Univariate and Multivariate Autoregressive Time Series Models of Offensive Baseball Performance: 1901-2005

Abstract

This paper sets out to estimate univariate time series models on a selected set of offensive baseball measures from 1901 to 2005. The measures include homeruns, bases on balls, runs batted in, doubles, and stolen bases. The paper next estimates the trends in these statistics simultaneously using a vector autoregressive time series model. Along the way, tests of assumptions underlying the time-series models are provided. Univariate time series results suggest that simple lag--1 models fit these offensive statistics quite well. The multivariate results show that a simple lag--1 vector autoregressive model also fits quite well. The results of the vector time series model indicate that most statistics are strongly predicted by their prior values. However, certain temporal dependencies among baseball measures are observed, suggesting the importance of examining covariation in baseball data over time.