Definitions
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 noun statistics The
covariance of asignal with another part of the same signal
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When the process is not variance stationary the autocovariance is not even defined.

It is well known that the classical estimators of the autocovariance are biased even when the process is stationary; even for series of length 100200 this bias can be surprisingly large.

Posted Oct 7, 2006 at 12:27 PM  Permalink  Reply looking at the definitions in waveslim, hoskings.sim asks for the “autocovariance sequence” or acvs.

Then the only question is how exactly are these autocovariance functions being estimated.

What hosking.sim does is generate random simulations of a process that has a certain autocovariance structure.

The autocovariance structure is passed to the function hosking.sim as one of its parameters.

I suspect that what is being passed is the autocovariance function of the 70 NOAMER series.

Fitting an AR(p) to the residuals and using it to compute the autocovariance matrix is a big improvement, though even that still understates the adjustment, even if the errors themselves are AR(p) — the residuals will show less s.c. than the errors, and even if we saw the errors, OLS estimates of AR are biased in finite samples away from persistence.
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