Estimation of inverse autocovariance matrices for long memory processes

Ing, Ching‐Kang; Chiou, Hai-Tang; Guo, Meng

doi:10.3150/14-bej692

Cited by 10 publications

(14 citation statements)

References 18 publications

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“…9.1.2; see Lemma 2 in the Appendix). A model averaging method akin to the construction of Yang (2012) was studied in Cheng, Ing, and Yu (2015), and a long-memory GLS estimator of the same form was considered by Ing, Chiou, and Guo (2016).…”

Section: Under [Gren1]-[gren4] and [Hann1]-[hann3]mentioning

confidence: 99%

Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

Nguyen

2019

Stat

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In linear models, the generalized least squares (GLS) estimator is applicable when the structure of the error dependence is known. When it is unknown, such structure must be approximated and estimated in a manner that may lead to misspecification. The large‐sample analysis of incorrectly specified GLS (IGLS) estimators requires careful asymptotic manipulations. When performing estimation in the frequency domain, the asymptotic normality of the IGLS estimator, under the so‐called Grenander assumptions, has been proved for a broad class of error dependence models. Under the same assumptions, asymptotic normality results for the time‐domain IGLS estimator are only available for a limited class of error structures. We prove that the time‐domain IGLS estimator is asymptotically normal for a general class of dependence models.

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Section: Under [Gren1]-[gren4] and [Hann1]-[hann3]mentioning

confidence: 99%

Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

Nguyen

2019

Stat

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“…We also prove a backward analogue of (1.3); see Corollary 6.10 below. We refer to [26] for the corresponding result for univariate long-memory processes and [1,36,39] for its application; see also [21] for other applications of results in [26]. In [11], Baxter's inequality (1.3) was proved for a class of multivariate short-memory stationary processes.…”

Section: Introductionmentioning

confidence: 99%

Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes

Inoue¹,

Kasahara²,

Pourahmadi³

2018

Bernoulli

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For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the Fourier coefficients of its phase function in the spectral domain. The derivation is based on a novel alternating projection technique and the use of the forward and backward innovations corresponding to predictions based on the infinite past and future, respectively. We show that such representations are ideal for studying the rates of convergence of the finite predictor coefficients, prediction error covariances, and the PACF as well as for proving a multivariate version of Baxter's inequality for a multivariate FARIMA process with a common fractional differencing order for all components of the process.2010 Mathematics Subject Classification. Primary 60G25; secondary 62M20, 62M10.

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“…The inverse matrix Σ −1 thus can be approximated by a truncated version that has less parameters. This method is previously adopted by Cheng et al (2015), Ing et al (2016) and Lin and Reuvers (2020b) with multiple applications as mentioned. The banded inverse autocovariance matrix (BIAM) is constructed as…”

Section: The Model and Infeasible Glsmentioning

confidence: 99%

“…That is, we replace true innovations by first stage OLS residuals u t = y t − Z t β OLS , and subsequently minimise a sample moment in estimated residuals rather than the population mean squared forecasting error. This method was previously used by Cheng et al (2015) and Ing et al (2016) for univariate time series. For a multivariate time series, we define…”

Section: Consistent Estimation Of σ −1mentioning

confidence: 99%

“…The elements are obtained by multiple autoregressions using the first-stage regression residuals. Similar constructions based on MCD have been adopted in several papers for different purposes, see Cheng et al (2015), Ing et al (2016) and Lin and Reuvers (2020b). Nonetheless, the consistency results in the previous studies can not be applied directly in the current context.…”

Section: Introductionmentioning

confidence: 99%

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Essays on nonstationary nonlinear time series models

Lin¹

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Estimation of inverse autocovariance matrices for long memory processes

Cited by 10 publications

References 18 publications

Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

Asymptotic normality of the time‐domain generalized least squares estimator for linear regression models

Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes

Essays on nonstationary nonlinear time series models

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