Closed-form expression for finite predictor coefficients of multivariate ARMA processes

Inoue, Akihiko

doi:10.1016/j.jmva.2019.104578

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…By Theorem 2 in [8], h −1 ♯ has the same m 0 and the same poles with the same multiplicities as h −1 , that is, for m 0 , K and (p 1 , m 1 ), . .…”

Section: Closed-form Formulasmentioning

confidence: 90%

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Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue¹

2021

Preprint

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We derive explicit formulas for the inverses of truncated block Toeplitz matrices that have a positive Hermitian matrix symbol with integrable inverse. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the symbol. The derivation of the formulas involves the dual process of a stationary process that has the symbol as spectral density. We illustrate the usefulness of the formulas by two applications. The first one is a strong convergence result for solutions of Toeplitz systems. The second application is closed-form formulas for the inverses of truncated block Toeplitz matrices that have a rational symbol. The significance of the closed-form formulas is that they provide us with a linear-time algorithm to compute the solutions of corresponding Toeplitz systems.

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“…By Theorem 2 in [8], h −1 ♯ has the same m 0 and the same poles with the same multiplicities as h −1 , that is, for m 0 , K and (p 1 , m 1 ), . .…”

Section: Closed-form Formulasmentioning

confidence: 90%

“…where the convention 0 0 = 1 is adopted; see Proposition 4 in [8]. We first consider the case of K = 0.…”

Section: Closed-form Formulasmentioning

confidence: 99%

Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue¹

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Aiming at the construction of prediction interval of ARMA (p, q) model with unknown order, Xingyu Lu [10] proposed a prediction interval bootstrap algorithm based on bootstrap distribution (p, q), which significantly improves the coverage accuracy of the prediction interval compared to the methods using preestimated values of orders. Akihiko Inoue et al [11] derive a closed-form expression for the finite predictor coefficients of multivariate ARMA processes，and apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes.…”

Section: )The Classic Linear Models (1) Prediction Model For Stationary Datamentioning

confidence: 99%

Forecast Methods for Time Series Data: A Survey

et al. 2021

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Research on forecasting methods of time series data has become one of the hot spots. More and more time series data are produced in various fields. It provides data for the research of time series analysis method, and promotes the development of time series research. Due to the generation of highly complex and large-scale time series data, the construction of forecasting models for time series data brings greater challenges. The main challenges of time series modeling are high complexity of time series data, low accuracy and poor generalization ability of prediction model. This paper attempts to cover the existing modeling methods for time series data and classify them. In addition, we make comparisons between different methods and list some potential directions for time series forecasting.

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Explicit formulas for the inverses of Toeplitz matrices, with applications

Inoue

2022

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

We derive novel explicit formulas for the inverses of truncated block Toeplitz matrices that correspond to a multivariate minimal stationary process. The main ingredients of the formulas are the Fourier coefficients of the phase function attached to the spectral density of the process. The derivation of the formulas is based on a recently developed finite prediction theory applied to the dual process of the stationary process. We illustrate the usefulness of the formulas by two applications. The first one is a strong convergence result for solutions of general block Toeplitz systems for a multivariate short-memory process. The second application is closed-form formulas for the inverses of truncated block Toeplitz matrices corresponding to a multivariate ARMA process. The significance of the latter is that they provide us with a linear-time algorithm to compute the solutions of corresponding block Toeplitz systems.

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Closed-form expression for finite predictor coefficients of multivariate ARMA processes

Cited by 6 publications

References 17 publications

Explicit formulas for the inverses of Toeplitz matrices, with applications

Explicit formulas for the inverses of Toeplitz matrices, with applications

Forecast Methods for Time Series Data: A Survey

Explicit formulas for the inverses of Toeplitz matrices, with applications

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