The Comparison of Means of Sets of Observations from Sections of Independent Stochastic Series

Abstract

SUMMARY A method of applying the formula for the sampling variance of the mean of a section of stationary time series, using an analysis of half the squared differences between sample values, is developed. The formula and method are generalized for application to the comparison of means of several independent stretches of series, with and without superimposed systematic patterns of variation, and to more general series such as spatial configurations of data. The methods are applied to some observed series.

Statistical Process Monitoring and Feedback Adjustment: A Discussion

“…The quantities G(m) plotted in Figure 3 as functions of m are the (standardized) variograms (e.g., Cressie 1988;Jowett 1952Jowett , 1955.…”

A Joint Portmanteau Test for Conditional Mean and Variance Time‐series Models

“…Both methods can be seen as extensions of usual heteroskedasticity and autocorrelation consistent (HAC) robust estimation of asymptotic covariance matrices of regression coefficients. The first reference proposes using non‐parametric spectral estimates as originally developed by Jowett , Hannan , and Brillinger and later popularized by Newey & West in the econometrics literature, while the second one uses a vector autoregression (VAR) approximation to build the spectral estimates as suggested by, for example, Den Haan & Levin following early ideas in Press & Tukey , Blackman & Tukey , and Grenander & Rosenblatt .…”

Jump Analysis

“…The statistic B C is a member of a class of statistics called local statistics, the general sampling properties of which have been discussed in Jowett (1955 a). It is a function of local comparisons, being a mean square of differences involving adjacent groups of terms of the series, and therefore its sampling formulae are dominated by terms involving d(r) for values of r which are small compared with the total time interval covered by the data.…”