马悦, 朱复康. 零修正Skellam整数值GARCH模型[J]. 应用概率统计. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022093
引用本文: 马悦, 朱复康. 零修正Skellam整数值GARCH模型[J]. 应用概率统计. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022093
MA Yue, ZHU Fukang. Zero-Modified Skellam Integer-Valued GARCH Model[J]. Chinese Journal of Applied Probability and Statistics. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022093
Citation: MA Yue, ZHU Fukang. Zero-Modified Skellam Integer-Valued GARCH Model[J]. Chinese Journal of Applied Probability and Statistics. DOI: 10.12460/j.issn.1001-4268.aps.2024.2022093

零修正Skellam整数值GARCH模型

Zero-Modified Skellam Integer-Valued GARCH Model

  • 摘要: Skellam 分布是一种定义在 Z 上的离散分布. 最近, 基于 Skellam 分布和修正 Skellam分布的 INGARCH 模型相继被提出. 本文在零修正 Skellam (ZMS) 分布的基础上, 提出了 ZMSINGARCH 模型. 该模型基于一个额外的参数对整数 0 进行了细致的处理, 并且对零膨胀或零收缩比例有着合理的解释, 可以更好地拟合数据和捕获非零均值时间序列中的波动性. 当模型的阶数 p = 1且 q = 1 时给出了模型的定义和统计性质, 通过数值模拟发现条件极大似然估计优于条件最小二乘估计. 基于对数似然比统计量, 检验了修正后的模型, 通过分析来自不同股票交易市场的两个实例说明了该模型具有良好的性质.

     

    Abstract: The Skellam distribution is a discrete distribution defined on Z. Recently, INGARCH models based on the Skellam and modified Skellam distributions have been proposed. In this paper, a ZMSINGARCH model based on the zero-modified Skellam (ZMS) distribution is proposed. This model takes into account an additional parameter to handle the integer 0 in detail, and has a reasonable explanation for the zero inflation or zero deflation ratio in order to fit the data better and capture volatility in non-zeromean time series. The definition and statistical properties of the model are given when the order p = 1 and q = 1, and numerical simulations show that the conditional maximum likelihood estimation is superior to the conditional least square estimation. The modified model is tested based on the log-likelihood ratio test statistic, and two examples from different stock trading markets are analyzed to show that the proposed model has a better performance.

     

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