Change point detection in vector autoregression

Prášková, Zuzana

doi:10.14736/kyb-2018-6-1122

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…where R pr is a commutation matrix such as Rvec𝛼 = vec𝛼 ′ . Under similar conditions to those given in Nicholls and Quinn (1982) and Prášková and Vaněček (2011), Θ has an asymptotic normal distribution with covariance matrix I(Θ) −1 . The variances of the parameter estimates are the main diagonal elements of the inverse information matrix evaluated at Θ.…”

Section: Hoyosmentioning

confidence: 99%

“…Otherwise, large values of

y (t)

over a long period of time may occur. Necessary and sufficient conditions for stability and stationarity were studied by Nicholls and Quinn (1982) for discrete time processes (see also Prášková and Vaněček, 2011). We observe that system (1) allows cointegration if

y (t)

I (1)

, that is, non‐stationary, but there exist a set of

1 \leq r < p

linear combinations of the form

β^{'} y (t)

that are stationary.…”

Section: The Modelmentioning

confidence: 99%

See 1 more Smart Citation

A first order continuous timeVARwith random coefficients

Hoyos

2023

Journal Time Series Analysis

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This article considers a first order continuous time vector autoregression with random coefficients. We discuss some difficulties that arise when the exact discrete analogue is used for estimating the continuous time parameters and provide an estimation method based on an approximate discrete model. Some expressions for the estimator of the drift parameter matrix, for its approximated bias and for the covariance matrix of the parameter estimates are derived. The finite sample performance of the proposed method is studied by a Monte Carlo experiment. We also illustrate the advantages of our model in an application on the expectations theory of the term structure of interest rates. Results show that the performance of the proposed methodology is good, and allowing for time variation on coefficients results in large reductions in the root mean square error of the parameter estimates.

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Section: Hoyosmentioning

confidence: 99%

“…Otherwise, large values of

y (t)

y (t)

I (1)

, that is, non‐stationary, but there exist a set of

1 \leq r < p

linear combinations of the form

β^{'} y (t)

that are stationary.…”

Section: The Modelmentioning

confidence: 99%

A first order continuous timeVARwith random coefficients

Hoyos

2023

Journal Time Series Analysis

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show abstract

“…Least squares estimation has been largely used Quinn, 1981, 1982;Tsay, 1987), and is often taken as benchmark for modern advances. Furthermore, since LS estimates are strongly consistent and under suitable conditions they obey the central limit theorem, they often serve as starting point for iterative schemes such as maximum likelihood (ML) (Nicholls and Quinn, 1982;Tjøstheim, 1986;Allal and Benmoumen, 2013), or in combination with other procedures such as estimating functions (EF) (Thavaneswaran and Abra 1988;Abdullah et al, 2011) and bootstrap methods (Prášková, 2003;Fink and Kreiss, 2013). Note that for ML estimation, autoregressive coefficients and residuals are also typically assumed to be jointly normal.…”

Section: Random Coefficient Autoregressive Models (Rca)mentioning

confidence: 99%

Random autoregressive models: A structured overview

Regis¹,

Serra²,

Heuvel³

2020

Preprint

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Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial, overlapping, and confusing. Most models focus on one property of the data, while much can be gained by combining the strength of various models and their sources of heterogeneity.We present a structured overview of the literature on autoregressive models with random coefficients. We describe hierarchy and analogies among models, and for each we systematically list properties, estimation methods, tests, software packages and typical applications.

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“…Finally, but not lastly, we would like to remind that the CUSUM-type methods are used to detect a change in the parameters of a time series. Here are some references from the recent literature: Song and Kang (2020), Gronneberg and Holcblat (2019), Prášková (2018), Chen and Hu (2017). The remainder of the paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Real-time detection of a change-point in a linear expectile model

Ciuperca¹

2020

Preprint

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In the present paper we address the real-time detection problem of a change-point in the coefficients of a linear model with the possibility that the model errors are asymmetrical and that the explanatory variables number is large. We build test statistics based on the cumulative sum (CUSUM) of the expectile function derivatives calculated on the residuals obtained by the expectile and adaptive LASSO expectile estimation methods. The asymptotic distribution of these statistics are obtained under the hypothesis that the model does not change. Moreover, we prove that they diverge when the model changes at an unknown observation. The asymptotic study of the test statistics under these two hypotheses allows us to find the asymptotic critical region and the stopping time, that is the observation where the model will change. The empirical performance is investigated by a comparative simulation study with other statistics of CUSUM type. Two examples on real data are also presented to demonstrate its interest in practice.

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Change point detection in vector autoregression

Cited by 3 publications

References 15 publications

A first order continuous timeVARwith random coefficients

A first order continuous timeVARwith random coefficients

Random autoregressive models: A structured overview

Real-time detection of a change-point in a linear expectile model

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