The Pearson correlation coefficient is frequently used in measuring time series temperature persistence. If the data are analyzed in standardized form, the coefficient is equivalent to the sum of all the individual z-score products divided by the sample size (N). With the observations in this form, the coefficient can be mechanically “decomposed” further into “above normal persistence” and “below normal persistence” values by substituting z-score product summations from appropriate subsets in the numerator but retaining N in the denominator. For example, "above normal" persistence would use in the numerator only a z-score product summation from those observations in which the leading temperature series had a positive z-score. "Below normal" persistence would use only those observations in which the lead series had a negative z-score. The sum of the "above normal" and "below normal" persistence values would yield the original correlation coefficient. A large difference in magnitudes between the two might suggest of a natural inherent tendency of one predominating over the other.

Using this method, the annual course of successive 30-days’ temperature persistence (overall, above normal, and below normal) is explored at one-day intervals (moving array of 365 correlations) for four U.S. stations with lengthy periods of record. These are New York City Central Park (125 years), Minneapolis-St. Paul (128 years), Salt Lake City (71 years), and the Los Angeles Civic Center (80 years). The analysis is done with linear trend removed.

To gauge the rough significance of the above normal/below normal persistence magnitude differences, a table of standard errors is utilized based on simulation-generated z-score data sets over a range of built-in correlations and sample sizes. The intepretation of the differences is necessarily complicated by the issues of multiple comparisons and using moving, overlapping time-series.

The four stations show a variety of patterns, overall correlations ranging from slightly less than .00 to near +.60, with discrepancies in above normal and below normal persistence magnitudes as high as .17.