MARKOVFIRSTORDER: Stata module for assessing whether a sequence follows an independent state model or a first-order Markov chain model

Ariel Linden

Statistical Software Components from Boston College Department of Economics

Abstract: markovfirstorder assesses whether a sequence of values follows an independent state model or a first-order Markov chain model (Avery and Henderson 1999). An independent state model assumes that the state in a particular position of the sequence is independent of the previous state. An independent state model is presented as a two-way table and evaluated using Pearson's chi-squared statistic. A statistically significant chi-squared indicates that the hypothesis of independent successive states should be rejected. Next, a first-order Markov chain model is assessed by analyzing a three-way table of the number of times that triplet (i, j, k) occurs where i, j, k = 1, 2, . . ., b. The Pearson's chi-squared statistic for a first-order Markov chain model is computed by summing the chi-squared statistic over all triplets (i, j, k), and where the degrees of freedom = k * (k - 1)^2. A statistically significant chi-squared statistic indicates that the sequence follows a higher order than a first-order Markov chain model. See Avery and Henderson (1999) for a comprehensive discussion.

Language: Stata
Requires: Stata version 11
Keywords: Markov chain model; discrete time Markov chain; first-order Markov chain; Pearson’s chi-squared (search for similar items in EconPapers)
Date: 2025-05-11, Revised 2025-05-12
Note: This module should be installed from within Stata by typing "ssc install markovfirstorder". The module is made available under terms of the GPL v3 (https://www.gnu.org/licenses/gpl-3.0.txt). Windows users should not attempt to download these files with a web browser.
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http://fmwww.bc.edu/repec/bocode/m/markovfirstorder.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/m/markovfirstorder.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/m/matchi2.ado program code (text/plain)
http://fmwww.bc.edu/repec/bocode/m/matchi2.sthlp help file (text/plain)
http://fmwww.bc.edu/repec/bocode/a/Avery_preproglucacon.dta sample data set (application/x-stata)

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