Simple Graphical Techniques for Calculating Serial and Spatial Correlations, and Mean Semi-Squared Differences

Abstract

Summary Two methods of calculating these lag statistics from the graph of a series are described. One, the slide method, uses a scale printed on a glass plate; the other, the tracing method, requires no special apparatus. Both methods give results which are accurate enough for most needs. They may be used for evenly or unevenly spaced series, and are readily adapted to the analysis of concomitant and spatial series. For evenly spaced series, which alone are conveniently analysed on a desk calculator, the graphical methods compare favourably with it in speed. The tracing method is much quicker when the statistics are required for a large number of lags.

Least Squares Regression Analysis for Trend-Reduced Time Series

“…In Fig. 3 are shown the variograms, computed graphically by the method described in Jowett and Scott (1953) of the coal (x) series, and of the series of residuals from the fitted regression line. In spite of their downward bias as estimates of a( )CD, the calculated variances tend to be high relative to the longer term serial variation statistics, suggesting that flattening out has not been attained at s = 25, and perhaps not even at s = 50.…”

“…While tables for the least-squares fitting of Markoff serial variation functions in the neighbourhood of the origin, though being computed, are not yet available, it is usually sufficient to calculate serial variation statistics for lags of, say, I, 2, 3, 4, 5, 10, 15, 25 and perhaps 50, to plot the logarithm of the variograms, and to try various curves of the family (cf Jowett (1955» log Os = log (I -p8) + const.…”

“…This formula may also be used with the series x(t), yet) to give statistics for thecalculated residuals eel). These statistics may be computed simultaneously in two runs through using a modified form of the tracing method given by Jowett and Scott (1953).…”