Least Squares Regression Analysis for Trend-Reduced Time Series

Abstract

THE difficulties of obtaining a valid estimate of the standard error of a regression coefficient between two time series are discussed. It is shown how a preliminary trend-reducing operation on the series, using a moving average, makes it possible to obtain such a valid estimate. A method of analysis is described, along with considerations which affect the best choice of moving average for the purpose, which is applicable when the local variational properties of the series resemble those of Markoff series. JOWETT-Least Squares Regression[Part I,

Sampling Properties of Local Statistics in Stationary Stochastic Series

“…Jowett, 1952) or a trend-reduced regression coefficient (Jowett, 1955a} which are functions of local comparisons alone, and suggests that the sampling properties of statistics which are built up entirely from local comparisons are essentially determined by the local variational properties (e.g. It is this which gives rise to the differencing in (4), which makes the formula, independent of C-2, and hence expressible entirely in terms of 8, and which enables var U to be estimated in many circumstances where it would be impossible to estimate var T. A corresponding property has been observed in other statistics, such as the mean of a systematics ample (cf.…”