Simulate AR(p) model
Auto-regressive (AR) models are a type of linear regression for time series where the predicted values depend upon the values at previous time points. Due to this dependence on previous time points, the model must be calculated one time point after another. That means using a for loop, so C++ comes in handy!
Here's the algorithm in R:
ar1 <- function(n, constant, phi, eps) {
p <- length(phi)
x <- numeric(n)
for(i in seq(p + 1, n)) {
value <- rnorm(1, constant, eps)
for(j in seq_len(p)) {
value <- value + phi[j] * x[i - j]
}
x[i] <- value
}
x
}
n is the number of simulated observations, c is a constant, phi is a numeric vector of autocorrelation coefficients, and eps is the standard deviation of the noise. Complete the definition of ar2(), a C++ translation of ar1().
Questo esercizio fa parte del corso
Optimizing R Code with Rcpp
Istruzioni dell'esercizio
- Generate a normally distributed random number with mean
cand standard deviationeps, using Rcpp's R API. - Make the inner for loop iterate from
0top. - Inside the inner loop, increase
valueby thejth element ofphitimes the "i minus j minus 1"th element ofx.
Esercizio pratico interattivo
Prova a risolvere questo esercizio completando il codice di esempio.
#include
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector ar2(int n, double c, NumericVector phi, double eps) {
int p = phi.size();
NumericVector x(n);
// Loop from p to n
for(int i = p; i < n; i++) {
// Generate a random number from the normal distribution
double value = ___::___(___, ___);
// Loop from zero to p
for(int j = ___; j < ___; j++) {
// Increase by the jth element of phi times
// the "i minus j minus 1"th element of x
value += ___[___] * ___[___];
}
x[i] = value;
}
return x;
}
/*** R
d <- data.frame(
x = 1:50,
y = ar2(50, 10, c(1, -0.5), 1)
)
ggplot(d, aes(x, y)) + geom_line()
*/