psd - Comparing models and data Suppose we would like to...

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Comparing models and data Suppose we would like to see whether output is more or less volatile than investment We want a measure of volatility that is invariant to scale Simple variance or standard deviation is not scale invariant Suppose for example that investment is a constant fraction λ of GDP x = λy Now sd ( x )= λsd ( y ) A simple remedy would be rescale both variables by their mean prior to computing the standard deviation sd ( x µ x )= 1 µ x sd ( x )= 1 λµ y λsd ( y )= sd ( y µ y ) Now if we have variables that are non-stationary we need to apply some sort of f lter prior to computing measures of dispersion. Suppose x gt is the value of the growth component at t, and x ct = x t x gt is the value of cyclical component Now rather than dividing by the mean, we should divide by the trend prior to computing the standard deviation The percentage standard deviation of the f ltered series is given by % sd ( x ct ) = 100 × sd μ x ct x gt In our simple example, if our
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This note was uploaded on 11/10/2011 for the course ECON 601 at Cornell University (Engineering School).

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psd - Comparing models and data Suppose we would like to...

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