MATRIX FORMULAS FOR NONSTATIONARY ARIMA SIGNAL EXTRACTION

The paper provides general matrix formulas for minimum mean squared error signal extraction for a finitely sampled time series whose signal and noise components are nonstationary autoregressive integrated moving average processes. These formulas are quite practical; in addition to being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters. We also extend these formulas to estimates of future values of the unobserved signal, and we show how this result combines signal extraction and forecasting.

[1]  J. Burman.  Seasonal Adjustment by Signal Extraction , 1980 .

[2]  Ali H. Sayed,et al.  Linear Estimation (Information and System Sciences Series) , 2000 .

[3]  Robert Kohn,et al.  Signal extraction for finite nonstationary time series , 1987 .

[4]  Siem Jan Koopman,et al.  Computing Observation Weights for Signal Extraction and Filtering , 2003 .

[5]  Jens Timmer,et al.  Handbook of Time Series Analysis , 2006 .

[6]  Steven C. Hillmer,et al.  U.S. Census Bureau , 1991 .

[7]  Piet de Jong,et al.  Covariances for smoothed estimates in state space models , 1988 .

[8]  David F. Findley,et al.  Frequency Domain Analyses of SEATS and X-11/12-ARIMA Seasonal Adjustment Filters for Short and Moderate-Length Time Series , 2006 .

[9]  D.S.G. Pollock.  Filters for Short Non-stationary Sequences , 2001 .

[10]  Siem Jan Koopman,et al.  State Space and Unobserved Component Models: Theory and Applications , 2004 .

[11]  Boualem Djehiche,et al.  Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization , 2009 .

[12]  Víctor Gómez,et al.  Seasonal Adjustment and Signal Extraction in Economic Time Series , 1998 .

[13]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[14]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[15]  W. Bell,et al.  Signal Extraction for Nonstationary Time Series , 1984 .

[16]  E. J. Hannan.  Measurement of a wandering signal amid noise , 1967 .

[17]  D. S. G. Pollock,et al.  A handbook of time-series analysis, signal processing and dynamics , 1999 .

[18]  Gene H. Golub,et al.  Matrix computations , 1983 .

[19]  G. C. Tiao,et al.  A Course in Time Series Analysis , 2000 .

[20]  J. Aston,et al.  Diagnostics for ARIMA-Model-Based Seasonal Adjustment , 2003 .

[21]  James Durbin,et al.  Benchmarking by State Space Models , 1997 .

[22]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[23]  William R. Bell,et al.  State Space and Unobserved Component Models: On RegComponent time series models and their applications , 2004 .

[24]  Jurgen A. Doornik,et al.  Statistical algorithms for models in state space using SsfPack 2.2 , 1999 .

[25]  Steven C. Hillmer,et al.  A MATRIX APPROACH TO LIKELIHOOD EVALUATION AND SIGNAL EXTRACTION FOR ARIMA COMPONENT TIME SERIES MODELS , 1988 .

[26]  Eugene Sobel,et al.  Prediction of a noise-distorted, multivariate, non-stationary signal , 1967, Journal of Applied Probability.

[27]  G. C. Tiao,et al.  Decomposition of Seasonal Time Series: A Model for the Census X-11 Program , 1976 .

[28]  INVESTIGATING MODEL-BASED TIME SERIES METHODS TO IMPROVE ESTIMATES FROM MONTHLY VALUE OF CONSTRUCTION PUT-IN-PLACE SURVEYS , 2002 .

[29]  Tucker McElroy,et al.  Matrix Formulas for Nonstationary Signal Extraction , 2005 .

[30]  G. Tunnicliffe Wilson,et al.  Some efficient computational procedures for high order ARMA models , 1979 .

[31]  Tucker McElroy,et al.  An iterated parametric approach to nonstationary signal extraction , 2006, Comput. Stat. Data Anal..

[32]  Steven C. Hillmer,et al.  An ARIMA-Model-Based Approach to Seasonal Adjustment , 1982 .

[33]  Donald E. K. Martin,et al.  Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models , 2004 .