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On geometric ergodicity of the MTAR process

✍ Scribed by Oesook Lee; Dong Wan Shin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
114 KB
Volume
48
Category
Article
ISSN
0167-7152

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✦ Synopsis

We consider the momentum threshold autoregressive (MTAR) process and characterize the region of the autoregressive coe cients for geometric ergodicity. The region is a proper subset of the ergodic region of the TAR process. We show that the process is geometrically ergodic inside the region and is transient outside the closure of the region.

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For the pth-order linear ARCH model, St = gt~/O{O q-~lXt2\_l q-0~2 X.2\_2 +-.-q-o~pXtLp, where c~0 > 0, c~i~>0, i = 1, 2, ..., p, {et} is an i.i.d, normal white noise with E~, = 0, Ee~ = 1, and et is independent of {X~, s < t}, Engle (1982) obtained the necessary and sufficient condition for the sec