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Exercise

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().

Instructions

100 XP
  • 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.