Forecasting Time Series

Chaos

Iteratng a Map

iterate <- function(n, f, x0, ...)
{
    x <- rep(NA, n)
    x[1] <- x0

    for (i in 1:(n-1)) {
        x[i+1] <- f(x[i], ...)
    }

    x
}

Linear Map

f <- function(x, alpha)
{
    alpha * x
}

alpha = +0.7

plot(iterate(30, f, x0=0.1, alpha=0.7), type="b", col=2)

alpha = -0.7

plot(iterate(30, f, x0=0.1, alpha=-0.7), type="b", col=2)

alpha = +1.7

plot(iterate(30, f, x0=0.1, alpha=1.7), type="b", col=2)