Search

The detection of serial dependence in binary or binomial valued time series is difficult using standard time series methods, particularly when there are regression effects to be modelled. In this paper we derive score-type tests for detecting departures from independence in the directions of the GLARMA\ and BARMA\ type observation driven models. These score tests can easily be applied using a standard logistic regression and so may have appeal to practitioners who wish to initially assess the need to incorporate serial dependence effects. To deal with the nuisance parameters in some GLARMA models a supremum type test is implemented., Comment: 15 pages, 5 tables, submitted for publication

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating equations leads to asymptotically biased estimates of regression coefficients for binomial responses. An alternative is to use marginal likelihood, in which the variance of the latent process but not the serial dependence is accounted for. In practice this is equivalent to using generalized linear mixed model estimation procedures treating the observations as independent with a random effect on the intercept term in the regression model. We prove this method leads to consistent and asymptotically normal estimates even if there is an autocorrelated latent process. Simulations suggest that the use of marginal likelihood can lead to GLM estimates result. This problem reduces rapidly with increasing number of binomial trials at each time point but, for binary data, the chance of it can remain over 45% even in very long time series. We provide a combination of theoretical and heuristic explanations for this phenomenon in terms of the properties of the regression component of the model and these can be used to guide application of the method in practice., Comment: 23 pages, 2 tables, submitted for publication

Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence of a latent process and, subsequent to that, evidence of serial dependence in that latent process. The test for the existence of a latent process is important because, if one is present, standard logistic regression methods will produce inconsistent estimates of the regression parameters. However the score test is non-standard and any serial dependence in the latent process will require consideration of nuisance parameters which cannot be estimated under the null hypothesis of no latent process. The paper describes how a supremum-type test can be applied. If a latent process is detected, consistent estimation of its variance and the regression parameters can be done using marginal estimation which is easily implemented using generalised linear mixed model methods. The test for serial dependence in a latent process does not involve nuisance parameters and is based on the covariances between residuals centered at functions of the latent process conditional on the observations. This requires numerical integration in order to compute the test statistic. Relevant asymptotic results are derived and confirmed using simulation evidence. Application to binary and binomial time series is made. For binary series in particular, a complication is that the variance of the latent process, even if present, can be estimated to be zero with a high probability., Comment: 12 page, 3 table, submitted for publication

This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given covariates, random effects and process history, the observed responses at each time in each series are independent and have an exponential family distribution. We develop maximum likelihood estimation of the mixed effects model using an observation driven generalized linear autoregressive moving average specification for the serial dependence in each series. The paper presents an easily implementable approach which uses existing single time series methods to handle the serial dependence structure in combination with adaptive Gaussian quadrature to approximate the integrals over the regression random effects required for the likelihood and its derivatives. The models and methods presented allow extension of existing mixed model procedures for count data by incorporating serial dependence which can differ in form and strength across the individual series. The structure of the model has some similarities to longitudinal data transition models with random effects. However, in contrast to that setting, where there are many cases and few to moderate observations per case, the time series setting has many observations per series and a few to moderate number of cross sectional time series. The method is illustrated on time series of binary responses to musical features obtained from a panel of listeners., Comment: 17 pages, 2 figures, 2 tables