We evaluate the performance of the

We evaluate the performance of the competing indicators in the forecasting exercise using several statistics. The out-of-sample R2 compares the predictive power of the regression with the historical sample mean. It is defined as where is the mean square error of the out-of-sample predictions based on the model and is the mean square error based on the sample mean (assuming no predictability). The adjusted is defined as where k is the number of regressors. The out-of-sample takes positive (negative) values when the model predicts returns with higher (lower) accuracy than the historical mean. We also use the encompassing ENC test statistic proposed by Harvey et al. (1998) and Clark and McCracken (2001), defined as(8)Under the null hypothesis, the forecasts based on the historical mean encompass the forecasts based on the model, meaning that the model does not help to predict future market returns. Because the test statistic has a nonstandard distribution under the null hypothesis in the case of nested models, we rely on the critical values computed by Clark and McCracken (2001).

結果 (繁體中文) 1:

We evaluate the performance of the competing indicators in the forecasting exercise using several statistics. The out-of-sample R2 compares the predictive power of the regression with the historical sample mean. It is defined as where is the mean square error of the out-of-sample predictions based on the model and is the mean square error based on the sample mean (assuming no predictability). The adjusted is defined as where k is the number of regressors. The out-of-sample takes positive (negative) values when the model predicts returns with higher (lower) accuracy than the historical mean. We also use the encompassing ENC test statistic proposed by Harvey et al. (1998) and Clark and McCracken (2001), defined as
(8)
在零假設下，基於歷史平均涵蓋預報的預測基於模型，這意味著模型並不能幫助預測未來的市場回報。由於檢驗統計量在嵌套模式的情況下，零假設下非標準的分佈，我們依靠克拉克和麥克拉肯（2001）計算的臨界值。

結果 (繁體中文) 2:

我們使用多個統計資料來評估預測中競爭指標的績效。樣本外 R2 將回歸的預測能力與歷史樣本平均值進行比較。它定義為基於模型的樣本外預測的平均平方誤差的位置，是基於樣本平均值（假設沒有可預測性）的平均平方誤差。調整後定義為其中 k 是回歸數。當模型預測返回的精度高於（較低）于歷史平均值時，樣本外採用正值（負值）。我們還使用哈威等人（1998年）和克拉克和麥克拉肯（2001年）提出的包含的ENC測試統計資料，該統計資料定義為
(8)
在零假設下，基於歷史平均值的預測包括基於模型的預測，這意味著模型無助于預測未來的市場回報。由於在嵌套模型的情況下，測試統計值在零假設下具有非標準分佈，因此我們依賴于 Clark 和 McCracken （2001 年）計算的臨界值。

結果 (繁體中文) 3:

我們使用幾個統計資料來評估預測過程中競爭性名額的表現。樣本外R2將回歸的預測能力與歷史樣本平均值進行比較。它的定義是where是基於模型的樣本外預測的均方誤差，並且是基於樣本平均值的均方誤差（假設沒有可預測性）。調整後的定義為k是回歸數。當模型以比歷史平均值更高（更低）的精度預測收益時，樣本外取正（負）值。我們還使用了Harvey等人提出的包含ENC檢驗統計量。（1998）和克拉克和麥克拉肯（2001），定義為
（八）
在零假設下，基於歷史平均值的預測包含了基於模型的預測，這意味著模型無助於預測未來市場收益。由於在嵌套模型的情况下，檢驗統計量在零假設下具有非標準分佈，我們依賴於Clark和McCracken（2001）計算的臨界值。