On identification of transfer function models by biased regression methods

This paper investigates a biased regression approach to the preliminary estimation of the Box-Jenkins transfer function weights. Using statistical simulation to generate time series, 14 estimators (various OLS, ridge and principal components estimators) are compared in terms of MSE and standard error of the weight estimators. The estimators are investigated for different levels of multicollinearity, signal-to-noise ratio, number of independent variables, length of time series and number of lags included in the estimation. The results show that the ridge estimators nearly always give lower MSE than the OLS estimator, and in the computationally difficult cases give much lower MSE than the OLS estimator. The principal components estimators can give lower MSE than the OLS, but also higher values. All biased estimators nearly always give much lower estimated standard error than OLS when estimating the weights.     

Laplace’s approximation for relative risk frailty models

Relative risk frailty models are used extensively in analyzing clustered and/or recurrent time-to-event data. In this paper, Laplace’s approximation for integrals is applied to marginal distributions of data arising from parametric relative risk frailty models. Under regularity conditions, the approximate maximum likelihood estimators (MLE) are consistent with a rate of convergence that depends on both the number of subjects and number of members per subject. We compare the approximate MLE against alternative estimators using limited simulation and demonstrate the utility of Laplace’s approximation approach by analyzing U.S. patient waiting time to deceased kidney transplant data.     

On causality test for time series of counts based on poisson ingarch models with application to crime and temperature data

In this study, we consider the causality test for the integer-valued time series. Using the mean equation of Poisson INGARCH models, we construct a regression that includes exogenous variables. The test is then constructed based on the least squares estimator and is shown to follow a chi-square distribution under the null of no causal relationships. A simulation study and real data analysis using the crime and temperature data in Chicago are provided for illustration.     

Testing for presence of a latent process in count series

This paper is concerned with the use of tests for overdispersion in order to detect the presence of a latent process in the framework of regression models for count series. In a Monte Carlo study, the impact of different types of regressors, the sample size and the properties of the latent process on the performance of tests for overdispersion is investigated.     

Grouped poisson regression models: theory and an application to public house visit frequency

In this paper we extend the Poisson regression model to deal with the situation in which the event count is observed le in “grouped” form, By this we mean that for some observations, all that is known about the count is that it falls within a certain range of integers, and the actual value is unknown, A typical likelihood contribution for this extended model is the sum of a set of consecutive Poisson probabilities, The log-likelihood function is derived for a general grouping rule, using a logarithmic link for the Poisson mean, This log-likelihood function is shown to be globally concave. The model is applied to grouped count data on the frequency of trips to pubs made over a one-week period by a sample of Norfolk young persons.     

Nonstationary regression models with a lagged dependent variable

This paper studies regression models with a lagged dependent variable when both the dependent and independent variables are nonstationary, and the regression model is misspecified in some dimension. In particular, we discuss the limiting properties of leastsquares estimates of the parameters in such regression models, and the limiting distributions of their test statistics. We show that the estimate of the lagged dependent variable tends to unity asymptotically independent of its true value, while the estimates of the independent variables tend to zero. The limiting distributions of their test statistics are shown to diverge with sample size.     

Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-Based Approach

A procedure is developed for seasonally adjusting weekly time series, based on a composite of regression and time series models. The procedure is applied to some weekly U.S. money supply series currently seasonally adjusted by the Federal Reserve.     

Unobserved components models with correlated disturbances

The paper deals with the decomposition of a time series process admitting an ARIMA representation into permanent and transitory components, with the intent of investigating whether the introduction of correlated disturbances provides meaningful extensions of the admissible parameter range. The main points are illustrated with reference to ARIMA(2,1,0) and IMA(2,2) models. It is argued that there is very little reason for such extensions, and that the restrictions implied by the assumption of uncorrelated components are sound.This research was supported by the MURST Cofin2000. The paper was presented at the XL Scientific Meeting of the Italian Statistical Society (Florence 2000), ISF 2000 (Lisbon), and at the Europaeisches Heimbildungswerk workshop, Helenau-Bernau (Berlin). I thank participants for their comments and in particular Jörg Breitung for very stimulating discussion. I also wish to thank the associate editor and the referee for their comments.     

On variable selection in generalized linear and related regression models

This paper is concerned with selection of explanatory variables in generalized linear models (GLM). The class of GLM's is quite large and contains e.g. the ordinary linear regression, the binary logistic regression, the probit model and Poisson regression with linear or log-linear parameter structure. We show that, through an approximation of the log likelihood and a certain data transformation, the variable selection problem in a GLM can be converted into variable selection in an ordinary (unweighted) linear regression model. As a consequence no specific computer software for variable selection in GLM's is needed. Instead, some suitable variable selection program for linear regression can be used. We also present a simulation study which shows that the log likelihood approximation is very good in many practical situations. Finally, we mention briefly possible extensions to regression models outside the class of GLM's.     

Spatial variation in teenage conceptions in south and west England

Multilevel Poisson models are used to identify factors influencing variation in census ward level teenage conception rates. Multilevel logistic models are also employed to examine the outcome of these conceptions. Demographic and socioeconomic characteristics are accounted for as well as access to family planning services. The paper emphasizes the importance of customized deprivation indices that are specific to the health outcome in urban and rural areas.     

Improving the bandwidth-free inference methods by prewhitening

In this paper we consider inference of parameters in time series regression models. In the traditional inference approach, the heteroskedasticity and autocorrelation consistent (HAC) estimation is often involved to consistently estimate the asymptotic covariance matrix of regression parameter estimator. Since the bandwidth parameter in the HAC estimation is difficult to choose in practice, there has been a recent surge of interest in developing bandwidth-free inference methods. However, existing simulation studies show that these new methods suffer from severe size distortion in the presence of strong temporal dependence for a medium sample size. To remedy the problem, we propose to apply the prewhitening to the inconsistent long-run variance estimator in these methods to reduce the size distortion. The asymptotic distribution of the prewhitened Wald statistic is obtained and the general effectiveness of prewhitening is shown through simulations.     

ON A TEST OF FIT IN TIME SERIES MODELS

It is shown that a test for adequacy of a fitted Arma (p, 4) model based on forecast errors, has the same asymptotic expected value whether the null hypothesis is true or false. A sampling study supports the conclusion in small to moderately large samples and indicates that for sample sizes commonly used by practitioners, the power of the test is very low.