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英文文献：Exponential Smoothing, Long Memory and Volatility Prediction-指数平滑，长记忆和波动预测
英文文献作者：Tommaso Proietti
英文文献摘要：
Extracting and forecasting the volatility of financial markets is an important empirical problem. The paper provides a time series characterization of the volatility components arising when the volatility process is fractionally integrated, and proposes a new predictor that can be seen as extension of the very popular and successful forecasting and signal extraction scheme, known as exponential smoothing (ES). First, we derive a generalization of the Beveridge-Nelson result, decomposing the series into the sum of fractional noise processes with decreasing orders of integration. Secondly, we consider three models that are natural extensions of ES: the fractionally integrated first order moving average (FIMA) model, a new integrated moving average model formulated in terms of the fractional lag operator (FLagIMA), and a fractional equal root integrated moving average (FerIMA) model, proposed originally by Hosking. We investigate the properties of the volatility components and the forecasts arising from these specification, which depend uniquely on the memory and the moving average parameters. For statistical inference we show that, under mild regularity conditions, the Whittle pseudo-maximum likelihood estimator is consistent and asymptotically normal. The estimation results show that the log-realized variance series are mean reverting but nonstationary. An out-of-sample rolling forecast exercise illustrates that the three generalized ES predictors improve significantly upon commonly used methods for forecasting realized volatility, and that the estimated model confidence sets include the newly proposed fractional lag predictor in all occurrences.
提取和预测金融市场的波动是一个重要的实证问题。本文提供了波动率过程的时间序列表征，并提出了一种新的预测器，可以看作是非常流行的和成功的预测和信号提取方案，即指数平滑(ES)的扩展。首先，我们推导了贝弗里奇-尼尔森结果的推广，将序列分解为积分阶数递减的分数阶噪声过程的和。其次，我们考虑了三种自然扩展ES的模型:分数积分一阶移动平均模型(FIMA)，一种用分数滞后算子(FLagIMA)表示的新的积分移动平均模型，以及Hosking最初提出的分数等根积分移动平均模型(FerIMA)。我们调查的性质的波动组成部分和预测从这些规格，这取决于唯一的记忆和移动平均参数。对于统计推断，我们证明，在温和的正则性条件下，惠特尔伪极大似然估计是一致的和渐近正态的。估计结果表明，对数实现的方差序列是均值回归但非平稳的。一个样本外滚动预测实践表明，三种广义ES预测器在预测已实现波动率的常用方法上有显著的改进，估计的模型置信集包含了所有事件中新提出的分数滞后预测器。
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