(WHEN) DO LONG AUTOREGRESSIONS ACCOUNT FOR NEGLECTED CHANGES IN PARAMETERS?
(WHEN) DO LONG AUTOREGRESSIONS ACCOUNT FOR NEGLECTED CHANGES IN PARAMETERS?
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DOI：
10.1017/s0266466615000225
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发表时间：
2015-07
影响因子：
0.8
通讯作者：
M. Demetrescu;U. Hassler
中科院分区：
文献类型：
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作者：
M. Demetrescu;U. Hassler
为了构建对时间序列的预测，本文研究了长自回归，其中滞后的数量随着T的增长而增长，并且可能的中断被简单地忽略。本文证明了当忽略均值突变时，对于真自回归系数，OLS估计仍然是元素相合的，但估计之和收敛于1。由于拟合模型的这种单位根行为，所得到的条件预测与真实值一致。只要动态结构是不变的，预测的鲁棒性保持a）在数据依赖的滞后长度选择下，B）对于分段平滑变化的均值函数，以及c）在可能无限阶的一般自回归动态（包括平稳长记忆）下。然而，在动态结构中的突变下，估计量是渐近有偏的，即使在极限下，长期自回归的预测也是有偏的。
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.