Imperial College London
Alternate

ProfessorRajBhansali

Faculty of Natural Sciences, Department of Mathematics

Visiting Professor
 
 
 
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Contact

 

r.bhansali

 
 
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Location

 

532Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

42 results found

Bhansali RJ, 2020, Model specification and selection for multivariate time series, Journal of Multivariate Analysis, Vol: 175, Pages: 1-19, ISSN: 0047-259X

Three major difficulties are identified with an established echelon form approach (see Hannan (1987)) to specifying a Vector Autoregressive Moving Average,V ARMA , model for an observed time series. A family of state space representations, valid for each integer, , is introduced, and collectively referred to as multistep state space representations. This family includes as its special case, with h = 0, a state space representation introduced earlier by Akaike (1974), and, with h = 1, that introduced by Cooper and Wood (1982). Appropriate generalizations of the notions of minimality, McMillan degree, left matrix fraction description and Kronecker indices, as applicable individually to each member of this family, are presented. The reverse echelon form and state space representation corresponding to the Kronecker indices for each h are derived, and the former illustrated with three examples of standard V ARMA processes. The question of how the presence of zero constraints on the coefficients of a reverse echelon form may be detected solely from an inspection of the Kronecker indices is examined. A canonical correlation procedure proposed originally by Akaike (1976) for h is considered for estimating the Kronecker indices with each . The efficacy of the estimation procedure is investigated by a simulation study. A procedure is suggested for implementing the new approach introduced in this paper with an observed time series, and three different applications of this approach are outlined. This approach is also related to some of its alternatives, including the Kronecker invariants of Poskitt (1992) and the scalar component approach of Tiao and Tsay (1989).

Journal article

Ippoliti L, Martin RJ, Bhansali RJ, 2013, Rational spectral density models for lattice data, SPATIAL STATISTICS, Vol: 6, Pages: 91-108, ISSN: 2211-6753

Journal article

Bhansali RJ, 2007, Long-Memory Time Series: Theory and Methods by Wilfredo Palma, International Statistical Review, Vol: 75, Pages: 271-272

Journal article

Bhansali RJ, Giraitis L, Kokoszka PS, 2007, Convergence of quadratic forms with nonvanishing diagonal, STATISTICS & PROBABILITY LETTERS, Vol: 77, Pages: 726-734, ISSN: 0167-7152

Journal article

Bhansali RJ, Giraitis L, Kokoszka PS, 2007, Approximations and limit theory for quadratic forms of linear processes, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, Vol: 117, Pages: 71-95, ISSN: 0304-4149

Journal article

Bhansali RJ, Holland MP, 2007, Frequency analysis of chaotic intermittency maps with slowly decaying correlations, STATISTICA SINICA, Vol: 17, Pages: 15-41, ISSN: 1017-0405

Journal article

Bhansali RJ, Giraitis L, Kokoszka PS, 2006, Estimation of the memory parameter by fitting fractionally differenced autoregressive models, JOURNAL OF MULTIVARIATE ANALYSIS, Vol: 97, Pages: 2101-2130, ISSN: 0047-259X

Journal article

Bhansali RJ, Ippoliti L, 2005, Inverse correlations for multiple time series and Gaussian random fields and measures of their linear determinism, Journal of Mathematics and Statistics, Vol: 1, Pages: 287-299, ISSN: 1549-3644

For a discrete-time vector linear stationary process, {X(t)}, admitting forward and backward autoregressive representations, the variance matrix of an optimal linear interpolator of X(t), based on a knowledge of {X(t-j), j?0}, is known to be given by Ri(0)-1 where Ri(0) denotes the inverse variance of the process. Let A=Is-1Ri(0)?1R(0)?1, where R(0) denotes the variance matrix of {X(t)} and Is an sXs, identity matrix. A measure of linear interpolability of the process, called an index of linear determinism, may be constructed from the determinant Det[Is - A], of Is - A = Ri(0)-1 R(0)-1. An alternative measure is constructed by relating tr[Ri(0)-1] the trace of Ri(0)-1, to tr[R(0)]. The relationship between the matrix A and the corresponding matrix, P, obtained by considering only an optimal one-step linear predictor of X(t) from a knowledge of its infinite past, {X(t-j),j>0}, is also discussed. The possible role the inverse correlation function may have for model specification of a vector ARMA model is explored. Close parallels between the problem of interpolation for a stationary univariate two-dimensional Gaussian random field and time series are examined and an index of linear determinism for the latter class of processes is also defined. An application of this index for model specification and diagnostic testing of a Gaussian Markov Random Field is investigated together with the question of its estimation from observed data. Results are illustrated by a simulation study.

