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- Title
Evolutionary spectral and bispectral analysis of periodic GARCH model.
- Authors
Kimouche, Karima; Bibi, Abdelouahab
- Abstract
This paper defines and analyzes the evolutionary transfer functions for conditional volatility in periodic generalized autoregressive conditional heteroscedasticity (PGARCH for short ) model in order to describe some probabilistic and statistical properties in both frequency and temporal behavior. So. in the first part. we consider a diagonal periodic bilinear representation of PGARCH (p, q) process with second-order Hermite polynomial with leading coefficient 1, and we give a necessary and sufficient condition for the existence of causal and second order periodically stationarity solution (or also periodically correlated (PC)). In a second part, we focus on the probabilistic structure of such a representation, more precisely, we analyze the so-called time-dependent autocovariance and the associated evolutionary spectral density function of such a representation and its squared version. As a consequence, it is shown that the second order properties is similar to a PARMA process with uncorrelated innovations and hence the resort to higher-order properties is seems to be necessary to identify the process. Therefore, the explicit expression of evolutionary bispectral density of the process and its squared version are used as useful property that characterizing the non linear models. Several illustrative examples are emphasized.
- Subjects
PARMA (Italy); GARCH model; SPECTRAL energy distribution; HERMITE polynomials; TRANSFER functions; HETEROSCEDASTICITY; NONLINEAR oscillators; SPECTRAL imaging
- Publication
Nonlinear Studies, 2023, Vol 30, Issue 3, p971
- ISSN
1359-8678
- Publication type
Article