預測績效檢定：簡單迴歸之應用

A Simple Test for Predictive Ability Using Autoregression

10.29628/AEP.200503.0001

欉清全(Ching-Chuan Tsong)；李政峰(Cheng-Feng Lee)；郭炳伸(Biing-Shen Kuo)

預測凖確性檢定 ； 預測涵蓋檢定 ； Forecast accuracy test ； Forecast encompassing test

經濟論文

33卷1期（2005 / 03 / 01）

1 - 33

繁體中文

樣本外預測績效的比較，有助於研究者選擇適當的模型設定或預測方法。評估預測績效的標準可從預測準確性或預測涵蓋性兩方面為之。本文提出一種計算程序，不僅可用於建立上述兩種檢定量，同時具有計算簡單的優點。我們的檢定程序是：在含戴距項的自我迴歸模型中，以AIC準則挑選適當的階次後，再利用OLS估計此模型中的參數，並以傳統的t檢定量檢驗截距項是否顯著異於零。我們並證明，在大樣本下，此檢定統計量仍為標準常態分配。對實證研究者而言，本文的檢定程序不僅概念易懂，且幾乎所有統計套裝軟體皆可使用，具有相當的方便性。另一方面，它規避了上述兩種預測檢定量的惱人問題：估計長期變異數的過程中，選擇不同核函數(kernel)將嚴重影響檢定量的表現。亦即，本文程序的t檢定量並沒有像上述兩種預測檢定對「核函數」存在不穩健(non-robust)的問題。模擬結果顯示，即使預測誤差具有異質性，相較於預測準確或預測涵蓋檢定原來的方式，整體而言，本文的檢定程序，在型一誤差的表現優於前兩者，並具有不錯的檢力。

It is becoming increasingly popular to evaluate forecasting schemes or to select competing models by conducting testing for equal forecast accuracy and encompassing. It has been by now well-documented that the extant tests suffer from size distortions, resulting from their sensitivity to the choice of kernel functions in estimation of the long-run variance. This paper proposes a simple regression test for post-sample predictive ability that can reduce the problem. Our testing procedure can be easily implemented in major available canned software packages. Specifically, we test for zero intercept in an autoregression with suitably chosen lags accounting for autocorrelation in forecast errors. Our test is based on the notion that testing for predictive ability amounts to testing whether the function of forecast errors has a zero population mean. We establish the asymptotic normality of the proposed test. Monte Carlo simulation demonstrates that our test fares better than the existing ones in size performance, even in the presence of heterogeneous forecast errors, while maintaining comparable power.

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