Level shifts,temporary changes and forecasting

The purpose of this paper is to analyze the effect of not treating Level Shift and Temporary Change outliers on the point forecasts and prediction intervals from ARIMA models. One of the principal conclusions is that the outliers of the type discussed here considerably increase the inaccuracy of point forecasts, although the latter depends not only on the time of occurrence of the outliers from the forecast origin but also on the type of ARIMA processes under consideration. However, regardless of the time of occurrence and of the type of ARIMA processes considered, Level Shifts and Temporary Changes significantly affect the width of the prediction intervals.     

The impact of measurement errors on ARMA prediction

Measurement errors can have dramatic impact on the outcome of empirical analysis. In this article we quantify the effects that they can have on predictions generated from ARMA processes. Lower and upper bounds are derived for differences in minimum mean squared prediction errors (MMSE) for forecasts generated from data with and without errors. The impact that measurement errors have on MMSE and other relative measures of forecast accuracy are presented for a variety of model structures and parameterizations. Based on these results the need to set up the models in state space form to extract the signal component appears to depend upon whether processes are nearly non‐invertible or non‐stationary or whether the noise‐to‐signal ratio is very high. Copyright © 1999 John Wiley & Sons, Ltd.     

Finite sample forecast results for vector autoregressive moving average models

Using the 'standard' approach to forecasting in the vector autoregressive moving average model, we establish basic general results on exact finite sample forecasts and their mean squared error matrices. Comparison between the exact and conditional methods of initiating the finite sample forecast calculations is presented, and a few illustrative cases are given.     

Disaggregation methods to expedite product line forecasting

This paper addresses the issue of forecasting individual items within a product line; where each line includes several independent but closely related products. The purpose of the research was to reduce the overall forecasting burden by developing and assessing schemes of disaggregating forecasts of a total product line to the related individual items. Measures were developed to determine appropriate disaggregated methodologies and to compare the forecast accuracy of individual product forecasts versus disaggregated totals. Several of the procedures used were based upon extensions of the combination of forecast research and applied to disaggregations of total forecasts of product lines. The objective was to identify situations when it was advantageous to produce disaggregated forecasts, and if advantageous, which method of disaggregation to utilize. This involved identification of the general conceptual characteristics within a set of product line data that might cause a disaggregation method to produce relatively accurate forecasts. These conceptual characteristics provided guidelines for forecasters on how to select a disaggregation method and under what conditions a particular method is applicable.     

Forecasting with preliminary data

This paper examines several methods to forecast revised US trade balance figures by incorporating preliminary data. Two benchmark forecasts are considered: one ignoring the preliminary data and the other applying a combination approach; with the second outperforming the first. Competing models include a bivariate AR error-correction model and a bivariate AR error-correction model with GARCH effects. The forecasts from the latter model outperforms the combination benchmark for the one-step forecast case only. A restricted AR error-correction model with GARCH effects is discovered to provide the best forecasts. © 1997 John Wiley & Sons, Ltd.     

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.     

Forecasts of power-transformed series

Consider a time series transformed by an instantaneous power function of the Box-Cox type. For a wide range of fractional powers, this paper gives the relative bias in original metric forecasts due to use of the simple inverse retransformation when minimum mean squared error (conditional mean) forecasts are optimal. This bias varies widely according to the characteristics of the data. A fast algorithm is given to find this bias, or to find minimum mean squared error forecasts in the original metric. The results depend on the assumption that the forecast errors in the transformed metric are Gaussian. An example using real data is given.