Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP

✍ Scribed by Bruce E. Hansen

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 143 KB
• Volume: 11
• Category: Article
• ISSN: 0883-7252
• DOI: 10.1002/(sici)1099-1255(199603)11:2<195::aid-jae375>3.0.co;2-2

✦ Synopsis

There was an error in Hansen (1992). I am very grateful to James Hamilton for pointing out the error.

Equations ( 2) and (3) in the original read where Q ( a ) is a mean zero Gaussian process with covariance function K(ai, a21 = E(q;(ai)~i(ad).

While equation ( 2) is correct, (3) is not. Instead, the correct expression is

The reason is that the likelihood components qi(a) will be serially correlated for some values of a. This will be the case even when the original data are iid, since the likelihood qi(a) is a function of all data up to time i. It should be noted that this problem does not apply to the testing methods of Hansen (1994), which involve application of empirical process theory to specific likelihood scores which are serially uncorrelated. This error implies that the method of calculating the asymptotic distribution in Section 3.2 is incorrect. Instead, set di(a) = qj(a, 8 ( a ) ) and i = 1

P -I L l s i G n -k I + t < i < n

J

where wkM = 1 -1 k 1 /(M + 1) is the Bartlett kernel and M is a bandwidth number (selected to grow to infinity slowly with sample size). Then a consistent estimate of CCC 0883-7252/96/020195-4