Dollars and Jens
Thursday, July 16, 2009
Initial Claims -- general notes
Incidentally, let me give some love to Karl Smith, whose posts on initial claims inspired me to start paying attention to (and posting on) a series I followed religiously for several years until about a year and a half ago.

He, like most of the world, smoothes the series with a 4-week sliding-window average; I use a three-week exponential, which I discovered a few years back frequently gave a better prediction of the next number than the consensus forecast did, except in the immediate post-Katrina period. I dislike sliding-window averages in particular for anything in which I'm looking for a trend; "trend" suggests I'm looking at changes from one week to the next, and the change from one week to the next with a sliding window is just a multiple of the change from one week to the week four weeks later, so it's noisy and is affected by a fair amount of old information. The change in an exponential moving average is more plausibly the innovation in that moving average.

It happens that the exponential-moving average amounts to modeling the series as an ARIMA(0,1,1). If you don't know what ARIMA is, it doesn't really matter; I didn't know what ARIMA was when I started doing this, and didn't actually work out that that's what this was until about a week ago; playing around in the last week, I find as a fairly robust result that ARIMA(0,1,2) seems to fit the data better, though the coefficients change a fair amount if I try fitting different 2-year data samples to that model. (ARIMA(0,1,1) seems to bounce around a bit, too, though a coefficient corresponding to a 3-week average doesn't seem to get much more than one standard error from the estimate regardless of the sample I look at.) I may start using a smoothing technique based on an ARIMA(0,1,2) at some point.


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