In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

(1991). Applied Linear Regression Models. Journal of Quality Technology: Vol. 23, No. 1, pp. 76-77.

Applied Linear Regression Models

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

Functional analysis methodology focuses on the identification of variables that influence the occurrence of problem behavior and has become a hallmark of contemporary approaches to behavioral assessment. In light of the widespread use of pretreatment functional analyses in articles published in this and other journals, we reviewed the literature in an attempt to identify best practices and directions for future research. Studies included in the present review were those in which (a) a pretreatment assessment based on (b) direct observation and measurement of (c) problem behavior was conducted under (d) at least two conditions involving manipulation of an environmental variable in an attempt (e) to demonstrate a relation between the environmental event and behavior. Studies that met the criteria for inclusion were quantified and critically evaluated along a number of dimensions related to subject and setting characteristics, parametric and qualitative characteristics of the methodology, types of assessment conditions, experimental designs, topographies of problem behaviors, and the manner in which data were displayed and analyzed.

Functional analysis of problem behavior: a review

Combining nonoverlap and trend for single-case research: Tau-U.

The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies

It has been recognized that the two-phase version of the interrupted time-series design can be frequently modeled using a four-parameter design matrix. There are differences across writers, however, in the details of the recommended design matrices to be used in the estimation of the four parameters of the model. Various writers imply that different methods of specifying the four-parameter design matrix all lead to the same conclusions; they do not. The tests and estimates for level change are dramatically different under the various seemingly equivalent design specifications. Examples of egregious errors of interpretation are presented and recommendations regarding the correct specification of the design matrix are made. The recommendations hold whether the model is estimated using ordinary least squares (for the case of approximately independent errors) or some more complex time-series approach (for the case of autocorrelated errors).

Design Specification Issues in Time-Series Intervention Models

Autocorrelation in applied behavior analysis: A myth.

A new method for the analysis of linear models that have autoregressive errors is proposed. The approach is not only relevant in the behavioral sciences for analyzing small-sample time-series intervention models, but it is also appropriate for a wide class of small-sample linear model problems in which there is interest in inferential statements regarding all regression parameters and autoregressive parameters in the model. The methodology includes a double application of bootstrap procedures. The 1st application is used to obtain bias-adjusted estimates of the autoregressive parameters. The 2nd application is used to estimate the standard errors of the parameter estimates. Theoretical and Monte Carlo results are presented to demonstrate asymptotic and small-sample properties of the method; examples that illustrate advantages of the new approach over established time-series methods are described.

A double bootstrap method to analyze linear models with autoregressive error terms.

The small sample properties of 6 autocorrelation estimators were investigated in an extensive Monte Carlo study. It was demonstrated that conventional estimators yield problems of estimation and inference in the form of(a) inconsistencies between theoretical and empirical expectations, (b) inconsistencies between theoretical and empirical error variances, and (c) dramatic differences between nominal and empirical Type I errors

Bradley E. Huitema

Papers

The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies

Design Specification Issues in Time-Series Intervention Models

Autocorrelation in applied behavior analysis: A myth.

A double bootstrap method to analyze linear models with autoregressive error terms.

Autocorrelation estimation and inference with small samples.