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QMLE for Quadratic ARCH Model with Long Memory
Author(s) -
Grublytė Ieva,
Surgailis Donatas,
Škarnulis Andrius
Publication year - 2017
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.12227
Subject(s) - mathematics , heteroscedasticity , conditional variance , arch , quadratic equation , conditional expectation , autoregressive model , statistics , autoregressive conditional heteroskedasticity , consistency (knowledge bases) , asymptotic distribution , parametric statistics , econometrics , discrete mathematics , estimator , volatility (finance) , civil engineering , geometry , engineering
We discuss parametric quasi‐maximum likelihood estimation for quadratic autoregressive conditional heteroskedasticity (ARCH) process with long memory introduced in Doukhan emphet al. (2016) and Grublytė and Škarnulis (2016) with conditional variance involving the square of inhomogeneous linear combination of observable sequence with square summable weights. The aforementioned model extends the quadratic ARCH model of Sentana ([Sentana E, 1995]) and the linear ARCH model of Robinson ([Robinson PM, 1991]) to the case of strictly positive conditional variance. We prove consistency and asymptotic normality of the corresponding quasi‐maximum likelihood estimates, including the estimate of long memory parameter 0 < d < 1/2. A simulation study of empirical mean‐squared error is included.