Abstract
This chapter first introduces the backshift operator, which is widely used for model simplicity and differencing, which is one way to make a nonstationary time series stationary. Then we present a statistical test on stationarity—the KPSS stationarity test. Third, we define MA, AR, and ARMA models and discuss their properties, including invertibility, causality, and more. We also distinguish the ARMA model from the ARMA process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson, T.W., Walker, A.M.: On the asymptotic distribution of the autocorrelations of a sample from a linear stochastic process. Ann. Math. Stat. 35, 1296–1303 (1964)
Brockwell, P.J., Davis, R.A.: Introduction to Time Series and Forecasting, 3rd edn. Springer, Switzerland (2016)
Durbin, J.: The fitting of time series models. Review of the International Institute of Statistics 28, 233–244 (1960)
Fan, J., Yao, Q.: Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York (2003)
Levinson, N.: The Weiner RMS error criterion in filter design and prediction. J. Math. Phys. 25, 261–278 (1947)
Quenouille, M.H.: Approximate tests of correlation in time-series. J. R. Stat. Soc. B 11, 68–84 (1949)
Shumway, R.H., Stoffer, D.S.: Time Series Analysis and Its Applications With R Examples, 4th edn. Springer, New York (2017)
Waerden, B.L.v.d.: Algebra I, 7th edn. Springer, Berlin (2003)
Yule, G.U.: On a method of investigating periodicities disturbed series, with special reference to Wolfer’s sunspot numbers. Philos. Trans. R. Soc. Lond. A 226, 267–298 (1927)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Huang, C., Petukhina, A. (2022). Stationary Time Series Models. In: Applied Time Series Analysis and Forecasting with Python. Statistics and Computing. Springer, Cham. https://doi.org/10.1007/978-3-031-13584-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-031-13584-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-13583-5
Online ISBN: 978-3-031-13584-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)