arima

This is what Ritson is criticizing, arguing that application of a standard arima function to a tree ring network without previously removing trends is incorrect.

More Tangled Webs « Climate Audit 2006

A typical command might look like arima(yourdata,order=c(2,0,1)) (this corresponds to an ARMA(2,1)).

Climate Models – the Next Generation « Climate Audit 2006

If you do an elementary arima fit on the residuals, one gets highly significant ARMA1,1 coefficients relative to the standard errors of the estimates:

Juckes – Meet the Durbin-Watson Statistic « Climate Audit 2006

To set parameters for the simulation, we calculated AR1 coefficients on the North American AD1400 tree ring network using a simple application of the arima function in R:

More Tangled Webs « Climate Audit 2006

The arima structure of the PDI data is quite different as shown below, with an insignificant coefficient modeled as AR1, but highly significant ARMA(1,1), but, in this case, anti-persistent (-0.5762,0.7738):

More bender and Willis on Emanuel « Climate Audit 2006

If one simply used AR1 coefficients from the function arima(x,order=c(1,0,0)), you get a HS effect from red noise.

Climate Models – the Next Generation « Climate Audit 2006

The xreg parameter in arima is used to specify the matrix of regressors.

More on MBH98 Figure 7 « Climate Audit 2006

In arima, d refers to the number of times the series is differenced before the ARMA model is fit; in fracdiff, d is a coefficient that must be fitted simultaneously with the ARMA model thus one does not specify d in the case of fractional differencing; its value is returned as part of the result.

Climate Models – the Next Generation « Climate Audit 2006

If you correctly specified the model as ARMA1,1, estimates of the AR1 coefficient using standard arima function in R were 0.8-.93, all pretty reasonable.

THe Ritson Coefficient « Climate Audit 2006

I also understand standard deviation, standard error, R2, arima models, the law of large numbers, skew, kurtosis, the Jarque-Bera test for normality, autocorrelation, and the power content of complex signals.

Jones et al [1998]: Confidence Intervals « Climate Audit 2005