A marginal contribution coefficient for sequences of nonstationary continuous Markov chains

Abstract

In this work, a set of sequences of information (time series), under nonstationary regime, with continuous space state, discrete time, and a Markovian dependence, is considered. A new model that expresses the marginal transition density function of one sequence as a linear combination of the marginal transition density functions of all sequences in the set is proposed. The coefficients of this combination are denominated marginal contribution coefficients and represent how much each transition density function contributes to the calculation of a chosen transition density function. The proposed coefficient is a marginal coefficient because it can be computed instantaneously, and it may change from one time to another time since all calculations are performed before stationarity is reached. This clearly differentiates the new coefficient from well‐known measures such as the cross‐correlation and the coherence. The idea behind the model is that if a specific sequence has a high marginal contribution for the transition density function from another sequence, the first may be replaced by the latter without losing much information that means that the knowledge of few densities should be enough to recover the overall behaviour. Simulations, considering 2 chains, are presented so as to check the sensitivity of the proposed model. The methodology is also applied to a real data originated from a wire‐drawing machine whose main function is to decrease the transverse diameter of metal wires. The behaviour of the level of acceleration of each bearing in relation to the other ones is then verified.