Journal article

Bhansali RJ, Holland MP, Kokoszka PS, 2004, Chaotic maps with slowly decaying correlations and intermittency, International Conference on Asymptotic Methods in Stochastics, Publisher: AMER MATHEMATICAL SOC, Pages: 99-126, ISSN: 1069-5265

Conference paper

Bhansali RJ, Kokoszka PS, 2003, Prediction of long-memory time series: A tutorial review, International Conference on Long Range Dependent Stochastic Processes, Publisher: SPRINGER-VERLAG BERLIN, Pages: 3-21, ISSN: 0075-8450

Conference paper

Bhansali RJ, Kokoszka PS, 2002, Computation of the forecast coefficients for multistep prediction of long-range dependent time series, International Journal of Forecasting, Vol: 18, Pages: 181-206, ISSN: 0169-2070

Journal article

Bhansali RJ, 1999, Autoregressive model selection for multistep prediction, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, Vol: 78, Pages: 295-305, ISSN: 0378-3758

Journal article

Beran J, Bhansali RJ, Ocker D, 1998, On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes, BIOMETRIKA, Vol: 85, Pages: 921-934, ISSN: 0006-3444

Journal article

Bhansali RJ, 1997, Direct autoregressive predictors for multistep prediction: Order selection and performance relative to the plug in predictors, STATISTICA SINICA, Vol: 7, Pages: 425-449, ISSN: 1017-0405

Journal article

Bhansali RJ, 1996, Asymptotically efficient autoregressive model selection for multistep prediction, ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, Vol: 48, Pages: 577-602, ISSN: 0020-3157

Journal article

BHANSALI RJ, 1994, RECURSIVE ORDER SELECTION FOR AN ARMA PROCESS, US / Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach, Publisher: KLUWER ACADEMIC PUBL, Pages: A105-A135

Conference paper

BHANSALI RJ, 1993, ESTIMATION OF THE IMPULSE-RESPONSE COEFFICIENTS OF A LINEAR PROCESS WITH INFINITE VARIANCE, JOURNAL OF MULTIVARIATE ANALYSIS, Vol: 45, Pages: 274-290, ISSN: 0047-259X

Journal article

BHANSALI RJ, PAPANGELOU F, 1991, CONVERGENCE OF MOMENTS OF LEAST-SQUARES ESTIMATORS FOR THE COEFFICIENTS OF AN AUTOREGRESSIVE PROCESS OF UNKNOWN ORDER, ANNALS OF STATISTICS, Vol: 19, Pages: 1155-1162, ISSN: 0090-5364

Journal article

BHANSALI RJ, 1991, CONSISTENT RECURSIVE ESTIMATION OF THE ORDER OF AN AUTOREGRESSIVE MOVING AVERAGE PROCESS, INTERNATIONAL STATISTICAL REVIEW, Vol: 59, Pages: 81-96, ISSN: 0306-7734

Journal article

BHANSALI RJ, 1990, ON A RELATIONSHIP BETWEEN THE INVERSE OF A STATIONARY COVARIANCE-MATRIX AND THE LINEAR INTERPOLATOR, JOURNAL OF APPLIED PROBABILITY, Vol: 27, Pages: 156-170, ISSN: 0021-9002

Journal article

BHANSALI RJ, 1988, CONSISTENT ORDER DETERMINATION FOR PROCESSES WITH INFINITE VARIANCE, JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, Vol: 50, Pages: 46-60, ISSN: 1369-7412

Journal article

BATTAGLIA F, BHANSALI RJ, 1987, ESTIMATION OF THE INTERPOLATION ERROR VARIANCE AND AN INDEX OF LINEAR DETERMINISM, BIOMETRIKA, Vol: 74, Pages: 771-779, ISSN: 0006-3444

Journal article

BHANSALI RJ, 1986, A DERIVATION OF THE INFORMATION CRITERIA FOR SELECTING AUTOREGRESSIVE MODELS, ADVANCES IN APPLIED PROBABILITY, Vol: 18, Pages: 360-387, ISSN: 0001-8678

Journal article

BHANSALI RJ, 1986, ASYMPTOTICALLY EFFICIENT SELECTION OF THE ORDER BY THE CRITERION AUTOREGRESSIVE TRANSFER-FUNCTION, ANNALS OF STATISTICS, Vol: 14, Pages: 315-325, ISSN: 0090-5364

Journal article

BHANSALI RJ, 1983, A SIMULATION STUDY OF AUTOREGRESSIVE AND WINDOW ESTIMATORS OF THE INVERSE CORRELATION-FUNCTION, JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS, Vol: 32, Pages: 141-149, ISSN: 0035-9254

Journal article

BHANSALI RJ, 1983, THE INVERSE PARTIAL CORRELATION-FUNCTION OF A TIME-SERIES AND ITS APPLICATIONS, JOURNAL OF MULTIVARIATE ANALYSIS, Vol: 13, Pages: 310-327, ISSN: 0047-259X

Journal article

BHANSALI RJ, 1982, THE EVALUATION OF CERTAIN QUADRATIC-FORMS OCCURRING IN AUTOREGRESSIVE MODEL-FITTING, ANNALS OF STATISTICS, Vol: 10, Pages: 121-131, ISSN: 0090-5364

Journal article

BHANSALI RJ, 1981, EFFECTS OF NOT KNOWING THE ORDER OF AN AUTOREGRESSIVE PROCESS ON THE MEAN SQUARED ERROR OF PREDICTION .1., JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, Vol: 76, Pages: 588-597, ISSN: 0162-1459

Journal article

BEENSTOCK M, BHANSALI RJ, 1980, ANALYSIS OF COCOA PRICE SERIES BY AUTOREGRESSIVE MODEL-FITTING TECHNIQUES, JOURNAL OF AGRICULTURAL ECONOMICS, Vol: 31, Pages: 237-242, ISSN: 0021-857X

Journal article

BHANSALI RJ, 1980, AUTOREGRESSIVE AND WINDOW ESTIMATES OF THE INVERSE CORRELATION-FUNCTION, BIOMETRIKA, Vol: 67, Pages: 551-566, ISSN: 0006-3444

Journal article

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