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Desmooth_AR1

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Returns an array corresponding to the AR(1) de-smoothed (or ‘de-correlated) values of a series, as described in the book Extreme Events. This involves:

 

(a)    Postulating (for, say, a return series) that there is some underlying ‘true’ return series, , and that the observed series, , derives from it via a first order autoregressive model, ;

 

(b)   Identifying the value of  (between 0 and 0.5) for which  has zero first order correlation (which implies that the covariance between  and  is zero; and

 

(c)    Using this value of  deriving  using the following formula:

 

 

The value of  in (b) can be accessed using MnDesmooth_AR1_rho.

 

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