st: tssmooth hw smoothing - not synchronised?

[Dave Mare <dave.mare@motu.org.nz>]

I have been using the Holt Winter smoothing algorithm available in tssmooth.  The smoothed series that I create seem to be one period out, and slightly inflated relative to the original series.  

The following code reproduces the problem:

webuse bsales, clear
tssmooth hwinters hw1=sales
tsline sales hw1 /* looks unsynchronised */

gen fhw1=f.hw1
tsline sales fhw1 /* looks synchronised, but slightly inflated */

/** The impact of the problem is evident in the following graphs: */
/** I repeatedly smooth the smoothed series */
foreach n of numlist 2 (1) 10 {
	local p=`n'-1
	tssmooth hwinters hw`n'=hw`p', iter(30) /* fails to converge for some - perhaps unsurprisingly! */
	gen fhw`n'=f`n'.hw`n'
	}

/** Here are the smoothed series, showing the increasing misalignment */
tsline sales hw*

/** However, if I use the realigned series, the level is increasingly inflated */
tsline sales fhw*

Am I doing something wrong?

Dave Mare

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