Municipal budget forecasting with multivariate ARMA models

In this paper multivariate ARMA models are applied to the problem of forecasting city budget variables. Unlike univariate time-series methods, multivariate models can use relationships among budget variables as well as relationships with economic and demographic indicators. Although available budget series are shorter than what is usually believed necessary for multivariate ARMA modelling, the forecasts seem to be of higher quality than those from univariate models.     

Temporal aggregation and systematic sampling in structural time-series models

Given a structural time-series model specified at a basic time interval, this paper deals with the problems of forecasting efficiency and estimation accuracy generated when the data are collected at a timing interval which is a multiple of the time unit chosen to build the basic model. Results are presented for the simplest structural models, the trend plus error models, under the assumption that the parameters of the model are known. It is shown that the gains in forecasting efficiency and estimation accuracy for having data at finer intervals are considerable for both stock and flow variables with only one exception. No gain in forecasting efficiency is achieved in the case of a stock series that follows a random walk.     

The approximation of long‐memory processes by an ARMA model

A mean square error criterion is proposed in this paper to provide a systematic approach to approximate a long‐memory time series by a short‐memory ARMA(1, 1) process. Analytic expressions are derived to assess the effect of such an approximation. These results are established not only for the pure fractional noise case, but also for a general autoregressive fractional moving average long‐memory time series. Performances of the ARMA(1,1) approximation as compared to using an ARFIMA model are illustrated by both computations and an application to the Nile river series. Results derived in this paper shed light on the forecasting issue of a long‐memory process. Copyright © 2001 John Wiley & Sons, Ltd.     

A Comparison of Box—Jenkins and objective methods for determining the order of a non-seasonal ARMA Model

This paper evaluates different procedures for selecting the order of a non-seasonal ARMA model. Specifically, it compares the forecasting accuracy of models developed by the personalized Box-Jenkins (BJ) methodology with models chosen by numerous automatic procedures. The study uses real series modelled by experts (textbook authors) in the BJ approach. Our results show that many objective selection criteria provide structures equal or superior to the time-consuming BJ method. For the sets of data used in this study, we also examine the influence of parsimony in time-series forecasting. Defining what models are too large or too small is sensitive to the forecast horizon. Automatic techniques that select the best models for forecasting are similar in size to BJ models although they often disagree on model order.     

Forecasting future canadian residential heating demand: An illustration of forecasting with aggregated and disaggregated data

This paper examines the sensitivity of forecasts to the level of aggregation of the data. A relative shares regression model and a multinominal logit model are tested with both aggregate and disaggregate survey data from 2109 respondents. The results indicate the appropriate model to use depends on whether the data are disaggregate or aggregate in form. Forecasts of solar heating of dwelling unit demand and market shares are also reported for Canada in terms of the solar price relative to the natural gas price and solar reliability relative to natural gas reliability.     

Simultaneous transfer functions versus vector arma models

This work compares two classes of multiple time series models which have been developed in past decades and are usually believed to be equivalent: the vector ARMA model and the system of simultaneous transfer functions (STF). The first part analyzes the mathematical structure of the two schemes; their properties of stability, structural identification and realization. In the second, algorithms of order identification and parameter estimation are derived, following the approach of stochastic approximation. The proposed solutions are easily implementable on standard statistical software and in an extended empirical example their performance is checked. The superiority of the STF model will be well established.