Note that the purpose of the lag length is to eliminate
all residual autocorrelation, so that the ADF tests can function properly.
All 741 regressions had
a residual autocorrelation of about 1.0 x e ^ -15
Models were tested to ensure a lack of
residual autocorrelation using the Ljung - Box portmanteau statistic [30], which indicated that all models discussed below had no residual structure (p ≥ 0.234).
Below I have linked to the images of the plots for anomaly trend, residual plots and
residual autocorrelation (AR1) for the monthly, annual, January and June GISS NH temperature series for the time periods 1880 - 2007 and 1979 - 2007.
When I get the chance, I'll run this through Cochrane - Orcutt iteration to account for
residual autocorrelation.
Not exact matches
There was some
autocorrelation of the
residuals, indicating that periods of under - and out - performance of equities over bonds tends to persist:
The estimator can be used to try to overcome
autocorrelation and heteroscedasticity of the
residuals, which can impact the standard errors and thus the calculated t - statistics and p - values.
In Exhibit 2, the sample
autocorrelation function shows significant
autocorrelation in the squared
residual series, calculated by the square of daily total return of the S&P 500 subtracted by the long - term average daily return.
The
autocorrelation structure might need a bit more work to accommodate long and short term serial correlation in
residuals.
If the
residual series generated by a model show no significant
autocorrelation, as tested by Ljung - Box portmanteau statistics, then they are not distinguishable from white noise — a covariance stationary process.
From what I can tell, the statistical model used (sorry if I'm mistaken about this) doesn't allow for
autocorrelation of
residuals and simply treats El Nino and all other forms of internal variability as white noise.
I found this, http://www.xplore-stat.de/tutorials/xegbohtmlnode18.html, but it doesn't seem to match with Parker's «taking into account
autocorrelation in the
residuals».
Spatial
autocorrelation (SAC) in the observed trend pattern is removed from the
residuals by a well - specified explanatory model.
I then used the
residuals and calculated the correlation, r, for AR1
autocorrelation and the goodness of fit of the
residuals to a normal distribution.
By the way, there are striking differences in the appearance of the plots of the
residuals of the regressions (not what you requested here) that make it rather easy to predict which will show better fits to a normal distribution and have less AR1
autocorrelation.
I have heard lately is a lot about the lack of temperature series fit to normal distributions and the presence of
autocorrelation in the
residuals of temperature anomalies and this post and some simple - minded analyses raise some questions in my mind.
We adjusted both the sample size and the degrees of freedom for indexing of the critical t - value according to the lag - 1
autocorrelation of the regression
residuals.
I also recall that the RSS and UAH temperature annual temperature anomaly series
residuals had little or no
autocorrelation (AR1) in the time period 1979 - 2007.
That is what makes the regression
residuals the important element in determining the
autocorrelations and goodness of fit to normal distribution.
I calculated the Durbin Watson statistic (DW) for
autocorrelation for the GISS time series 1979 - 2007 (using the
residuals from the anomaly regression) for monthly data and determined a DW = 0.83 indicating a strong positive
autocorrelation.
Looking at these results, that are admittedly anecdotal at this point, I see generally better fits to a normal distribution and lower
autocorrelation (AR1) in the
residuals as one goes from monthly to individual months to annual data series and as one goes to sub periods of a long term temperature anomaly series.
I have not done the monthly lag correlations for RSS, but when I did it for the GISS data 1979 - 2007, the DW statistic on the regression
residuals showed a very significant positive
autocorrelation.
Please note that when I subject an OLS regression of dT on ln CO2 for 1880 - 2008, and then perform Cochrane - Orcutt iteration on it to compensate for
autocorrelation in the
residuals, I still wind up with 60 % of variance accounted for when rho has dropped to an insignificant level.
Satisfaction of the assumption of a first - order Markov process was assessed by examination of the
residuals of the lag - 1 regression, which were found to exhibit no further significant
autocorrelation.
Uncertainty is estimated by the variance of the
residuals about the fit, and accounts for serial correlation in the
residuals as quantified by the lag - 1
autocorrelation.
But if you look at the
residuals and test for the presence of
autocorrelation you'll get very strong evidence that the error term is autocorrelated.
First Schmidt claims that M&M ought to have allowed for spatial
autocorrelation, but appears to have confused
autocorrelation in the dependent variable, which is not per se a problem, with
autocorrelation in the
residuals of the regression, which would be a problem if it existed in M&M.
McKitrick: Yes, but there is no spatial
autocorrelation in hte model
residuals, and that's the issue.