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The Limiting Distribution of a Non‐Stationary Integer Valued GARCH(1,1) Process
Author(s) -
Michel Jon
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12496
Subject(s) - mathematics , limiting , autoregressive conditional heteroskedasticity , integer (computer science) , asymptotic distribution , distribution (mathematics) , process (computing) , combinatorics , statistics , mathematical analysis , econometrics , volatility (finance) , computer science , mechanical engineering , estimator , engineering , programming language , operating system
We consider the integer valued GARCH(1,1) process defined by the two equation systemY n~ d Poisson ( λ n ) and λ n + 1 = ω + αY n + βλ n . When α + β < 1 this process has a stationary solution and properties are well understood. In this note we find the limiting distribution of λ n and Y n for the case of α + β = 1.
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