Abstract Fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, new realized stochastic volatility (RSV) models are developed: one is a RSV model with general Gegenbauer long memory (GGLM), while the other is a RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks, apart from the origin in the power spectrum. For estimating the RSV–GGLM model, a two step method is suggested: the location parameters for the peaks of the power spectrum are estimated in the first step, while the remaining parameters are estimated based on the Whittle likelihood in the second step. Monte Carlo experiments give results for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of the RSV–SLM model against the RSV–GGLM model. The RSV–GGLM and RSV–SLM models are applied to three stock market indices, for which the estimation and forecasting results indicate the adequacy of considering general long memory.

中文翻译：

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具有广义Gegenbauer长记忆的已实现的随机波动率模型

摘要小数差分处理由于其在具有长记忆力的金融应用中的灵活性而备受关注。在本文中，开发了新的实现的随机波动率（RSV）模型：一种是具有一般Gegenbauer长记忆（GGLM）的RSV模型，而另一种是具有季节性长记忆（SLM）的RSV模型。RSV模型同时使用来自收益的信息和已实现的波动率度量。两种模型的长存储结构都可以描述无穷大的峰，除了功率谱中的原点。为了估算RSV-GGLM模型，建议采用两步法：第一步估算功率谱峰值的位置参数，第二步根据Whittle可能性估算其余参数。蒙特卡洛实验给出了调查估计量的有限样本属性的结果，并通过对RSV-SLM模型相对于RSV-GGLM模型的准似然比检验。RSV–GGLM和RSV–SLM模型适用于三个股票市场指数，其估计和预测结果表明考虑了一般的长期记忆是足够的。