2006/08/22 by René Ferland, Alain Latour, Driss Oraichi · 502 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Autoregressive conditional heteroskedasticity #Autoregressive integrated moving average #Autoregressive model #Computer science #Econometrics #Financial Risk and Volatility Modeling #Heteroscedasticity #Integer (computer science) #Mathematics #STAR model #Series (stratigraphy) #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics #Time series #Volatility (finance)
paper · doi:10.1111/j.1467-9892.2006.00496.x
published in Journal of Time Series Analysis 27(6), 923-942 (Wiley)
crossref issued 2006/08/22 · crossref published 2006/08/22 · crossref published-online 2006/08/22 · openalex publication_date 2006/08/22 · crossref created 2006/08/22 · crossref published-print 2006/11/01 · crossref deposited 2023/10/31 · openalex created_date 2025/10/10 · crossref indexed 2026/08/06 · openalex updated_date 2026/08/06
Abstract. An integer‐valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) ( p , q ) model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case p = 1, q = 1, it is explicitly shown that an integer‐valued GARCH process is a standard autoregressive moving average (1, 1) process. The problem of maximum likelihood estimation of parameters is treated. An application of the model to a real time series with a numerical example is given.