Abstract:
Markov chains provide a flexible model for dependent random variables with-applications in such disciplines as physics, environmental science and economics. Recently the bootstrap has been used to aid in the development of statistical methods based on observed realizations from Markov chains. The bootstrap method estimates parameters of the Markov chain with an unknown transition probability matrix with those from a Markov chain with a transition probability matrix estimated using the observed realization. Unfortunately, when the length of the observed realization is not sufficiently large, the properties of the estimated transition probability matrix are often very different from those of the actual transition probability matrix. This can lead to large errors associated with the bootstrap estimates. This paper presents simple multinomial type smoothing techniques that can be applied to the estimated transition probability matrix to alleviate some of these difficulties. It is demonstrated through empirical studies that the use of the smoothed transition probability matrix can increase the reliability of the bootstrap method for Markov chains. The practical use of the method is demonstrated through an example.
Page(s):
553-570
DOI:
DOI not available
Published:
Journal: Pakistan Journal of Statistics, Volume: 25, Issue: 4, Year: 2009