autocovariance

When the process is not variance stationary the autocovariance is not even defined.

Climate Insensitivity and AR(1) Models « Climate Audit 2007

It is well known that the classical estimators of the autocovariance are biased even when the process is stationary; even for series of length 100–200 this bias can be surprisingly large.

Climate Insensitivity and AR(1) Models « Climate Audit 2007

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.

Climate Models – the Next Generation « Climate Audit 2006

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

Climate Models – the Next Generation « Climate Audit 2006

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

Climate Models – the Next Generation « Climate Audit 2006

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

Climate Models – the Next Generation « Climate Audit 2006

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

Climate Models – the Next Generation « Climate Audit 2006

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.

Thompson et al [1993] on Dunde « Climate Audit 2005