Abstract
Times series modeling plays an important role in the field of engineering, Statistics, Biomedicine etc. Model identification is one of crucial steps in the modeling of an AutoRegreesive Moving Average (ARMA(p,q)) process for real world problems. Many techniques have been developed in the literature (Salas et al., McLeod et al. etc.) for the identification of an ARMA(p,q) Model. In this paper, a new technique called The Generalised Parameters Technique is formulated for seasonal and non-seasonal ARMA model identification. This technique is very simple and can be applied to any given time series. Initial estimates of the AR parameters of the ARMA model are also obtained by this method. This model identification technique is validated through many theoretical and simulated examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. E. P. Box and G.M. JenkinsTime Series Analysis: Forecasting and Control, Holden - Day, 1976.
G. De Gooijer, B. Abraham, Ann Gould and L. Robinson,Methods for determining the oredr of an Autoregressive Moving Average process: A survey, International Statistical Review, Vol. 53(1985), No.3, 301–329.
C.W.J. Granger and R. Joyeux,An introduction to long memory time series models and fractional differencing, Journal of Time Series Analysis, Vol. 1(1980), No.1, 15–29.
U. Hassler,(Mis) specification of Long Memory in Seasonal Time series, Journal of Time Series Analysis, Vol. 15(1994), No. 1, 19–30.
J.R.M. Hosking,Fractional differencing, Biometrika, Vol. 68(1980), 165–176.
L. Kavalieris,A note on estimating autoregressive Moving Average order, Biometrika, Vol. 78(1991), No.4, 920–922.
S.G. Koreisha and T. Pukkila, S.G. Koreisha and T. Pukkila,Determining the order of a vector auto regression when the number of component series is large, Journal of time series Analysis, Vol. 14(1993), No. 1, 47–69.
A.I McLeod, K.N. Hipel and W.C. Lennox,Advances in Box — Jenkins modeling, Water Resources Research, Vol. 13(1977), No.3, 567 - 586.
M.S. Peiris and J.R. Court,A note on the estimation of degree of differencing in Long memory Time Series Analysis, Journal of Probability and Mathematical Statistics, Vol. 14(1993), 223 - 229.
T. Pukkila and S.G. Koreisha,The identification of ARMA models, Biometrika, Vol. 77(1990), No.3, 537–548.
J.D. Salas and J.T.B. Obeysekera,ARMA Model identification of Hydrologic time series, Water Resources Research, Vol. 18(1982), No.4, 1011 - 1021.
X.D. Zhang and Y.S. Zhang,Determination of the MA order of an ARMA process using sample correlations, IEEE Transactions on Signal processing, Vol. 41(1993), No. 6, 2277 - 2280.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sreenivasan, M., Sumathi, K. Generalised parameters technique for identification of seasonal ARMA (SARMA) and non seasonal ARMA (NSARMA) models. Korean J. Comp. & Appl. Math. 4, 135–146 (1997). https://doi.org/10.1007/BF03011385
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03011385