I am trying to get EWMA volatility from a series of stock daily returns from a data frame called base_retorno_diario
Data IBOV ABEV3 AEDU3 ALLL3 BBAS3 BBDC3 BBDC4
1 2000-01-04 -0.063756245 0.00000000 0 0 -0.029935852 -0.080866107 -0.071453347
2 2000-01-05 0.024865308 -0.03762663 0 0 -0.008082292 0.043269231 0.060889055
3 2000-01-06 -0.008510238 -0.03157895 0 0 0.014074074 0.014285714 0.008098592
4 2000-01-07 0.012557359 -0.02484472 0 0 -0.022644266 0.017719219 0.000000000
5 2000-01-10 0.043716564 0.00000000 0 0 0.050074738 0.005357143 0.006985679
6 2000-01-11 -0.026401514 -0.02388535 0 0 -0.008540925 -0.059058615 -0.046479362
First row of the new data frame ( n_row
and n_col
is the number of rows and columns on the returns data frame base_retorno_diario
)
EWMA_VARIANCE = as.data.frame( base_retorno_diario[1,2:n_col]^2 )
then I created the following loop
i = 2
while(i<=n_row){
EWMA_VARIANCE = rbind(EWMA_VARIANCE,
EWMA_VARIANCE[(i-1), 1:(n_col-1)] * DECAY_FACTOR +
(1-DECAY_FACTOR) * base_retorno_diario[i,2:n_col]^2
)
i=i+1
}
It works fine but it is taking too long (the original data frame has 3560 obs of 101 variables), is there anyway to avoid the loop in this case ? DECAY_FACTOR = 0.97
You can avoid this loop with some matrix algebra. Let's assume the raw data is a vector (a_1, a_2, a_3, ..., a_n)
and we want to create the EWMA variance (x_1, x_2, x_3, ..., x_n)
according to your definition. Let d
be the decay factor. If i understood your code correctly, you currently have a recursive definition
which makes things difficult. I believe this non-recursive definition is identical
This allows us to take advantage of some linear algebra to get the job done with matrix multiplication. For brevity, I will assign shorter variable names to your data.frame and decay factor
dd <- base_retorno_diario
d <- DECAY_FACTOR
Now we begin by calculating all the squared values first, and then take the pairwise difference that we can see are part of the non-recursive definition.
asquare <- as.matrix(dd[,2:7])^2
asqdiffs <-sapply(data.frame(asq), diff)
Now we create an appropriate matrix with the values of d
to take are of the summing part of the non-recursive definition and then perform the subtraction (with a little offset for the initial term)
dx <- outer(1:nrow(asqdiffs), 1:nrow(asqdiffs), FUN=function(x,y)
ifelse(x>=y, d^(x-y+1),0 )
)
EWMA_VARIANCE <- asq - rbind(0, dx %*% asqdiffs)
This method seem to produce the same results are yours, but it is about 20x faster in my tests.
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