Unit 21 Forecasting

Some helpers:

tswgen <- function(n, sn = 0) {
    sig <- function(...) {
        gen.sigplusnoise.wge(n = n, ..., sn = sn)
    }
    ari <- function(..., dif) {
        gen.arima.wge(n = n, ..., sn = sn)
    }
    aru <- function(...) {
        gen.aruma.wge(n = n, ..., sn = sn)
    }
    
    arma <- function(...) {
        gen.arma.wge(n = n, ..., sn = sn)
    }
    list(sig = sig, ari = ari, aru = aru, arma = arma)
}

21.1 Forecasts from Signal-Plus-Noise

\[X_t = s_t + Z_t\] Where:

• \(s_t\) is a deterministic signal
• \(Z_t\) is a zero-mean, stationary process

Examples:

• \(s_t = a + b t\) is a linear signal

• \(s_t = a + b t + c t^2\) is a quadratic signal

• \(s_t = \cos \left(2 \pi f t + C \right)\)