Skewed Binomial Markov Chains

Damba Lkhagvasuren

Annals of Economics and Statistics, 2023, issue 150, 81-122

Abstract: In recent years, Markov chains whose stationary distributions belong to the locationscale families of binomial distributions (hereafter referred to as binomial Markov chains) have become an increasingly popular device for generating shocks with desirable statistical properties. The existing applications of binomial Markov chains are limited to those with a symmetric stationary distribution. In this paper, we analyze binomial Markov chains with skewed stationary distributions. First, we derive the key moments of the Markov chains in closed form. Second, we develop an analytically tractable procedure by targeting five moments: the mean, variance, serial correlation, skewness, and kurtosis. Third, we conduct a comprehensive analysis of how the approximation quality varies over the permissible range of the targeted moments. The analytical results in the paper show that a negative serial correlation imposes a strong restriction on the shape of the stationary distribution of a Markov chain.

Keywords: Discrete Process; Finite-State Approximation; Kurtosis; Persistent Shock; Skewness; Transition Matrix (search for similar items in EconPapers)
JEL-codes: C63 E37 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:2023:i:150:p:81-122

DOI: 10.2307/48731470

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