Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

Baek, Changryong; Kechagias, Stefanos; Pipiras, Vladas

doi:10.1016/j.jspi.2019.07.007

Cited by 10 publications

(25 citation statements)

References 15 publications

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“…The main goal of this work is to study a class of parametric models, that allows for a general phase, and to examine it through a simulation study and an application to real data, which suggest the need for models beyond the special phase (1.3). For the latter point, in particular, a local Whittle analysis of Robinson (2008) (see also Baek et al, 2019) suggests a phase different from (1.3) and the fitted models of this work will match the local Whittle phase very closely. To achieve the described goal, we follow Kechagias and Pipiras (2015) who constructed a two-sided VARFIMA(0, D, 0) model with a general phase by taking…”

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confidence: 54%

“…The results should be extended to two-sided models, or alternatively, one-sided representations of the models considered here should be established. On the other hand, some insight might be gained (and certainly reflected in our simulations) from the theoretical analysis of local Whittle estimators in Robinson (2008) and Baek et al (2019). For example, these works suggest that the phase parameter might be the most difficult one to estimate, especially when cross correlation is 'weak'.…”

Section: Estimationmentioning

confidence: 70%

“…The two lines being visibly different suggest that the special phase parameter and the associated VARFIMA model are not appropriate. A more detailed local Whittle analysis of the dataset can be found in Baek et al (2019): it includes confidence intervals in local Whittle plots and also the results under fractional cointegration.…”

Section: Applicationmentioning

confidence: 99%

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Modeling bivariate long‐range dependence with general phase

Kechagias

Pipiras

2019

Journal Time Series Analysis

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Bivariate time series models are considered that are suitable for estimation, that have interpretable parameters and that can capture the general semi-parametric formulation of bivariate long-range dependence, including a general phase. The models also allow for short-range dependence and fractional cointegration. A simulation study to test the performance of a conditional maximum likelihood estimation method is carried out, under the proposed models. Finally, an application is presented to the U.S. inflation rates in goods and services where models not allowing for general phase suffer from misspecification. 1 The following convention is used here. The autocovariance function is defined as (n) = X n X ′ 0 and the spectral density f ( ) satisfies (n) = ∫ − e in f ( )d . The convention is different from Kechagias and Pipiras (2015), where X 0 X ′ n is used as the autocovariance function, but is the same as in Brockwell and Davis (2009) and Pipiras and Taqqu (2017). We conclude this section by arguing that the model (1.6) and (1.7) can also be used to capture general phase when one of the component series is SRD (with the corresponding d = 0) and the other is LRD. (The component series can also be both SRD but this case is not particularly interesting since for two SRD series, their spectral density at zero is the sum of autocovariances at all lags and hence has zero phase = 0.) We formulate this as The one-sided FIVARMA(p, D, q) series (with c = 0 in (3.10)) have been more popular in the literature, with Lobato (1997), Sela and Hurvich (2009) and Tsay (2010) being notable exceptions. In particular, Sela and Hurvich 3 The names VARFIMA and FIVARMA refer to the facts that the fractional integration (FI) operator Δ c (B) −1 is applied to the MA part in (3.9) and after writing X n = Δ c (B) −1 Φ(B) −1 Θ(B)Z n , it is applied to the VARMA series in (3.10).wileyonlinelibrary.com/journal/jtsa Since (Y n+h−s |Y 1 , … , Y N ) =Ŷ n+h−s|n , the relation (4.17) yields (4.12).Next, we subtract (4.12) from (4.16) to get

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confidence: 54%

Section: Estimationmentioning

confidence: 70%

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Modeling bivariate long‐range dependence with general phase

Kechagias

Pipiras

2019

Journal Time Series Analysis

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“…It was closest to the oracle, and outperformed other methods as dependency and sample size increase. It also remains an interesting future work on extension to bivariate LRD series as studied in Baek et al (2020).…”

Section: Discussionmentioning

confidence: 99%

Estimation of long memory parameter in nonparametric regression

Cho¹,

Baek²

2019

CSAM

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This paper considers the estimation of the long memory parameter in nonparametric regression with strongly correlated errors. The key idea is to minimize a unified mean squared error of long memory parameter to select both kernel bandwidth and the number of frequencies used in exact local Whittle estimation. A unified mean squared error framework is more natural because it provides both goodness of fit and measure of strong dependence. The block bootstrap is applied to evaluate the mean squared error. Finite sample performance using Monte Carlo simulations shows the closest performance to the oracle. The proposed method outperforms existing methods especially when dependency and sample size increase. The proposed method is also illustreated to the volatility of exchange rate between Korean Won for US dollar.

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“…Hence, neuroscientific data modeling requires the reliable detection of non-zero delays and the accurate estimation of the joint parameters for delayed components. Accordingly, the estimation of parameters associated with time irreversibility has received considerable attention recently [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Detection and Estimation of Delays in Bivariate Self-similarity: Bootstrapped Complex Wavelet Coherence

Didier

Wendt

Abry

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The self-similarity paradigm enables the analysis of scale-free temporal dynamics and has been widely used in a large set of real-world applications. However, in a multivariate setting, delays amongst components significantly impair the estimation of scale-free parameters. The first framework for the modeling, detection and estimation of delay parameters and for the joint estimation of scale-free parameters is proposed here. It is assumed that a single realization of a multivariate, self-similar time series is available. Use is made of C-valued wavelets and, based on the imaginary part of the wavelet coherence, an original bootstrap-based delay estimation procedure based is constructed. Moreover, a consistent wavelet eigenanalysisbased semiparametric estimation for scale-free parameters that accounts for delay is defined. Monte Carlo experiments conducted over various instances of the model show that the proposed methodology enables the detection of delays with high probability and provides very satisfactory estimates of the delay and scale-free parameters.

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Asymptotics of bivariate local Whittle estimators with applications to fractal connectivity

Cited by 10 publications

References 15 publications

Modeling bivariate long‐range dependence with general phase

Modeling bivariate long‐range dependence with general phase

Estimation of long memory parameter in nonparametric regression

Detection and Estimation of Delays in Bivariate Self-similarity: Bootstrapped Complex Wavelet Coherence

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