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

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  • Kaplan David

    (University of Wisconsin at Madison)

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.

Suggested Citation

  • Kaplan David, 2008. "Univariate and Multivariate Autoregressive Time Series Models of Offensive Baseball Performance: 1901-2005," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(3), pages 1-23, July.
    • Handle: RePEc:bpj:jqsprt:v:4:y:2008:i:3:n:6
    DOI: 10.2202/1559-0410.1122
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    References listed on IDEAS

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    1. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, June.
    2. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    3. Kaplan David, 2006. "A Variance Decomposition of Individual Offensive Baseball Performance," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 2(3), pages 1-18, July.
    4. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    5. Rodney Fort & Young Hoon Lee, 2006. "Stationarity and Major League Baseball Attendance Analysis," Journal of Sports Economics, , vol. 7(4), pages 408-415, November.
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    Cited by:

    1. Piette James & Jensen Shane T., 2012. "Estimating Fielding Ability in Baseball Players Over Time," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 8(3), pages 1-36, October.

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