Paul Newbold’s research while affiliated with Bureau of Materials & Physical Research and other places

In the last few years there has been considerable interest in the accounting literature in time series methods. This paper briefly surveys those areas of accounting in which time series analysis has proved useful and discusses the analytical procedures that have been employed.

The variance ratio test is often used as a check of the hypothesis that a time series is generated by a random walk. A natural extension of the test is developed to cover the case where the assumed model is ARIMA(p, 1, q), with unknown parameters. Small sample properties of the generalized test are investigated, and the test is applied to a frequently analysed data set on US quarterly real gross national product. In effect, we are testing for low frequency misspecification in assumed autoregressive moving-average (ARMA) models for a differenced series.

Beveridge and Nelson (A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the business cycle. J. Monet. Econ. 7 (1981), 151–74) introduced a decomposition into trend plus irregular components for time series generated by models that are integrated of order one. The components are functions of current and past, but not future, values of the series. Therefore, these components can be viewed as estimates available to an agent at the time. Moreover, the decomposition exists whenever the generating process is stationary after first differencing. In this paper we extend the decomposition to generating processes that are integrated of order two, and to the seasonal models of Box and Jenkins (Time Series Analysis, Forecasting and Control. San Francisco:Holden Day, 1970). The analysis leads to the estimation of stochastic growth rates, as well as component series. The methodology is applied to monthly UK industrial production data.

This paper develops Lagrange multiplier tests of ARMA(p, q) models against fractional ARIMA(p, d, q) alternatives. The performance of the tests is investigated for moderate-sized samples. It is concluded that fractional difference will be difficult to detect when the orders (p, q) are over-specified in an autoregressive moving-average (ARMA) analysis. The importance of distinguishing between the mean known and mean estimated cases in fractional difference models is illustrated in the context of these tests.

An estimator of the difference parameter in a class of long-memory time series models is examined. It is shown that, in particular circumstances, the estimator can be badly biased, and tests based on it consequently seriously misleading. The source of this bias is identified, and it is shown that its magnitude can readily be predicted through straightforward analytical arguments.

In attempting to develop a procedure for fitting linear multiple autoregressive-moving average models to observed data, perhaps the most difficult problem is to achieve a reasonable initial model selection. A recent paper by Jenkins and Alavi suggests, as one possibility, the examination of so-called q-conditioned partial correlations. We show that the sampling properties of these statistics are such as to render them of dubious value for this purpose.

The empirical performance of tests of the Dickey–Fuller type for unit autoregressive roots in the generating model of a time series is studied. In particular, the case where the true generating model structure is unknown and may involve a substantial moving-average component is examined.

We apply the idea of using reversed time series to improve the power of Johansen tests. We suggest computationally simple variants of the trace and maximum eigenvalue statistics and establish their limit distributions. Both are shown, via simulation, to yield nontrivial power gains.

Forecast combination is often found to improve forecast accuracy. This chapter considers dierent types of forecast combination and tests of forecast encompassing. The latter indicate when a combination is more accurate than an individual forecast ex post, in a range of cir- cumstances: when the forecasts themselves are the objects of interest; when the forecasts are derived from models with unknown parameters; and when the forecast models are nested. We then consider forecast encompassing tests which are framed in terms of the model's estimated parameters and recognise that parameter estimation uncertainty aects forecast accuracy, as well as conditonal tests of encompassing. We also look at the conditions under which forecast encompassing can be established irrespective of the form of the loss function.

Time series analysts have long been concerned with distinguishing stationary “generating processes” from processes for which differencing is required to induce stationarity. In practical applications, this issue is addressed almost invariably through formal hypothesis testing. In this paper, we explore some aspects of the Bayesian approach to the problem, leading to the calculation of posterior odds ratios. Interesting features arise in the simplest possible variant of the problem, where a choice has to be made between a random walk and a stationary first order autoregressive model. We discuss in detail the analysis of this case, and also indicate how our approach extends to the more general comparison of an ARIMA model with a stationary competitor. Les chercheurs intéresseés par l'analyse des données chronologiques sont préoccupés de discemer les procesus générant des séies stationnaries des processus générant des séries stationnaies dans la différence. Typiquement, cette question est adressée au moyen d'un test d'hypothése. Les auteurs appliquent ici la méthode bayesienne pour faire un choix. Meme dans le cas simple où le choix est entre un modèle de chocs aleatoires et un modèle stationnaire autoregreif de premier ordre, l'approche présente des propriétés notables. l'application de la méthode proposée pour comparer un modèle ARIMA à un modéle stationnaire alternatif.