Search results for "Companion matrix"

showing 4 items of 4 documents

General Solution of a Second-Order Nonhomogenous Linear Difference Equation with Noncommutative Coefficients

2010

The detailed construction of the general solution of a second-order nonhomogenous linear operator-difference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by studying some applications belonging to different mathematical contexts.

Difference equation noncommutativity companion matrix generating functions
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On complete set of solutions for polynomial matrix equations

1990

Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.

Discrete mathematicsAdjugate matrixMinimal polynomial (linear algebra)Stable polynomialApplied MathematicsCompanion matrixApplied mathematicsMonic polynomialPolynomial matrixCharacteristic polynomialMatrix polynomialMathematicsApplied Mathematics Letters
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Tests against stationary and explosive alternatives in vector autoregressive models

2008

.  The article proposes new tests for the number of unit roots in vector autoregressive models based on the eigenvalues of the companion matrix. Both stationary and explosive alternatives are considered. The limiting distributions of test statistics depend only on the number of unit roots. Size and power are investigated, and it is found that the new test against some stationary alternatives compares favourably with the widely used likelihood ratio test for the cointegrating rank. The powers are prominently higher against explosive than against stationary alternatives. Some empirical examples are provided to show how to use the new tests with real data.

Statistics and ProbabilityAutoregressive modelExplosive materialRank (linear algebra)Applied MathematicsLikelihood-ratio testCompanion matrixEconometricsUnit rootStatistics Probability and UncertaintyEigenvalues and eigenvectorsMathematicsStatistical hypothesis testingJournal of Time Series Analysis
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Tests for real and complex unit roots in vector autoregressive models

2014

The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…

Statistics and Probabilityta112Numerical AnalysisAngular frequencyCointegrationMathematical analysisNull (mathematics)Companion matrixAutoregressive modelStatistics Probability and UncertaintyUnit (ring theory)Eigenvalues and eigenvectorsBrownian motionMathematicsJournal of Multivariate Analysis
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