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We study estimation on parameter-driven models for time series of counts. This class of models follows the structure of a generalized linear model in which the serial dependency is included in the model by the link function through a time-dependent latent process. The likelihood function for this class of models commonly cannot be calculated explicitly and computationally intensive methods like importance sampling and Markov chain Monte Carlo are used to estimate the model parameters. Here, we propose a simple and fast estimation procedure in a wide class of models that accommodate both discrete and continuous data. The maximum likelihood methodology is used to obtain the parameter estimates for the models under study. The simplicity of the procedure allows for build bootstrap confidence intervals for the hyperparameters and latent states of parameter-driven models. We perform extensive simulation studies to verify the asymptotic behavior of the parameter estimates, as well as present application of the proposed procedure through set of real data. [ABSTRACT FROM AUTHOR]

Multilevel autoregressive models are popular choices for the analysis of intensive longitudinal data in psychology. Empirical studies have found a positive correlation between autoregressive parameters of affective time series and the between-person measures of psychopathology, a phenomenon known as the staging effect. However, it has been argued that such findings may represent a statistical artifact: Although common models assume normal error distributions, empirical data (for instance, measurements of negative affect among healthy individuals) often exhibit the floor effect, that is response distributions with high skewness, low mean, and low variability. In this paper, we investigated whether—and to what extent—the floor effect leads to erroneous conclusions by means of a simulation study. We describe three dynamic models which have meaningful substantive interpretations and can produce floor-effect data. We simulate multilevel data from these models, varying skewness independent of individuals' autoregressive parameters, while also varying the number of time points and cases. Analyzing these data with the standard multilevel AR(1) model we found that positive bias only occurs when modeling with random residual variance, whereas modeling with fixed residual variance leads to negative bias. We discuss the implications of our study for data collection and modeling choices [ABSTRACT FROM AUTHOR]

We revisit the generalized method of moments (GMM) estimation of the non-Gaussian structural vector autoregressive (SVAR) model. It is shown that in the n-dimensional SVAR model, global and local identification of the contemporaneous impact matrix is achieved with as few as n 2 + n (n − 1) / 2 suitably selected moment conditions, when at least n – 1 of the structural errors are all leptokurtic (or platykurtic). We also relax the potentially problematic assumption of mutually independent structural errors in part of the previous literature to the requirement that the errors be mutually uncorrelated. Moreover, we assume the error term to be only serially uncorrelated, not independent in time, which allows for univariate conditional heteroscedasticity in its components. A small simulation experiment highlights the good properties of the estimator and the proposed moment selection procedure. The use of the methods is illustrated by means of an empirical application to the effect of a tax increase on U.S. gasoline consumption and carbon dioxide emissions. [ABSTRACT FROM AUTHOR]

Mixture transition distribution (MTD) time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary MTD models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a prespecified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

We consider estimation of the structural vector autoregression (SVAR) by the generalized method of moments (GMM). Given non-Gaussian errors and a suitable set of moment conditions, the GMM estimator is shown to achieve local identification of the structural shocks. The optimal set of moment conditions can be found by well-known moment selection criteria. Compared to recent alternatives, our approach has the advantage that the structural shocks need not be mutually independent, but only orthogonal, provided they satisfy a number of co-kurtosis conditions that prevail under independence. According to simulation results, the finite-sample performance of our estimation method is comparable, or even superior to that of the recently proposed pseudo maximum likelihood estimators. The two-step estimator is found to outperform the alternative GMM estimators. An empirical application to a small macroeconomic model estimated on postwar United States data illustrates the use of the methods. [ABSTRACT FROM AUTHOR]

This article investigates maximum a-posteriori (MAP) estimation of autoregressive model parameters when the innovations (errors) follow a finite mixture of distributions that, in turn, are scale-mixtures of skew-normal distributions (SMSN), an attractive and extremely flexible family of probabilistic distributions. The proposed model allows to fit different types of data which can be associated with different noise levels, and provides a robust modelling with great flexibility to accommodate skewness, heavy tails, multimodality and stationarity simultaneously. Also, the existence of convenient hierarchical representations of the SMSN random variables allows us to develop an EM-type algorithm to perform the MAP estimates. A comprehensive simulation study is then conducted to illustrate the superior performance of the proposed method. The new methodology is also applied to annual barley yields data. [ABSTRACT FROM AUTHOR]

We develop methods for performing smoothing computations in general state-space models. The methods rely on a particle representation of the filtering distributions, and their evolution through time using sequential importance sampling and resampling ideas. In particular, novel techniques are presented for generation of sample realizations of historical state sequences. This is carried out in a forward-filtering backward-smoothing procedure that can be viewed as the nonlinear, non-Gaussian counterpart of standard Kalman filter-based simulation smoothers in the linear Gaussian case. Convergence in the mean squared error sense of the smoothed trajectories is proved, showing the validity of our proposed method. The methods are tested in a substantial application for the processing of speech signals represented by a time-varying autoregression and parameterized in terms of time-varying partial correlation coefficients, comparing the results of our algorithm with those from a simple smoother based on the filtered trajectories. [ABSTRACT FROM AUTHOR]

Environmental epidemiologists often encounter time series data in the form of discrete or other nonnormal outcomes, for example, in modeling the relationship between air pollution and hospital admissions or mortality rates. We present a case study examining the association between pollen counts and meteorologic covariates. Although such time series data are inadequately described by standard methods for Gaussian time series, they are often autocorrelated, and warrant an analysis beyond those provided by ordinary generalized linear models (GLMs). Transitional regression models (TRMs), signifying nonlinear regression models expressed in terms of conditional means and variances given past observations, provide a unifying framework for two mainstream approaches to extending the GLM for autocorrelated data. The first approach models current outcomes with a GLM that incorporates past outcomes as covariates, whereas the second models individual outcomes with marginal GLMs and then couples the error terms with an autoregressive covariance matrix. Although the two approaches coincide for the Gaussian GLM, which serves as a helpful introductory example, in general they yield fundamentally different models. We analyze the pollen study using TRM's of both types and present parameter estimates together with asymptotic and bootstrap standard errors. In several cases we find evidence of residual autocorrelation; however, when we relax the TRM to allow for a nonparametric smooth trend, the autocorrelation disappears. This kind of trade-off between autocorrelation and flexibility is to be expected, and has a natural interpretation in terms of the covariance function for a nonparametric smoother. We provide an algorithm for fitting these flexible TRM's that is relatively easy to program with the generalized additive model software in S-PLUS. [ABSTRACT FROM AUTHOR]

The nonparametric bootstrap is applied to the problem of prediction in autoregression. Let {Yt t = 0, ±1, ±2, ...} be a stationary autoregressive process of known order p [AR(p)]. Given a realization of the series up to time t, (y1, y2, ..., Yt), a 100β% prediction interval for Yt+k is desired Standard forecasting techniques, which assume that the error sequence of the process {Yt} is Gaussian, rely on the fact that the conditional distribution of Yt+k, given the data, is Gaussian as well. As a nonparametric alternative, the bootstrap provides an estimate of the conditional distribution of Yt+k. The method is similar to other applications of the bootstrap for linear models, because the residuals are resampled. The proposed methodology represents a different approach, since an alternative representation for AR(p) series is used, allowing for bootstrap replicates generated backward in time. It follows that the resulting replicates all have the same conditionally fixed values at the end of every series. A simulation that compares the proposed technique with the standard technique for low-order Gaussian and non-Gaussian autoregressive models demonstrates the potential of the bootstrap technique. [ABSTRACT FROM AUTHOR]