Henderson Filters in JavaScript

I wrote in a recent post that I’d added a function to calculate Henderson filters to the ssci.js library. This post will expand on that (slightly).

To quote the Australian Bureau of Statistics:

Henderson filters were derived by Robert Henderson in 1916 for use in actuarial applications. They are trend filters, commonly used in time series analysis to smooth seasonally adjusted estimates in order to generate a trend estimate. They are used in preference to simpler moving averages because they can reproduce polynomials of up to degree 3, thereby capturing trend turning points.

The filters themselves have an odd number of terms and can be generated for sequences of 3 terms and more. To use the function contained within the JavaScript library you can just use:

ssci.smooth.henderson(term)

where term is the number of terms you want to return. These are returned as an array. So if term was 5 you would get:
[
-0.07342657342657342,
0.2937062937062937,
0.5594405594405595,
0.2937062937062937,
-0.07342657342657342
]

The equation to generate the filters was taken from here.

To actually filter a set of data this would be combined with the ssci.smooth.filter() function i.e.:

var ft = ssci.smooth.filter()
.filter(ssci.smooth.henderson(23))
.data(data);

And here’s an example using the data from the kernel smoothing post.