Tests for time series of counts based on the probability-generating function

We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability-generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.     

Analyzing multiple vector autoregressions through matrix-variate normal distribution with two covariance matrices

Abstract

This article proposes a new approach to analyze multiple vector autoregressive (VAR) models that render us a newly constructed matrix autoregressive (MtAR) model based on a matrix-variate normal distribution with two covariance matrices. The MtAR is a generalization of VAR models where the two covariance matrices allow the extension of MtAR to a structural MtAR analysis. The proposed MtAR can also incorporate different lag orders across VAR systems that provide more flexibility to the model. The estimation results from a simulation study and an empirical study on macroeconomic application show favorable performance of our proposed models and method.     

LS estimation of periodic autoregressive models with non-Gaussian errors: a simulation study

In this article, the least squares (LS) estimates of the parameters of periodic autoregressive (PAR) models are investigated for various distributions of error terms via Monte-Carlo simulation. Beside the Gaussian distribution, this study covers the exponential, gamma, student-t, and Cauchy distributions. The estimates are compared for various distributions via bias and MSE criterion. The effect of other factors are also examined as the non-constancy of model orders, the non-constancy of the variances of seasonal white noise, the period length, and the length of the time series. The simulation results indicate that this method is in general robust for the estimation of AR parameters with respect to the distribution of error terms and other factors. However, the estimates of those parameters were, in some cases, noticeably poor for Cauchy distribution. It is also noticed that the variances of estimates of white noise variances are highly affected by the degree of skewness of the distribution of error terms.     

Tests for Structural Changes in Time Series of Counts

We propose methods for detecting structural changes in time series with discrete‐valued observations. The detector statistics come in familiar L2‐type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.     

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.     

On the Specification of Propensity Scores,With Applications to the Analysis of Trade Policies

A vector autoregression is fit to recent U.S. data on wheat prices, wheat export sales, wheat export shipments, and exchange rates. Forecast error decompositions and out-of-sample forecasts indicate that exchange rates have little influence on wheat sales and shipments.     

Extreme Quantile Estimation for Autoregressive Models

ABSTRACT

A quantile autoregresive model is a useful extension of classical autoregresive models as it can capture the influences of conditioning variables on the location, scale, and shape of the response distribution. However, at the extreme tails, standard quantile autoregression estimator is often unstable due to data sparsity. In this article, assuming quantile autoregresive models, we develop a new estimator for extreme conditional quantiles of time series data based on extreme value theory. We build the connection between the second-order conditions for the autoregression coefficients and for the conditional quantile functions, and establish the asymptotic properties of the proposed estimator. The finite sample performance of the proposed method is illustrated through a simulation study and the analysis of U.S. retail gasoline price.     

Random-effect models with singular precision

We show that smoothing spline, intrinsic autoregression (IAR) and state-space model can be formulated as partially specified random-effect model with singular precision (SP). Various fitting methods have been suggested for the aforementioned models and this paper investigates the relationships among them, once the models have been placed under a single framework. Some methods have been previously shown to give the best linear unbiased predictors (BLUPs) under some random-effect models and here we show that they are in fact uniformly BLUPs (UBLUPs) under a class of models that are generated by the SP of random effects. We offer some new interpretations of the UBLUPs under models of SP and define BLUE and BLUP in these partially specified models without having to specify the covariance. We also show how the full likelihood inferences for random-effect models can be made for these models, so that the maximum likelihood (ML) and restricted maximum likelihood (REML) estimators can be used for the smoothing parameters in splines, etc.     

Forecasting mortality rates via density ratio modeling

The authors propose a semiparametric approach to modeling and forecasting age‐specific mortality in the United States. Their method is based on an extension of a class of semiparametric models to time series. It combines information from several time series and estimates the predictive distribution conditional on past data. The conditional expectation, which is the most commonly used predictor in practice, is the first moment of this distribution. The authors compare their method to that of Lee and Carter.