Casualty and Error Correction in Markov Chain: Inflation in India Revisited

The present paper proposes certain statistical tests, both conceptually simple and computationally easy, for analysing state-specific prima facie probabilistic causality and error correction mechanism in the context of a Markov chain of time series data arranged in a contingency table of present versus previous states. It thus shows that error correction necessarily follows causality (that is temporal dependence) or vice versa, apparently suggesting that the two represent the same aspect! The study also yields a simple estimate of steady state probabilities of a Markov chain from such time-series data, useful when the number of states considered is very large. The result is applied to an analysis of inflation in India during the last three decades separately and also together based on the monthly general price level (WPI - all commodities) and 23 constituent groups/items, as well as on the three consumer price index (CPI) numbers.