Résultats de recherche pour « Time series prediction »

This chapter suggests and experimentally investigates new methods of forecasting based on data compression algorithms. The main task is the application of these algorithms to the prediction of processes that generate values from a continuous interval. The chapter presents some theoretical descriptions of the application of data compression algorithms to this case and the practical results of prediction using these algorithms. A new modification, applicable to any forecasting algorithm, is also introduced. It is called the method of alphabet grouping. It allows the use of large alphabets without increasing complexity for forecasting algorithms. Using the examples of predicting currency exchange rates, the consumer price index, and the producer price index, the results show that the precision of these methods is relatively high.

Abstract. A test for non‐linearity of prediction in time series is suggested; the test makes use of the partial correlation between a series and its square, eliminating linear terms. The distribution of partial correlation estimates is considered both theoretically and by simulation. Extensions of the test to include partial correlations with other nonlinear functions of the observed data are suggested. The nature of optimum predictors for some particular non‐linear time series is described, and the performance of the test when used with simulated non‐linear series is investigated.

Recursive relations are established between the coefficients of the finite past multistep linear predictors of a stationary time series. These relations generalize known results when the prediction is based on infinite past and permit simplification of the numerical calculation of the finite past predictors.

The problem of developing measures of worth of observations in time series has not received much attention in the literature. Any meaningful measure of worth should naturally depend on the position of the observation as well as the objectives of the analysis, namely parameter estimation or prediction of future values. We introduce a measure that quantifies worth of a set of observations for the purpose of prediction of outcomes of stationary processes. The worth is measured as the change in the information content of the entire past due to exclusion or inclusion of a set of observations. The information content is quantified by the mutual information, which is the information theoretic measure of dependency. For Gaussian processes, the measure of worth turns out to be the relative change in the prediction error variance due to exclusion or inclusion of a set of observations. We provide formulae for computing predictive worth of a set of observations for Gaussian autoregressive moving‐average processs. For non‐Gaussian processes, however, a simple function of its entropy provides a lower bound for the variance of prediction error in the same manner that Fisher information provides a lower bound for the variance of an unbiased estimator via the Cramer‐Rao inequality. Statistical estimation of this lower bound requires estimation of the entropy of a stationary time series.