Selecting Individual Models For Forecast Combinations Using Encompassing Tests

Forecast encompassing tests is an important research field of the combination forecasts.Combined forecasts more effectively use the information of the given sample and become a hot spot of the research field of the forecast over the past decade. However,there are little attention on selecting approach of the individual models for combination forecasts.At the present,the selecting approach of the individual forecasts for combination are based on forecast accuracy.Theoretically,if the number of the model is m,then the number of selection is 2~m.It is hard work.Thus it is necessity for us to establish a approach and a principle for selecting the individual models for forecast combinations to reduce the complexity of the modeling and improve the ability for forecasts.Turgut Kisinbay constructs a approximately pivot statistic whose limiting distribution is t-distribution,and it is used for selecting the individual models for combination.It was a creative work.He proposes to eliminate the encompassed models and reduce the number of the individual models of the combined forecasts.Currently, the approach of encompassing tests is based on the statistical hypothesis.At first,a statistic is defined for??ecasting errors of two forecasts,then its limiting distribution is analysed using the Monte Carlo method.Once we derived the limiting distribution from the analysis,we can use the null hypothesis for encompssing test,based on the limiting distribution which has been obtained.This method emphasize particularly on three aspects:the first is to use comparisons of out-of-sample forecasts to determine whether one variable has predictive power for another.If the variable has low predictive power, then it is encompassed by another,and it would be excluded from the model.The second is to evaluate the forecast capabality of the equal accuracy forecasts,i.e. consider two or more equal accuracy forecasts,which more effectively use the information of the given sample and reduce the forecasting risk.The third is to demonstrate why forecasts may be combind to produce a composite forecast which is super to the individual forecasts.We can learn from the three aspects that it is very feasible to select the individual forecasts for combining the models based on the encompassing tests theory.In this thesis we begin with systematically summarizing the encompassing tests proposed by many papers,and pointing out the shortcomings of these methods. Secondly,we integrate the equal accuracy with the unequal encompassing tests. According to the theory of the encompassing tests,if a low capability model has the useless boundary information(encompassed),or the equal accuracy forecasts are equipollence(or encompassed),it is no use to combine them into the combination,and the complexity of the modeling is increasing,the power of the forecast is reduced.So it is necessary to select the individual models for combining forecasts using the encompassing tests.Thirdly,we define a new statistic of the forecast errors whose limiting distribution is t-distribution,thus the encompassing tests is standardized and the operations are simple.To assess the usefulness of this approach,an extensive empirical analysis is undertaken by using an averages of daily figures data set of daily Japan/U.S. Foreign Exchange Rates.And we empirically analyse the validity of the combination encompassing tests by using simple average combination.At last,we chart a new direction for research of the encompassing test in the future.