simple examples of filter function, recursive option specifically

Question

I am seeking some simple (i.e. - no maths notation, long-form reproducible code) examples for the filter function in R I think I have my head around the convolu

Answer 1

With recursive, the sequence of your "filters" is the additive coefficient for the previous sums or output values of the sequence. With filter=c(1,1) you're saying "take the i-th component in my sequence x and add to it 1 times the result from the previous step and 1 times the results from the step before that one". Here's a couple examples to illustrate

I think the lagged effect notation looks like this:

## only one filter, so autoregressive cumsum only looks "one sequence behind"
> filter(1:5, c(2), method='recursive')
Time Series:
Start = 1 
End = 5 
Frequency = 1 
[1]  1  4 11 26 57

1 = 1
2*1 + 2 = 4
2*(2*1 + 2) + 3 = 11
...

## filter with lag in it, looks two sequences back
> filter(1:5, c(0, 2), method='recursive')
Time Series:
Start = 1 
End = 5 
Frequency = 1 
[1]  1  2  5  8 15

1= 1
0*1 + 2 = 2
2*1 + 0*(0*1 + 2) + 3 = 5
2*(0*1 + 2) + 0 * (2*1 + 0*(0*1 + 2) + 3) + 4 = 8
2*(2*1 + 0*(0*1 + 2) + 3) + 0*(2*(0*1 + 2) + 0 * (2*1 + 0*(0*1 + 2) + 3) + 4) + 5 = 15

Do you see the cumulative pattern there? Put differently.

1 = 1
0*1 + 2 = 2
2*1 + 0*2 + 3 = 5
2*2 + 0*5 + 4 = 8
2*5 + 0*8 + 5 = 15