The DOI matches its Crossref record; 21 of the 21 references it cites were found in a registry or an index.
The Statistical Theory of Linear Systems
Abstract
Publisher Summary The chapter discusses the development of a rather complete inferential theory for ARMAX models. The first problem in the development is the coordinatization of spaces of such structures. Coordinates are needed both for computations and because a central limit theorem must be expressed in terms of them. One such coordinatization would follow from the use of the coefficient matrices in g, h, j in the scalar m.f.d., but there are many others. The chapter highlights the algebraic and topological description of ARMAX systems. In this connection, control engineers have played a premier part. The chapter focuses on the asymptotic properties of maximum likelihood (ML) estimators. The ML estimator is obtained by optimizing this likelihood. The chapter explains the asymptotic properties of these estimators without assuming the data to be Gaussian and also discusses the basis of the assumptions that appear to be minimal.
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Cites
A New Approach to Linear Filtering and Prediction Problems
Kalman, R. E. (1960) · Journal of Basic Engineering · doi:10.1115/1.3662552 · Cited by 31,751
Kailath, T. (1980) · Cited by 6,215
Techniques for Testing the Constancy of Regression Relationships Over Time
Brown, R. L., Durbin, J., & Evans, J. M. (1975) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1975.tb01532.x · Cited by 5,128
Hannan, E. J. (1970) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316429 · Cited by 2,369
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Selection of the order of an autoregressive model by Akaike's information criterion
SHIBATA, R. (1976) · Biometrika · doi:10.1093/biomet/63.1.117 · Cited by 789
Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
Forney, Jr. (1975) · SIAM Journal on Control · doi:10.1137/0313029 · Cited by 718
Hamming, R. W. (1980) · Cited by 693
(2005) · Lecture Notes in Control and Information Sciences · doi:10.1007/bfb0005213 · Cited by 674
Canonical Correlation Analysis of Time Series and the Use of an Information Criterion
Akaike, H. (1976) · Mathematics in Science and Engineering · doi:10.1016/s0076-5392(08)60869-3 · Cited by 654
Cited by
Detection of Abrupt Changes: Theory and Application
Riedel, K. S. (1994) · Technometrics · doi:10.1080/00401706.1994.10485821 · Cited by 3,518
Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag
Ng, S., & Perron, P. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476510 · Cited by 1,457
Forecasting Time Series With Complex Seasonal Patterns Using Exponential Smoothing
De Livera, A. M., Hyndman, R. J., & Snyder, R. D. (2011) · Journal of the American Statistical Association · doi:10.1198/jasa.2011.tm09771 · Cited by 1,049
Estimating Long-Run Economic Equilibria
Phillips, P. C. B., & Loretan, M. (1991) · The Review of Economic Studies · doi:10.2307/2298004 · Cited by 853
Solved problems for Granger causality in neuroscience: A response to Stokes and Purdon
Barnett, L., Barrett, A. B., & Seth, A. K. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2018.05.067 · Cited by 73
Metadata
- Authors
- Cryer, J. D.
- Venue
- Technometrics
- Publisher
- Informa UK Limited
- Published
- 1990-02
- Volume
- 32
- Issue
- 1
- Pages
- 111-111
- ISSN
- 0040-1706 (ISSN-L)
- 1537-2723
- OpenAlex
- W2041001113
- Cited by
- 745
- References
- 21
- FWCI
- 45.52
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
