Dynamic forecasting the data.table way? - r

Question

I need to create dynamic forecast using
v(t) = b0 + b1*v(t-1) + b2*v(t-2) + b3*x(t-1) + b4*x(t-2)
The dataset looks like this at time 0. In actual data, there are 80 different x's and 100K "dates".
date v vLag1 vLag2 x xLag1 xLag2 b1 b2 b3 b4
2016-06-30 NA 105 95 33 11 23 0.2 3.2 -1.2 0.4
2016-07-01 NA NA NA 43 33 11 0.2 3.2 -1.2 0.4
2016-07-02 NA NA NA 52 43 33 0.2 3.2 -1.2 0.4
The goal is to predict v's, replacing all NA's with values. I created vLag1, vLag2, xLag1, xLag2 so that I have all I need to calculate v in one row.
All x's and b's are known ahead of time, so I created lags of x shown above. The b's are the coefficients.
For each date, the v(t) would be predicted, and the predicted v(t)'s will feed into the next date's v prediction as the lagged regressors.
To avoid looping over rows like this:
for (i in 2:nrows){
df$v[i] <- df$v[i-1] * df$coeff[i]
}
I have tried to use repeated substitution, so that all the future v's only reference v1, which is easy to calculate because v1's calculation involves other values in the same row.
v2 = b0 + b1*v1 + b2*v0 + b3*x1 + b4*x0
v3 = b0 + b1*v2 + b2*v1 + b3*x2 + b4*x1
(substitute v2) v3 = b0 + b1*(b0 + b1*v1 + b2*v0 + b3*x1 + b4*x0) + b2*v1 + b3*x2 + b4*x1
v4 = ...
But with so many lags of v's and x's to keep track, this also got out of control.
I have been browsing the data.table's shift function in SO. But, in my case, where the the values need to be dynamically obtained and then shifted, is there any way to dynamically predict in data.table's functions?

Answer 1

Instead of data.table (where you can't do this easily) this looks like an easy job for Rcpp:
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
NumericVector dyn_fore(const NumericVector x,
const double v1, const double v2,
const double x1, const double x2,
const double b0, const double b1, const double b2,
const double b3, const double b4) {
int n = x.size();
NumericVector v(n);
v(0) = b0 + b1*v1 + b2*v2 + b3*x1 + b4*x2;
v(1) = b0 + b1*v(0) + b2*v1 + b3*x(0) + b4*x1;
for (int i = 2; i < n; i++) {
v(i) = b0 + b1*v(i-1) + b2*v(i-2) + b3*x(i-1) + b4*(i-2);
}
return v;
}
(If you use Windows, make sure you have a working Rtools installation, put this in an C++ File in RStudio and source it. Check if I got coefficients and indices right.)
Then in R:
x <- c(33, 43, 52, 67)
dyn_fore(x, 105, 95, 11, 23, 0, 0.2, 3.2, -1.2, 0.4)
#[1] 321.00 365.00 1048.60 1315.72