Estimation and asymptotic inference in the first order AR-ARCH model
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Estimation and asymptotic inference in the first order AR-ARCH model. / Lange, Theis; Rahbek, Anders; Jensen, Søren Tolver.
In: Econometric Reviews, Vol. 30, No. 2, 03.2011, p. 129-153.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Estimation and asymptotic inference in the first order AR-ARCH model
AU - Lange, Theis
AU - Rahbek, Anders
AU - Jensen, Søren Tolver
N1 - JEL Classification: C22, C52
PY - 2011/3
Y1 - 2011/3
N2 - This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individual terms of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We show that the MQMLE is asymptotically normal irrespectively of the existence of finite moments, as geometric ergodicity alone suffice. Moreover, our included simulations show that the MQMLE is remarkably well-behaved in small samples. On the other hand, the ordinary QMLE, as is well-known, requires finite fourth order moments for asymptotic normality. But based on our considerations and simulations, we conjecture that in fact only geometric ergodicity and finite second order moments are needed for the QMLE to be asymptotically normal. Finally, geometric ergodicity for AR-ARCH processes is shown to hold under mild and classic conditions on the AR and ARCH processes.
AB - This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individual terms of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We show that the MQMLE is asymptotically normal irrespectively of the existence of finite moments, as geometric ergodicity alone suffice. Moreover, our included simulations show that the MQMLE is remarkably well-behaved in small samples. On the other hand, the ordinary QMLE, as is well-known, requires finite fourth order moments for asymptotic normality. But based on our considerations and simulations, we conjecture that in fact only geometric ergodicity and finite second order moments are needed for the QMLE to be asymptotically normal. Finally, geometric ergodicity for AR-ARCH processes is shown to hold under mild and classic conditions on the AR and ARCH processes.
KW - Faculty of Social Sciences
U2 - 10.1080/07474938.2011.534031
DO - 10.1080/07474938.2011.534031
M3 - Journal article
VL - 30
SP - 129
EP - 153
JO - Econometric Reviews
JF - Econometric Reviews
SN - 0747-4938
IS - 2
ER -
ID: 15456847