Computing Quadratic Variation in R

Question

In order to compute the quadratic variation of a timeseries in R, I would like to to sum for every point the square of log returns of the current point and the last x points.

I know that you can build the square of log returns of py by typing

diff(log(py))^2

However how can I build a timeseries which is summing at every point the last 5 points in order to build the quadratic variation ?

Answer 1

The function embed combined with rowSums gives what you need:

cbind(
  AirPassengers, 
  sum5=c(rep(NA, 4), rowSums(embed(AirPassengers, 5)))
)

         AirPassengers sum5
Jan 1949           112   NA
Feb 1949           118   NA
Mar 1949           132   NA
Apr 1949           129   NA
May 1949           121  612
Jun 1949           135  635
Jul 1949           148  665
...

---

What embed does is to create a matrix with lagged values of your initial vector:

embed(AirPassengers, 5)
       [,1] [,2] [,3] [,4] [,5]
  [1,]  121  129  132  118  112
  [2,]  135  121  129  132  118
  [3,]  148  135  121  129  132
  [4,]  148  148  135  121  129
  [5,]  136  148  148  135  121
  [6,]  119  136  148  148  135
  [7,]  104  119  136  148  148
  [8,]  118  104  119  136  148
  ...

You can them use rowSums or any other manipulation on the rows of this matrix.