估计高维马尔可夫切换VAR
Estimating high-dimensional Markov-switching VARs
摘要：
大型马尔可夫切换向量自回归（MS-VAR）的最大似然估计可能是具有挑战性的或不可行的，由于参数增殖。为了适应的情况下，维度可能是可比的顺序或超过样本量，我们采用了稀疏的框架，并提出了两个惩罚最大似然估计与套索或平滑剪切绝对偏差（SCAD）的罚款。我们证明了这两种估计是估计一致的，而SCAD估计也选择相关的参数的概率接近1。针对高斯误差的情况，提出了一种改进的EM算法，仿真结果表明，该算法具有良好的有限样本性能。在美国短期收益可预测性的应用中，我们估计了一个15变量的2状态MS-VAR（1），并获得了经常报告的可预测性的反周期性。我们的估计量的变量选择属性有助于识别预测，有助于在经济收缩期间的可预测性，但在其他方面无关的扩张。此外，样本外分析表明，大的MS-VAR可以显着优于“难以击败”的预测，如历史平均值。
英文摘要：
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or exceeds the sample size, we adopt a sparse framework and propose two penalized maximum likelihood estimators with either the Lasso or the smoothly clipped absolute deviation (SCAD) penalty. We show that both estimators are estimation consistent, while the SCAD estimator also selects relevant parameters with probability approaching one. A modified EM-algorithm is developed for the case of Gaussian errors and simulations show that the algorithm exhibits desirable finite sample performance. In an application to short-horizon return predictability in the US, we estimate a 15 variable 2-state MS-VAR(1) and obtain the often reported counter-cyclicality in predictability. The variable selection property of our estimators helps to identify predictors that contribute strongly to predictability during economic contractions but are otherwise irrelevant in expansions. Furthermore, out-of-sample analyses indicate that large MS-VARs can significantly outperform "hard-to-beat" predictors like the historical average.
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