Introduction to Box and Jenkins (1962) Some Statistical Aspects of Adaptive Optimization and Control

Abstract

This paper is a long paper full of insights and innovations, many of which have become key elements in modern time series analysis. The paper is a discussion paper and many of the discussants seem to have recognized it as a landmark paper, but perhaps not for the reasons modern statisticians would find it important. While ostensibly on optimization and control, it contains many gems that are precursors to modern statistical and data analytic notions. Indeed, the not unrelated papers by Kalman (1960) and Kalman and Bucy (1961) have proven to have more direct impact on control and linear filtering theory. Nonetheless, this paper surely ranks among the most important statistics papers in the modern era. It represents the first in a series of collaborations between Box and Jenkins that came to full fruition in 1970 with the publication of the now classic text on time domain parametric time series models including autoregressive, moving average, and mixed models. Preliminary discussions of these models appear in this paper. In addition, a description of technical feedback is given that anticipates modern exploratory data analysis. The treatment of nonstationarity using difference operators is also noted, as well as the suggestion of modern so-called high-resolution spectral analysis.