Calculate the autocorrelation of an MA(q) filter applied to a stationary process.

Calculate the autocorrelation of an MA(q) filter applied to a stationary process.

ma_acf(acf, rho = numeric())

Arguments

acf

Vector of length N + q of autocorrelations of the original stationary process.

rho

Vector of q >= 0 coefficients of the MA(q) filter (see 'Details').

Value

A vector of length N giving the autocorrelation of the filtered process.

Details

Let X_n denote the observation of the original process at time n, and Y_n denote the corresponding observation of the filtered process. The MA(q) filter model is defined as

Y_n = X_n + sum_{j=1}^q rho_j X_{n-j}.