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首页> 外文期刊>Journal of Time Series Analysis >THE SLOW CONVERGENCE OF ORDINARY LEAST SQUARES ESTIMATORS OF α,β AND PORTFOLIO WEIGHTS UNDER LONG-MEMORY STOCHASTIC VOLATILITY
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THE SLOW CONVERGENCE OF ORDINARY LEAST SQUARES ESTIMATORS OF α,β AND PORTFOLIO WEIGHTS UNDER LONG-MEMORY STOCHASTIC VOLATILITY

机译：长记忆随机波动下α，β和投资组合权重的最小二乘估计的慢收敛性

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摘要

We consider inference for the market model coefficients based on simple linear regression under a long memory stochastic volatility generating mechanism for the returns. We obtain limit theorems for the ordinary least squares (OLS) estimators of alpha and beta in this framework. These theorems imply that the convergence rate of the OLS estimators is typically slower than T if both the regressor and the predictor have long memory in volatility, where T is the sample size. The traditional standard errors of the OLS-estimated intercept (alpha(boolean AND)) and slope (beta(boolean AND)), which disregard long memory in volatility, are typically too optimistic, and therefore the traditional t-statistic for testing, say, alpha = 0 or beta = 1, will diverge under the null hypothesis. We also obtain limit theorems (which imply slow convergence) for the estimated weights of the minimum variance portfolio and the optimal portfolio in the same framework. In addition, we propose and study the performance of a subsampling-based approach to hypothesis testing for alpha and beta. We conclude by noting that analogous results hold under more general conditions on long-memory volatility models and state these general conditions which cover certain fractionally integrated exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models.
机译：我们考虑在收益的长记忆随机波动产生机制下，基于简单线性回归的市场模型系数推断。我们在此框架中获得了α和β的普通最小二乘（OLS）估计的极限定理。这些定理表明，如果回归变量和预测变量对波动率的记忆都较长，则OLS估计量的收敛速度通常比T慢，其中T为样本量。 OLS估计的截距（alpha（boolean AND））和斜率（beta（boolean AND））的传统标准误差通常会过于乐观，因此他们不愿考虑波动率中的长时间记忆，因此，传统的t统计量用于测试，则alpha = 0或beta = 1，将在原假设下发散。我们还获得了在同一框架中最小方差投资组合和最优投资组合的估计权重的极限定理（这意味着收敛缓慢）。此外，我们提出并研究了基于二次抽样的alpha和beta假设检验方法的性能。通过得出结论，指出类似的结果在更长的波动率模型上更通用的条件下成立，并陈述了这些通用条件，它们涵盖了某些分数积分指数广义自回归条件异方差（EGARCH）模型。

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