More and more environmentalist are having to admit that earth's warming is not at alarming levels, proving the hoax of the Alarmist warming crowd, and validating true and objective science.

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After you read the following "Conclusion,"   you won’t have a clue.  So,  let me simplify:  the climate models used to sustain the Alarmists' Warming debate,  do not match data collected from atmospheric observation.  In fact, warming trends are  “not statistically different from zero in either [atmospheric] . . . .   layers.”  So goes statements in the “Conclusion,” presented below.  In the preface of the same article,  we have this confirming statement:  Model overestimation of warming is significant whether or not we account for a level shift, although null rejections are much stronger when the level shift is included. © 2014 The Authors. Environmetrics published by John Wiley & Sons, Ltd." 

 

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CONCLUSIONS  (taken from this Wiley Online Library, here,  as it reproduces an critical article from Environmetrics,  the official journal of the International Environmetrics Society.  This is as authoritarian a climate science document as there is.  In the article,  we find the authors are forced to admit certain “matrix estimators” do not support the more drastic warming trends of the Alarmists.  I do not use the word,  “disprove” because such is not included in the referenced article,  but,  of course, that is what is being suggested.  ~  blog editor. 

 

Heteroskedasticity and autocorrelation robust (HAC) covariance matrix estimators have been adapted to the linear trend model, permitting robust inferences about trend significance and trend comparisons in data sets with complex and unknown autocorrelation characteristics. Here, we extend the multivariate HAC approach of Vogelsang and Franses (2005) to allow more general deterministic regressors in the model. We show that the asymptotic (approximating) critical values of the test statistics of Vogelsang and Franses (2005) are nonstandard and depend on the specific deterministic regressors included in the model. These critical values can be simulated directly. Alternatively, a simple bootstrap method is available for obtaining valid critical values and p-values.

The empirical focus of the paper is a comparison of trends in climate model-generated temperature data and corresponding observed temperature data in the tropical troposphere. Our empirical innovation is to make the trend model robust to the possibility of a level shift in the observed data corresponding to the PCS that occurred around 1978. With respect to the Vogelsang and Franses (2005) approach, this amounts to adding a level shift dummy to the model that requires a new set of critical values that we provide.

As our empirical findings show, the detection of a trend in the tropical lower troposphere and mid-troposphere data over the 1958–2012 interval is contingent on the decision of whether or not to control for a level shift coinciding with the PCS. If the term is included, a time trend regression with autocorrelation-robust error terms indicates that the trend is small and not statistically different from zero in either the LT or MT layers. Also, most climate models predict a significantly larger trend over this interval than is observed in either layer. We find a statistically significant discrepancy between the average climate model trend and observational trends whether or not the mean-shift term is included. However, with the shift term included, the null hypothesis of trend equivalence is rejected much more strongly (at much smaller significance levels).

Regarding the question of preferred specification (that is, whether to include a shift or not), where the researcher suspects a break has occurred, results ought to be robust to controlling for the possibility. In the multivariate tests, when we fix the break at 1977:12, the shift terms are not significant in either level, but when we use the grid search method, the shift is significant at 10% in the LT layer and at 5% in the MT layer. Because breaks are harder to identify than trends, these findings indicate the importance of controlling for the possibility that one is present.

The testing method used herein is both powerful and relatively robust to over-rejections under the null hypothesis caused by strong serial correlation. The power of the test is indicated by the span of test scores in Table 8 in which relatively small changes in modeled trends translate into smaller p-values. Using the data-mining method provides a check on the extent to which the results depend on the assumption of a known shift date.

As such, our empirical approach has many other potential applications on climatic and other data sets in which level shifts are believed to have occurred. Examples could include stratospheric temperature trends that are subject to level shifts coinciding with major volcanic eruptions and land surface trends where it is believed that the measuring equipment has changed or was moved. Generalizing the approach to allow more than one unknown break point is left for subsequent work.