Control charts to check yearly predictions by monthly observations

In many cases an organization makes predictions of a variable on a yearly scale although the variable is actually observed at shorter time intervals. Given such a yearly prediction, the question will arise as to under which conditions one can say that the actual development of the variable at shorter time intervals deviates so much from the year estimate as to render the latter implausible. Policy makers confronted with such a problem tend to use rather primitive statistical methods of inference. In this paper the situation is judged from a statistical point of view and placed in the context of the ‘significance test’ approach to control chart theory. It is assumed that the variables are generated by a multivariate autoregressive moving average model. Thus we derive an approximate distribution of the future observations of the series given the values of some linear compounds of the variables. With this, three control charts can be constructed. The approach is illustrated by an example based on the monthly tax returns of the Dutch central government. The example suggests the usefulness of the approach in many practical situations of forecasting and planning.     

Judging the probability that the next point in an observed time-series will be below,or above,a given value

We presented people with trended and untrended time series and asked them to estimate the probability that the next point would be below each of seven different reference values. The true probabilities that the point would be below these values were 0.01, 0.10, 0.25, 0.50, 0.75, 0.90 and 0.99. People overestimated probabilities of less than 0.50 and underestimated those of more than 0.50. Consequently, their subjective probability distributions were flatter than they should have been: people appeared to be under confident in their estimates of where the next point would lie. This bias was greater for the trended series. It was also greater in a second experiment in which people estimated the probability that the next item would be above the reference values. We discuss reasons for these effects and consider their implications for decision making.     

Linear and Non-linear (Non-)Forecastability of High-frequency Exchange Rates

This paper forecasts Daily Sterling exchange rate returns using various naive, linear and non-linear univariate time-series models. The accuracy of the forecasts is evaluated using mean squared error and sign prediction criteria. These show only a very modest improvement over forecasts generated by a random walk model. The Pesaran–Timmerman test and a comparison with forecasts generated artificially shows that even the best models have no evidence of market timing ability.©1997 John Wiley & Sons, Ltd.     

Why do EMD‐based methods improve prediction? A multiscale complexity perspective

Empirical mode decomposition (EMD)‐based ensemble methods have become increasingly popular in the research field of forecasting, substantially enhancing prediction accuracy. The key factor in this type of method is the multiscale decomposition that immensely mitigates modeling complexity. Accordingly, this study probes this factor and makes further innovations from a new perspective of multiscale complexity. In particular, this study quantitatively investigates the relationship between the decomposition performance and prediction accuracy, thereby developing (1) a novel multiscale complexity measurement (for evaluating multiscale decomposition), (2) a novel optimized EMD (OEMD) (considering multiscale complexity), and (3) a novel OEMD‐based forecasting methodology (using the proposed OEMD in multiscale analysis). With crude oil and natural gas prices as samples, the empirical study statistically indicates that the forecasting capability of EMD‐based methods is highly reliant on the decomposition performance; accordingly, the proposed OEMD‐based methods considering multiscale complexity significantly outperform the benchmarks based on typical EMDs in prediction accuracy.     

Requirements for effective use of graphical methods in interactive forecasting

The construction of forecasts using interactive data analysis systems is greatly aided by the availability of graphical procedures. Data exploration, model identification and estimation, and interpretation of final forecasts are made considerably easier by the visual relay of information. This article discusses some recent developments in time series graphics designed to assist in the forecasting process. A discussion of requirerients for effective use of graphics in interactive forecasting is included as illustrated through an application of the Box-Jenkins methodology. Illustrations are included from the STATGRAPHICS system, a prototype implementation in APL.