An evaluation of bayesian forecasting

‘Bayesian forecasting’ is a time series method of forecasting which (in the United Kingdom) has become synonymous with the state space formulation of Harrison and Stevens (1976). The approach is distinct from other time series methods in that it envisages changes in model structure. A disjoint class of models is chosen to encompass the changes. Each data point is retrospectively evaluated (using Bayes theorem) to judge which of the models held. Forecasts are then derived conditional on an assumed model holding true. The final forecasts are weighted sums of these conditional forecasts. Few empirical evaluations have been carried out. This paper reports a large scale comparison of time series forecasting methods including the Bayesian. The approach is two fold: a simulation study to examine parameter sensitivity and an empirical study which contrasts Bayesian with other time series methods.     

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.