回歸係數和基本交易策略
這個問題可能非常基本，但我仍然無法在任何地方找到令人滿意的答案。我想通過回歸（使用 GARCH 波動率模型）分析重複事件（數據發布）對特定資產價格（我有每日數據）的影響。我已經進行了一項事件研究，但我希望看到一種不同的方法。
所以我執行一個線性回歸解釋 $ R_{t+1} $ with several regressors : lagged return [Math Processing Error] $ R_{t} $ , exogenous variable [Math Processing Error] $ E_{t} $ and the z-score of the released data [Math Processing Error] $ Z_{t} $ (equal to 0 on non-release days). For the sake of the argument, suppose that the regression coefficients are all significant.
My question is : how can I use these results to build a basic trading strategy ? So far I could think of three approaches, but I would like to know whether some/all are wrong/useless/good :
- Using the coefficient of the lagged return to build basic trend following (if the coeff is > 0 ) or mean-reversion (is it is < 0)
- Using the coefficient of the z-score of the data to determine whether a positive value has a positive or negative effect on the return. Then, for future data, if the coeff is positive, then if [Math Processing Error] $ Z_{t} $ is positive, go long, else go short.
- Using all the coefficients to later on forecast the value of [Math Processing Error] $ R_{t+1} $ and invest accordingly.
Are these ways to interpret regression results investment-wise flawed or correct ? Are there others ?
I will give an answer focusing on the econometric aspect of the question. (I could be missing some basic ideas in finance, though.)
If each different regressor is roughly uncorrelated with any linear combination of the remaining regressors, then each of the strategies could work and seem reasonable within the given model. However, focusing on the effect of a single variable is less efficient than focusing on all the effects together, so the last approach should dominate the former ones. (There is one caveat, though, which is overfitting if you are using OLS estimation without regularization/shrinkage.)
If the different regressors are (somewhat highly) correlated with some linear combination of other regressors, the first two approaches could be dominated by estimating simple regresions omitting all variables but the regressors of interest. While this may seem strange in the context of explanatory modelling (why would you omit relevant regressors and thus get inconsistent estimates?), it actually works in predictive modelling; see e.g. F. X. Diebold’s blog post on the so-called “predictive consistency”: “Causality and T-Consistency vs. Correlation and P-Consistency”. In any case, these approaches would still be dominated by the third approach (using prediction from the full model) (but again, the same caveat applies).
您可以使用 GARCH 模型作為過濾器 - 擬合（可能帶有一些 AR/MA/ARIMA 部分），並在第二步中在獲得的殘差和
Z(t)變數之間建立回歸模型。您認為
Z(t)對 GARCH 模型的殘差的影響是加法還是乘法？
err(t) = e(t)*sigma(t) + Z(t)或
err(t) = e(t)*sigma(t)*Z(t)或可能比
err(t)=e(t)*sigma(t)+Z(t)*sigma(t)？第三種情況看起來最適合我，您可以使用上述方法處理它。