### Stationarity of the transition probabilities in the Markov chain formulation of owner payments on projects

#### Abstract

Markov chain theory has been used to model the likelihood of payment to contractors based on historical owner payment practices. An important assumption in this modelling of owner payment behaviour is that the transition probability matrices are stationary. We study this assumption: the null hypothesis postulated is that the transition matrices are stationary; the alternate hypothesis is that they are not. This article also explores the impact of this assumption on the performance of the model. The outcomes of the model, in the form of payment likelihood of an outstanding amount against its age, given by both stationary and non-stationary approaches are compared. Tests performed on two project data sets show that the null hypothesis is rejected at the 5% level of significance. However, the payment probabilities estimated using non-stationary transition matrices are shown to approach a steady state after a relatively short fluctuation. These steady state values of payment probabilities are almost identical to those estimated under a stationary assumption. Therefore, we recommend users of the model adopt the stationary transition matrix approach to avoid the extra mathematical complication caused by non-stationarity. This article reinforces the validity of the existing Markov chain formulation of owner payments and its assumption of stationarity. The analysis presented, although based on case study data, can be translated to any project, provided data in the right form are available.

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#### Keywords

Markov chain, stationarity, transition probability, payment likelihood

DOI: http://dx.doi.org/10.21914/anziamj.v53i0.5111

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