I'm trying to do a little research project on the seasonal behaviour of some stocks and I've run into a bit of a conundrum that I hope you can give me some quick advice on please! I wrote a small program to do some calcs and spit out some charts... my idea was to take around 15 years of daily data for a stock, tally up the % changes of each unique trading day of the year (ie. 7th trading day of April, 8th trading day, and so on), take the average (ie. arithmetic mean) of those 15 values and chart them to see if they have any predictive value.
At first, I tried using just the plain old Arithmetic Mean to find an "average" figure... you can see the charted result of that in attachment "seas-arithmean.jpg" - doesn't look too too bad (historical seasonal avg in yellow, actual stock price in green). Then I thought "well, maybe arithmetic mean is not quite the way to go here, as a few 'outliers' among the 15 %chg values could really skew things one way or the other", so I tried using the Median value instead. Well, that really threw everything for a loop as you can see in attached chart "seas-median.jpg".
I'm no statistician, so I decided to google up some research about minimum sample sizes for median and such. I found some sites recommending that median does not do very well at all with sample sizes less than 25, so I think I will forget about median. But while doing this research, it mentioned about Geometric Mean and Harmonic Mean. The same site that poo-poo'ed on median, said that for sample sizes of 25 or less, that Geometric Mean was shown to reflect the best "middle value" for all the types of means tested. Could I have your thoughts/recommendations on this please? Would Geometric Mean, in fact, be my best choice here? I really wouldn't be using any bigger a sample size than 25 years of history maximum - as any more than that would really be "ancient history" as far as the life of the stock is concerned and not really relevant to its current behaviour. Thanks very much!


Shawn

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