Subset ARMA model identification using genetic algorithms (Q2742780)

A zero-mean stationary process \(\{X_t\}\) is said to be a subset ARMA(k,i) model, \(k=(k_1,\dots,k_p)\), \(i=(i_1,\dots,i_q)\), with \(k_1<\dots<k_p\) and \(i_1<\dots<i_q\), if it satisfies the equation NEWLINE\[NEWLINEX_t-a_{k_1}X_{t-k_1}-\dots-a_{k_p}X_{t-k_p}= W_t-b_{i_1}W_{t-i_1}-\dots-b_{i_q}W_{t-i_q},NEWLINE\]NEWLINE where \(W_t\) is a white noise with zero mean and variance \(\sigma ^2>0\). In this paper, a selection procedure for subset ARMA models is developed. The procedure is based on innovation regression methods and stochastic binary search algorithms (genetic algorithms). After encoding each ARMA model as a binary string, the iterative algorithm attempts to mimic the natural evolution of the population of such strings to reproduce, creating new models that compete for survival in the next population. The performance of the proposed procedure is illustrated by identifying the true model for simulated and real data.