Friday, December 10, 2010

Autocorrelation in Presidential Approval Ratings

Corrections examined President Obama's Approval Ratings and noticed that they appeared more noisy than white noise, e.g. that they were negatively autocorrelated.  They are displayed graphically below (click to enlarge):
To check that they were too noisy, we graphed out the distribution of "up up", "up down" "down up", etc. in a contour plot, where "darker" means more density, and "lighter" means less density.  A "-1" means down, a "0" means same, and "1" means up.  Therefore, "Same Up happens 5% of the time" would correspond to "x=0 y=1 z=.05".  This is displayed graphically below (click to enlarge).  As a reader can see, most of the time approval ratings stay the same.  But the point is that we have skew--rarely do we get "up up" or "down down", the upper right and lower left corners, respectively. 
The main point here is that for reasons inexplicable to Corrections, a "down" tick is more likely to be met by an "up" tick than a noisy process would predict.  We posit this warrants further analysis.  Suggestions as to causes are welcome.

Update: Upon further reflection, Corrections suggests this is likely due to the absence of a unit root with noise.  That is, every movement we see is one of two types.  The first is a "real" movement.  The second is a "noisy" movement.  Noisy movements are transitory and likely to disappear.  Real movements are permanent, in expectation (letting opinions be a random walk, for example).  Any movement due to noise will likely go away next period--up noise will be met with down, and down will be met with up.  This explanation doesn't completely satisfy Corrections, but it seems relevant. 

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