(WHEN) DO LONG AUTOREGRESSIONS ACCOUNT FOR NEGLECTED CHANGES IN PARAMETERS?
研究了在时间序列存在结构突变时，忽略突变而使用长自回归模型进行预测的效果，发现均值突变下预测仍一致，但动态结构突变下预测有偏。
To construct forecasts for time series exhibiting breaks, the paper examines long autoregressions, where the number of lags is growing with T , and possible breaks are simply ignored. The paper shows that the OLS estimators are still elementwise consistent for the true autoregressive coefficients when neglecting a break in mean, but the sum of the estimators converges to unity. Thanks to this unit-root like behavior of the fitted model, the resulting conditional forecasts are consistent for the true values. As long as the dynamic structure is invariant, the robustness property of the forecasts holds a) under data-dependent lag length selection, b) for a piecewise smoothly varying mean function, and c) under general autoregressive dynamics of possibly infinite order including stationary long memory. Under breaks in the dynamic structure, however, estimators are asymptotically biased, and the forecasts from long autoregressions are biased themselves even in the limit.