Simulate MA(q) model

Moving average (MA) models also depend upon the previous iteration. Unlike AR models, the dependency is on the noise part.

Here's the algorithm in R:

ma1 <- function(n, mu, theta, sd) {
  q <- length(theta)
  x <- numeric(n)
  eps <- rnorm(n, 0, sd)
  for(i in seq(q + 1, n)) {
    value <- mu + eps[i]
    for(j in seq_len(q)) {
      value <- value + theta[j] * eps[i - j]
    }
    x[i] <- value
  }
  x
}

n is the number of simulated observations, mu is the expected value, theta is a numeric vector of moving average coefficients, and sd is the standard deviation of the noise.

Earlier in the chapter, you used R::rnorm() to generate a single number from a normal distribution. There is also Rcpp::rnorm(), which can generate a whole numeric vector worth in one go. This takes the same arguments as R's rnorm(). Complete the function definition of ma2(), a C++ translation of ma1().

Generate the noise vector as eps. Use rnorm() from the Rcpp namespace (not the R namespace).
Inside the outer for loop, calculate value as mu plus the ith noise value.
Inside the inner for loop, increase value by the jth element of theta times the "i minus j minus 1"th element of eps.
After the loops, set ith element of x to value.

Exercise

Simulate MA(q) model

Instructions