Abstract
This chapter introduces time series models which are most commonly used in statistical forecasting: regression models, including trend models, stationary time series models, the ARIMA(p, d, q) model, nonlinear models, multivariate time series models (including VARMA(p, q) and simultaneous equations models), as well as models of discrete time series with a specific focus on high-order Markov chains.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alzaid, A., Al-Osh, M.: An integer-valued pth-order autoregressive structure (INAR(p)) process. J. Appl. Probab. 27, 314–324 (1990)
Amagor, H.: A Markov analysis of DNA sequences. J. Theor. Biol. 104, 633–642 (1983)
Anderson, T.: The Statistical Analysis of Time Series. Wiley, New York (1994)
Borovkov, A.: Mathematical Statistics. Gordon & Breach, Amsterdam (1998)
Box, G., Jenkins, G., Reinsel, G.: Time Series Analysis: Forecasting and Control. Wiley-Blackwell, New York (2008)
Brillinger, D.: Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, New York (1975)
Brockwell, P., Davis, R.: Introduction to Time Series and Forecasting. Springer, New York (2002)
Bulinsky, A., Shyryaev, A.: Theory of Random Processes (in Russian). Fizmatlit, Moscow (2003)
Chatfield, C.: Time Series Forecasting. Chapman & Hall/CRC, Boca Raton (2001)
Collet, D.: Modeling Binary Data. Chapman & Hall, London (2002)
Davison, A.: Statistical Models. Cambridge University Press, Cambridge (2009)
Doob, J.: Stochastic Processes. Wiley, New York (1953)
Draper, N., Smith, H.: Applied Regression Analysis. Wiley, New York (1998)
Fan, J., Yao, Q.: Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York (2003)
Fokianos, K., Kedem, B.: Regression theory for categorical time series. Stat. Sci. 18, 357–376 (2003)
Fried, R., Gather, U.: Fast and robust filtering of time series with trends. In: Härdle, W., RönzComp, B. (eds.) COMPSTAT 2002, pp. 367–372. Physica, Heidelberg (2002)
Gather, U., Schettlinger, K., Fried, R.: Online signal extraction by robust linear regression. Comput. Stat. 21, 33–51 (2006)
Gelper, S., Fried, R., Croux, C.: Robust forecasting with exponential and Holt–Winters smoothing. J. Forecast. 29, 285–300 (2010)
Granger, C., Andersen, A.: An Introduction to Bilinear Time Series Models. Vandenhoeck and Ruprecht, Gottingen (1978)
Hannan, E.: Multiple Time Series. Wiley, New York (1970)
Jacobs, P., Lewis, A.: Discrete time series generated by mixtures. J. Roy. Stat. Soc. B 40(1), 94–105 (1978)
Kemeny, J., Snell, J.: Finite Markov Chains. Springer, New York (1976)
Kharin, Y.: Markov chains with r-partial connections and their statistical estimation (in Russian). Trans. Natl. Acad. Sci. Belarus 48(1), 40–44 (2004)
Kharin, Y.: Robustness of autoregressive forecasting under bilinear distortions. In: Computer Data Analysis and Modeling, vol. 1, pp. 124–128. BSU, Minsk (2007)
Kharin, Y.: Robustness of the mean square risk in forecasting of regression time series. Comm. Stat. Theor. Meth. 40(16), 2893–2906 (2011)
Kharin, Y., Piatlitski, A.: A Markov chain of order s with r partial connections and statistical inference on its parameters. Discrete Math. Appl. 17(3), 295–317 (2007)
Kharin, Y., Piatlitski, A.: Statistical analysis of discrete time series based on the MC(s, r)-model. Aust. J. Stat. 40(1-2), 75–84 (2011)
Kharin, Y., Staleuskaya, S.: Robustification of “approximating approach” in simultaneous equation models. In: New Trends in Probability and Statistics, vol. 5, pp. 143–150. TEV, Vilnius (2000)
Kolmogorov, A.: On the use of statistically estimated forecasting formulae (in Russian). Geophys. J. 3, 78–82 (1933)
Kolmogorov, A.: Interpolation and extrapolation of stationary stochastic series (in Russian). Izv. Akad. Nauk SSSR Ser. Mat 5(1), 3–14 (1941)
Koroljuk, V.: Handbook on Probability Theory and Mathematical Statistics (in Russian). Nauka, Moscow (1985)
Lewis, P.: Simple models for positive-valued and discrete-valued time series with ARMA correlation structure. Multivariate Anal. 5, 151–166 (1980)
Lutkepohl, H.: Introduction to Multiple Time Series Analysis. Springer, Berlin (1993)
Makridakis, S., Hyndman, R., Wheelwright, S.: Forecasting: Methods and Applications. Wiley, New York (1998)
Mosteller, F., Tukey, J.: Data Analysis and Regression: A Second Course in Statistics. Addison-Wesley, Reading (1977)
Ozaki, T.: Non-linear time series models and dynamical systems. In: Time Series in the Time Domain. Handbook of Statistics, vol. 5, pp. 25–83. Elsevier, Amsterdam (1985)
Priestley, M.: Spectral Analysis and Time Series. Academic Press, New York (1999)
Raftery, A.: A model for high-order Markov chains. J. Roy. Stat. Soc. B 47(3), 528–539 (1985)
Seber, G., Lee, A.: Linear Regression Analysis. Wiley-Interscience, Hoboken (2003)
Shephard, N.: Statistical aspects of ARCH and stochastic volatility. In: Cox, D., Hinkley, D. (eds.) Time Series Models in Econometrics, Finance and Other Fields, pp. 1–67. Chapman & Hall, London (1996)
Tong, H.: Non-linear Time Series. Clarendon Press, Oxford (1993)
Waterman, M.: Mathematical Methods for DNA Sequences. CRC Press, Boca Raton (1989)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kharin, Y. (2013). Time Series Models of Statistical Forecasting. In: Robustness in Statistical Forecasting. Springer, Cham. https://doi.org/10.1007/978-3-319-00840-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-00840-0_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00839-4
Online ISBN: 978-3-319-00840-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)