|Abstract: ||「預測性迴歸」(predictive regression) 在財務金融領域的應用相當廣泛。在此類迴歸模型中, 解釋變數通常為某資產價格的報酬, 而預測變數則為與前述資產價格相關的落後變數。雖然模型形式相當簡單, 但由於資產價格報酬的高度波動性(volatile), 輔以解釋變數的自我迴歸性質 (autoregressive), 使得常用的最小平方估計式面臨有限樣本偏誤(finite sample bias) 與高變異數的估計風險。影響所及, 除了降低樣本外預測的精確性外, 據以形成檢定與推論也不可信賴。本計劃嘗試發展一種適合於預測性迴歸的「間接推論法」(indirect inference method), 藉以修正有限樣本估計問題。該方法的優點在於不需要暸解基礎估計式(base estimator, 如最小平方估計式) 偏誤函數的確切型式, 而是透過電腦模擬基礎估計式的均數與真實參數值間的對應關係, 逆向獲得不偏的參數估計。再者, 間接推論估計式的分配性質與基礎估計式直接相關。因此, 若基礎估計式選取得當, 間接推論估計式將可同時具備不偏與低變異數的優良性質。預期透過間接推論估計式低估計風險的性質, 除可有效解決預測性迴歸文獻上常面臨的型一誤差扭曲(size distortion) 問題外, 同時可強化檢定的對立假設偵測能力。|
Predictive regression has been widely used in the empirical financial literature. It is to investigate whether some fundamental predictors in lagged form could explain the variation of the rate of return of the assets of concern. The least-squares (LS) estimator which is usually applied to the regression, however, suffers from considerable estimation risks, consisting of bias and high errors. The problems come from both the excessive volatility in the rate of return series and the high persistence of the predicting variables, 2 typical features of the financial time series. Inference based on the estimator tends to be not as trustworthy, because of the size distortion resulting from the bias. The situation is further compounded by the high estimation errors, leading to a likely inability of the tests to detect the existence of the predictability. This project attempts to address the problems by the indirect inference. The simulationbased approach has the advantage that it corrects the bias of the base estimator (in our case the LS estimator) with accuracy, without requiring any explicit form for the bias function. This merit is particularly notable in the context where the predictor is commonly characterized by a high-order autoregression. Moreover, the efficency gains may well be anticipated when alternative base estimator is appropriately chosen. The predictability hypothesis can then be soundly examined by tests with proper size and more power when based on the proposed indirect inference estimator in sample or out of sample.