On the Forecasting Accuracy of Multivariate GARCH Models
On the Forecasting Accuracy of Multivariate GARCH Models
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DOI：
10.1002/jae.1248
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发表时间：
2010-05
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通讯作者：
S. Laurent;J. Rombouts;Francesco Violante
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作者：
S. Laurent;J. Rombouts;Francesco Violante
本文讨论的问题，选择多变量GARCH模型的方差矩阵的预测精度，特别侧重于相对较大规模的问题。我们考虑10个资产从纽约证券交易所和纳斯达克和比较125模型为基础的一步提前条件方差预测在一段时间内的10年，使用模型置信集（MCS）和上级预测能力（SPA）测试。模型性能评估使用四个统计损失函数，占不同类型和程度的不对称相对于过/欠预测。当考虑完整样本时，MCS结果受到短期市场高度不稳定性的强烈驱动，在此期间，多变量GARCH模型似乎不准确。在相对不稳定的时期，即互联网泡沫时期，上级模型集由更复杂的规范组成，如正交和动态条件相关（DCC），两者都具有条件方差的杠杆效应。然而，与DCC模型不同，我们的结果表明，正交规格往往低估了条件方差。在平静时期，一个简单的假设，如恒定的条件相关性和对称性的条件方差不能被拒绝。最后，在2007-2008年金融危机期间，考虑到条件方差过程中的非平稳性，可以产生上级预测。SPA测试表明，独立于时期，最好的模型并没有提供比Engle（2002）的DCC模型更好的预测，并利用收益的条件方差。
This paper addresses the question of the selection of multivariate GARCH models in terms of variance matrix forecasting accuracy with a particular focus on relatively large scale problems. We consider 10 assets from NYSE and NASDAQ and compare 125 model based one-step-ahead conditional variance forecasts over a period of 10 years using the model confidence set (MCS) and the Superior Predicitive Ability (SPA) tests. Model per- formances are evaluated using four statistical loss functions which account for different types and degrees of asymmetry with respect to over/under predictions. When consid- ering the full sample, MCS results are strongly driven by short periods of high market instability during which multivariate GARCH models appear to be inaccurate. Over rel- atively unstable periods, i.e. dot-com bubble, the set of superior models is composed of more sophisticated specifications such as orthogonal and dynamic conditional correlation (DCC), both with leverage effect in the conditional variances. However, unlike the DCC models, our results show that the orthogonal specifications tend to underestimate the conditional variance. Over calm periods, a simple assumption like constant conditional correlation and symmetry in the conditional variances cannot be rejected. Finally, during the 2007-2008 financial crisis, accounting for non-stationarity in the conditional variance process generates superior forecasts. The SPA test suggests that, independently from the period, the best models do not provide significantly better forecasts than the DCC model of Engle (2002) with leverage in the conditional variances of the returns.