Linear Combination Of Forecasts Research Articles

TIME SERIES FORECASTING BY USING A NEURAL ARIMA MODEL BASED ON WAVELET DECOMPOSITION

In the prediction of (stochastic) time series, it has been common to suppose that an individual predictive method – for instance, an Auto-Regressive Integrated Moving Average (ARIMA) model – produces residuals like a white noise process. However, mainly due to the structures of auto-dependence not mapped by a given individual predictive method, this assumption may easily be violated, in practice, as pointed out in Firmino et al. (2015). In order to correct it (and accordingly to produce more forecasts with more accuracy power), this paper puts forward a Wavelet Hybrid Forecaster (WHF) that integrates the following numerical techniques: wavelet decomposition; ARIMA models; Artificial Neural Networks (ANNs); and linear combination of forecasts. Basically, the proposed WHF can map simultaneously linear – by means of a linear combination of ARIMA forecasts – and non-linear – through a linear combination of ANN forecasts – auto-dependence structures exhibited by a given time series. Differently of other hybrid methodologies existing in literature, the WHF forecasts are produced carrying into account implicitly the information from the frequency presenting in the underlying time series by means of the Wavelet Components (WCs) obtained by the wavelet decomposition approach. All numerical results show that WHF method has achieved remarkable accuracy gains, when comparing with other competitive forecasting methods already published in specialized literature, in the prediction of a well-known annual time series of sunspot.

Quadratic radical function better than fisher z transformation

A new explicit quadratic radical function is found by numerical experiments, which is simpler and has only 70.778% of the maximal distance error compared with the Fisher z transformation. Furthermore, a piecewise function is constructed for the standard normal distribution: if the independent variable falls in the interval (−1.519, 1.519), the proposed function is employed; otherwise, the Fisher z transformation is used. Compared with the Fisher z transformation, this piecewise function has only 38.206% of the total error. The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.

Linear combination of forecasts: A general Bayesian model

AbstractWe provide a general Bayesian model for combining forecasts from experts (or forecasting models) who might be biased and correlated with each other. The combination procedure involves debiasing and then combining unbiased forecasts. We also provide a sequential method for learning about the forecasters' biases in the process of combining information from them.

N‐step combinations of forecasts

AbstractWhile there is general agreement that a linear combination of forecasts can outperform the individual forecasts, there is controversy about the appropriateness of the combination method to be used in a given situation. Hence, in any given application it may be more beneficial to combine different sets of combined forecasts rather than picking one of them. This paper introduces the concept of N‐step combinations of forecasts which involves combining the combined forecasts obtained from different combination procedures used at the preceding step. Using quarterly GNP data, evidence supporting the increase in the accuracy of the one‐period‐ahead ex‐ante forecasts as the combination step increases is provided. The MSE, MAE, MAPE and their corresponding standard deviations are used to evaluate the accuracy of the forecasts obtained.

Forecasting and testing in co-integrated systems

This paper examines the behavior of forecasts made from a co-integrated system as introduced by Granger (1981), Granger and Weiss (1983) and Engle and Granger (1987). It is established that a multi-step forecast will satisfy the co-integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance. A simulation study compares the multi-step forecast accuracy of unrestricted vector autoregression with the two-step estimation of the vector autoregression imposing the co-integration restriction. To test whether a system exhibits co-integration, the procedures introduced in Engle and Granger (1987) are extended to allow different sample sizes and numbers of variables.

Linear combination of forecasts with an intercept: A bayesian approach

AbstractThe standard approach to combining n expert forecasts involves taking a weighted average. Granger and Ramanathan proposed introducing an intercept term and unnormalized weights. This paper deduces their proposal from Bayesian principles. We find that their formula is equivalent to taking a weighted average of the n expert forecasts plus the decision‐maker's prior forecast.

Statistical efficiency in the linear combination of forecasts

In seeking an efficient combination of forecasts which minimises the forecast error variance, many methods have been suggested. Through analysis, simulation and case studies, this paper seeks to develop insights into the statistical circumstances which influence the relative accuracy of six of these methods. The six methods chosen have all been advocated in various publications and consist of ‘equal weighting’ (i.e., pooled average), ‘optimal’ (i.e., error variance minimising), ‘optimal with independence assumption’ (i.e., error variance minimising assuming zero correlation between individual forecast errors) and three variations on the formulation of a Bayesian combination based upon posterior probabilities. The statistical circumstances reflected varying conditions of relative forecast errors, error correlations and outliers.

Efficiency of the independence assumption in the combination of forecasts

In seeking to minimise the composite forecast error variance of a linear combination of forecasts, contradictory suggestions have been reported concerning the practice of making the assumption of independence between forecast errors. This assumption can introduce robustness though its avoidance of sampling errors in the estimation of correlation coefficient(s), although it does render the composite forecast theoretically suboptimal. By means of theory and experimental simulation, this paper examines the circumstances whereby the independence assumption may produce more efficient composite forecasts. Its applicability is shown to depend both upon the underlying correlation structure and relative size of forecast errors as well as the observation base available for estimation.

A Comparison of Autoregressive Univariate Forecasting Procedures for Macroeconomic Time Series

The actual performance of several automated univariate autoregressive forecasting procedures, applied to 150 macroeconomic time series, are compared. The procedures are the random walk model as a basis for comparison; long autoregressions, with three alternative rules for lag length selection; and a long autoregression estimated by minimizing the sum of absolute deviations. The sensitivity of each procedure to preliminary transformations, data, periodicity, forecast horizon, loss function employed in parameter estimation, and seasonal adjustment procedures is examined. The more important conclusions are that Akaike's lag-length selection criterion works well in a wide variety of situations, the modeling of long memory components becomes important for forecast horizons of three or more periods, and linear combinations of forecasts do not improve forecast quality appreciably.

Improved methods of combining forecasts

AbstractIt is well known that a linear combination of forecasts can outperform individual forecasts. The common practice, however, is to obtain a weighted average of forecasts, with the weights adding up to unity. This paper considers three alternative approaches to obtaining linear combinations. It is shown that the best method is to add a constant term and not to constrain the weights to add to unity. These methods are tested with data on forecasts of quarterly hog prices, both within and out of sample. It is demonstrated that the optimum method proposed here is superior to the common practice of letting the weights add up to one.

Linear-Combination of Forecasts: A Reply

"Linear-Combination of Forecasts: A Reply." Journal of the Operational Research Society, 32(12), p. 1145

Linear-Combination of Forecasts: A Reply

Linear-Combination of Forecasts: A Reply

Linear Combination of Forecasts — A Comment

Linear Combination of Forecasts — A Comment

Two Methodologies for the Linear Combination of Forecasts

Two Methodologies for the Linear Combination of Forecasts