Algorithm 808: ARfit—a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models

ABSTRACT

ARfit is a collection of Matlab modules for modeling and analyzing multivariate time series with autoregressive (AR) models. ARfit contains modules to given time series data, for analyzing eigen modes of a fitted model, and for simulating AR processes. ARfit estimates the parameters of AR models from given time series data with a stepwise least squares algorithm that is computationally efficient, in particular when the data are high-dimensional. ARfit modules construct approximate confidence intervals for the estimated parameters and compute statistics with which the adequacy of a fitted model can be assessed. Dynamical characteristics of the modeled time series can be examined by means of a decomposition of a fitted AR model into eigenmodes and associated oscillation periods, damping times, and excitations. The ARfit module that performs the eigendecomposition of a fitted model also constructs approximate confidence intervals for the eigenmodes and their oscillation periods and damping times.

REFERENCES

• 1: AKAIKE, H. 1971. Autoregressive model fitting for control. Ann. Inst. Stat. Math. 23, 163-180.
• 2: George Edward Pelham Box , Gwilym Jenkins, Time Series Analysis, Forecasting and Control, Holden-Day, Incorporated, 1990
• 3: BOX,G.E.P.AND PIERCE, D. A. 1970. Distribution of the residual autocorrelations in autoregressive-integrated moving average time series models. J. Amer. Statist. Assoc. 65, 1509-1526.
• 4: Peter J Brockwell , Richard A Davis, Time series: theory and methods, Springer-Verlag New York, Inc., New York, NY, 1986
• 5: LI,W.K.AND MCLEOD, A. I. 1981. Distribution of the residual autocorrelations in multivariate ARMA time series models. J. Roy. Statist. Soc. B43, 231-239.
• 6: L~TKEPOHL, H. 1985. Comparison of criteria for estimating the order of a vector autoregressive process. J. Time Ser. Anal. 6, 35-52. Correction, Vol 8 (1987), page 373.
• 7: L~TKEPOHL, H. 1993. Introduction to Multiple Time Series Analysis. 2nd. Springer- Verlag, Berlin, Germany.
• 8: Arnold Neumaier , Tapio Schneider, Estimation of parameters and eigenmodes of multivariate autoregressive models, ACM Transactions on Mathematical Software (TOMS), v.27 n.1, p.27-57, March 2001 [doi>10.1145/382043.382304]
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• 10: TIAO,G.C.AND BOX, G. E. P. 1981. Modeling multiple time series with applications. J. Amer. Statist. Assoc. 76, 802-816.
• 11: VON STORCH,H.AND ZWIERS, F. W. 1999. Statistical Analysis in Climate Research. Cambridge University Press, New York, NY.
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Markov processes

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Stochastic processes; Time series analysis; Multivariate statistics; Statistical software
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Documentation
      Nouns: MATLAB

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Earth and atmospheric sciences

General Terms:
Algorithms, Documentation, Theory

Keywords:
Matlab, confidence intervals, eigenmodes, least squares, model identification, order selection, parameter estimation, principal oscillation pattern