Unmasking spurious correlation induced by apparent similarities in means is the subject of this secttion. We have two series , the Y variable is upward trending while the X variable is a 0/1 variable respesenting two states of nature. Sometimes this kind of a variable (binary) is used to represent law changes , before and after.

A plot of the two series.

The statistically significant regression.

After one augments the regression model with a model for the errors the spurious significance goes away.

Finally in first differences we conclude about the unmasking of the spurious relationship.

Estimating a combined regression and noise model we find that the input series X is not significant. We can then conclude that we have unmasked the spurious correlation between these two series.

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