Thresholds of moving averages of stationary processes for given target significant levels (Q964658)

Let \(X_n\), \(n\in Z\), be a stationary Gaussian process, and \(Y_n=k^{-1}\sum_{i=0}^{k-1} X_{n-i}\) be its moving average. The authors consider a chain \(V_n\) of states defined by \(Y_n\in I_j=\{x: L_j\leq | x| \leq L_{j+1}\}\), where \(L_j\) are some non-random thresholds. It is shown that \(V_n\) is a Markov chain with transition probabilities independent of \(k\). Equations are derived connecting \(L_j\) with given stationary probabilities \(\pi_i\) of the chain \(V_n\). First-order autoregression and moving averages \(X_n\) are considered as examples.