3.5 Two simple and classic time series models

White noise: \(x_t \sim N(0,1)\)

par(mai = c(0.9, 0.9, 0.1, 0.1), omi = c(0, 0, 0, 0))
matplot(ww, type = "l", lty = "solid", las = 1, ylab = expression(italic(x[t])), 
    xlab = "Time", col = gray(0.5, 0.4))

Random walk: \(x_t = x_{t-1} + w_t,~\text{with}~w_t \sim N(0,1)\)

par(mai = c(0.9, 0.9, 0.1, 0.1), omi = c(0, 0, 0, 0))
matplot(apply(ww, 2, cumsum), type = "l", lty = "solid", las = 1, 
    ylab = expression(italic(x[t])), xlab = "Time", col = gray(0.5, 
        0.4))