Consistent order estimation for linear stochastic feedback control systems (CARMA model)

Chen, H.-F.; Zhang, J.-F.

doi:10.1016/0005-1098(89)90131-3

Cited by 17 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

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Order By: Relevance

“…Similar to Guo, Chen & Zhang (1989), we proof (p T ,q T ) → (p 0 , q 0 ) a.s. by showing that the only limit point of (p T ,q T ) is indeed (p 0 , q 0 ) with probability one, where p 0 and q 0 are the true lag orders. Thus, the convergence ofp T andq T follows, which is equivalent to joint convergence.…”

supporting

confidence: 65%

Cointegrated VARMA Models and Forecasting US Interest Rates

Kascha¹,

Trenkler

2011

SSRN Journal

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We bring together some recent advances in the literature on vector autoregressive moving-average models creating a relatively simple specification and estimation strategy for the cointegrated case. We show that in the cointegrated case with fixed initial values there exists a so-called final moving representation which is usually simpler but not as parsimonious than the usual Echelon form. Furthermore, we proof that our specification strategy is consistent also in the case of cointegrated series. In order to show the potential usefulness of the method, we apply it to US interest rates and find that it generates forecasts superior to methods which do not allow for moving-average terms.

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supporting

confidence: 65%

Cointegrated VARMA Models and Forecasting US Interest Rates

Kascha¹,

Trenkler

2011

SSRN Journal

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“…λ p,q min (t) ≥ s 2 (log t) 1+s3 , for (p, q) ∈ M * , a.s., then Assumption 3.3 can be also satisfied by taking a t = (log t) log log t. Remark 3.3. For the case where there is only one sensor (n = 1), Guo et al in [7] investigated the strong consistency of the order estimate under the following conditions,…”

Section: Assumption 33 (Cooperative Excitation Condition I)mentioning

confidence: 99%

“…In order to simplify the analysis of the estimation error, we need to introduce an assumption on the input and output signals which implies that the system is not explosive. This assumption is commonly used in the stability analysis of the closedloop feedback control systems for a single sensor case (see e.g., [7], [8] and [15]). Assumption 4.2.…”

Section: Case IImentioning

confidence: 99%

“…In order to estimate the order of the statistical models, some criterions are proposed including AIC (Akaikes Information Criterion) [5], BIC (Bayesian Information Criterion) [6], CIC [7] ( the first "C" emphasizes that the criterion is designed for feedback control systems) and their variants [8]. Based on these information criterions, considerable progresses have been made on the order estimation in time series analysis and adaptive estimation and control (e.g., [9]- [13]).…”

mentioning

confidence: 99%

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Distributed order estimation of ARX model under cooperative excitation condition

Gan¹,

Liu²

2021

Preprint

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In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs (ARX) when both the system orders and parameters are unknown. We design distributed algorithms to estimate the unknown orders and parameters by combining the proposed local information criterion (LIC) with the distributed least squares method. The simultaneous estimation for both the system orders and parameters brings challenges for the theoretical analysis. Some analysis techniques, such as double array martingale limit theory, stochastic Lyapunov functions, and martingale convergence theorems are employed. For the case where the upper bounds of the true orders are available, we introduce a cooperative excitation condition, under which the strong consistency of the estimation for the orders and parameters is established. Moreover, for the case where the upper bounds of true orders are unknown, similar distributed algorithm is proposed to estimate both the orders and parameters, and the corresponding convergence analysis for the proposed algorithm is provided. We remark that our results are obtained without relying on the independency or stationarity assumptions of regression vectors, and the cooperative excitation conditions can show that all sensors can cooperate to fulfill the estimation task even though any individual sensor can not.

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Simple Identification and Specification of Cointegrated Varma Models

Kascha

Trenkler

2014

J. Appl. Econ.

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SummaryWe bring together some recent advances in the literature on vector autoregressive moving‐average models, creating a simple specification and estimation strategy for the cointegrated case. We show that in this case with fixed initial values there exists a so‐called final moving‐average representation. We prove that the specification strategy is consistent. The performance of the proposed method is investigated via a Monte Carlo study and a forecasting exercise for US interest rates. We find that our method performs well relative to alternative approaches for cointegrated series and methods which do not allow for moving‐average terms. Copyright © 2014 John Wiley & Sons, Ltd.

show abstract

Consistent order estimation for linear stochastic feedback control systems (CARMA model)

Cited by 17 publications

References 9 publications

Cointegrated VARMA Models and Forecasting US Interest Rates

Cointegrated VARMA Models and Forecasting US Interest Rates

Distributed order estimation of ARX model under cooperative excitation condition

Simple Identification and Specification of Cointegrated Varma Models

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