Testing homogeneity over time of a parameter of a markov sequence
We develop the score test for the hypothesis that a parameter of a Markov sequence is constant over time, against the alternatives that it varies over time, i.e., θt = θ + Ut; t = 1,2,…, where {Ut; t = 1,2,...} is a sequence of independently and identically distributed random variables with mean zero and variance σz u and θ is a fixed constant. The asymptotic null distribution of the test statistic is proved to be normal. We illustrate our procedure by examples and a real life data analysis.