial logit regression model studied in the literature for time series of counts, generalized linear model (GLM) estimation of the regression coefficient vector, which suppresses the latent process and maximizes the corresponding pseudo-likelihood, cannot produce a consistent estimator. As a remedial measure, in this article, we propose a modified GLM estimation procedure and show that the resulting estimator is consistent and asymptotically normal. Moreover, we develop two procedures for estimating the asymptotic covariance matrix of the estimator and establish their consistency property. Simulation studies are conducted to evaluate the finite-sample performance of the proposed procedures. An empirical example is also presented. [ABSTRACT FROM AUTHOR]

We study inference and diagnostics for count time series regression models that include a feedback mechanism. In particular, we are interested in negative binomial processes for count time series. We study probabilistic properties and quasi-likelihood estimation for this class of processes. We show that the resulting estimators are consistent and asymptotically normally distributed. These facts enable us to construct probability integral transformation plots for assessing any assumed distributional assumptions. The key observation in developing the theory is a mean parameterized form of the negative binomial distribution. For transactions data, it is seen that the negative binomial distribution offers a better fit than the Poisson distribution. This is an immediate consequence of the fact that transactions can be represented as a collection of individual activities that correspond to different trading strategies. [ABSTRACT FROM AUTHOR]

This article discusses the modelling of integer-valued time series with overdispersion and potential extreme observations. For the problem, a negative binomial INGARCH model, a generalization of the Poisson INGARCH model, is proposed and stationarity conditions are given as well as the autocorrelation function. For estimation, we present three approaches with the focus on the maximum likelihood approach. Some results from numerical studies are presented and indicate that the proposed methodology performs better than the Poisson and double Poisson model-based methods. [ABSTRACT FROM AUTHOR]

Testing for first-order autocorrelation in small samples using the standard asymptotic test can be seriously misleading. Recent methods in likelihood asymptotics are used to derive more accurate p-value approximations for testing the autocorrelation parameter in a regression model. The methods are based on conditional evaluations and are thus specific to the particular data obtained. A numerical example and three simulations are provided to show that this new likelihood method provides higher order improvements and is superior in terms of central coverage even for autocorrelation parameter values close to unity. [ABSTRACT FROM AUTHOR]

The topic of serial correlation in regression models has attracted a great deal of research in the last 50 years. Most of these studies have assumed that the structure of the error covariance matrix Ω was known or could be consistently estimated from the data. In this article, we describe a new procedure for generating forecasts for regression models with serial correlation based on ordinary least squares and on an approximate representation of the form of the autocorrelation. We prove that the predictors from this specification are asymtotically efficient under some regularity conditions. In addition, we show that there is not much to be gained in trying to identify the correct form of the serial correlation since efficient forecasts can be generated using autoregressive approximations of the autocorrelation. A large simulation study is also used to compare the finite sample predictive efficiencies of this new estimator vis-à-vis estimators based on ordinary least squares and generalized least squares. [ABSTRACT FROM AUTHOR]

In linear regression models with autocorrelated errors, we apply the residual likelihood approach to obtain a residual information criterion (RIC), which can jointly select regression variables and autoregressive orders. We show that RIC is a consistent criterion. In addition, our simulation studies indicate that it outperforms heuristic selection criteria– the Akaike information criterion and the Bayesian information criterion– when the signal-to-noise ratio is not weak. [ABSTRACT FROM AUTHOR]

This paper studies correlation and partial autocorrelation properties of periodic autoregressive moving-average (PARMA) time series models. An efficient algorithm to compute PARMA autocovariances is first derived. An innovations based algorithm to compute partial autocorrelations for a general periodic series is then developed. Finally, periodic moving averages and autoregressions are characterized as periodically stationary series whose autocovariances and partial autocorrelations, respectively, are zero at all lags that exceed some periodically varying threshold. [ABSTRACT FROM AUTHOR]

In models of the form Y[sub t] = r(X[sub t] ) + Z[sub t] , where r is an unknown function and {X[sub t] } is a covariate process independent of the stationary error {Z[sub t] }, we give conditions under which estimators based on residuals Z[sub 1] , ..., Z[sub n] obtained from linear smoothers are asymptotically equivalent to those based on the actual errors Z[sub 1] , ..., Z[sub n] . [ABSTRACT FROM AUTHOR]