On the stationarity and existence of moments of the periodic EGARCH process

IF 0.8 Q3 STATISTICS & PROBABILITY Monte Carlo Methods and Applications Pub Date : 2023-08-01 DOI:10.1515/mcma-2023-2011
Ines Lescheb, Walid Slimani
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引用次数: 0

Abstract

Abstract In this paper, we will consider periodic EGARCH ⁡ ( p , p ) {\operatorname{EGARCH}(p,p)} (exponential generalized autoregressive conditional heteroscedastic) processes denoted by PEGARCH ⁡ ( p , p ) {\operatorname{PEGARCH}(p,p)} . These processes are similar to the standard EGARCH processes, but include seasonally varying coefficients. We examine the probabilistic structure of an EGARCH-type stochastic difference equation with periodically-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions (in a periodic sense) based on a Markovian representation. The closed forms of higher moments are, under these conditions, established. Furthermore, the expressions for the Kurtosis coefficient and the autocorrelations of squared observations are derived. The general theory is illustrated by considering special cases such as the symmetric and the asymmetric cases of the second order PEGARCH model.
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关于周期EGARCH过程的平稳性和矩的存在性
本文将考虑周期EGARCH (p,p) {\operatorname{EGARCH}(p,p)}(指数广义自回归条件异方差)过程,表示为PEGARCH (p,p) {\operatorname{PEGARCH}(p,p)}。这些过程类似于标准EGARCH过程,但包括季节变化的系数。研究了一类参数周期性变化的egarch型随机差分方程的概率结构。基于马尔可夫表示,给出了周期平稳解存在的充分必要条件。在这些条件下,高矩的封闭形式就确立了。此外,还推导了峰度系数和平方观测值的自相关表达式。通过考虑二阶PEGARCH模型的对称和非对称情况来说明一般理论。
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来源期刊
Monte Carlo Methods and Applications
Monte Carlo Methods and Applications STATISTICS & PROBABILITY-
CiteScore
1.20
自引率
22.20%
发文量
31
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