ON THE ASYMPTOTIC DISTRIBUTION OF BARTLETT'S Up‐STATISTIC

Rainer Dahlhaus ()

Journal of Time Series Analysis, 1985, vol. 6, issue 4, 213-227

Abstract: Abstract. In this paper the asymptotic behaviour of Bartlett's Up‐statistic for a goodness‐of‐fit test for stationary processes, is considered. The asymptotic distribution of the test process is given under the assumption that a central limit theorem for the empirical spectral distribution function holds. It is shown that the Up‐statistic tends to the supremum of a tied down Brownian motion. By a counterexample we refute the conjecture that this distribution is in general of the Kolmogorov‐Smirnov type. The validity of the central limit theorem for the spectral distribution function is then discussed. Finally a goodness‐of‐fit test for ARMA‐processes based on the estimated innovation sequence is given, and it is shown that this test statistic is asymptotically Kolmogorov‐Smirnov distributed.

Date: 1985
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/j.1467-9892.1985.tb00411.x

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:6:y:1985:i:4:p:213-227

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by M.B. Priestley

More articles in Journal of Time Series Analysis from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().