Asymptotic Properties of Higher-Order Periodograms

Alekseev, V. G.

doi:10.1137/1140046

Cited by 6 publications

(10 citation statements)

References 13 publications

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“…The estimation of in the general case (that is, when is of dimension m 3) can be done analogously to Anh et al [6]. We mention that the spectral estimatesˆ 2,T (w) = I 2 T ( )w( ) d andˆ (1) k,T ,ˆ…”

Section: Remarkmentioning

confidence: 97%

“…is a consistent estimator of the parameter , that is,ˆ T → 0 in P 0 -probability as T → ∞, and the estimatorsˆ (1) k,T andˆ (2) k,T , k = k 1 , k 2 , given by the formulae (3.10) and (3.11) are consistent estimators of (1) k ( ) and (2) …”

Section: Theorem 2 Let Conditions Iv-xii Be Satisfied Then As T → ∞mentioning

confidence: 99%

“…w (1) Further, to prove the consistency of the estimator T given by (3.9), we need to show that the convergence (5.5) holds uniformly in ∈ . Here, we use the conditions IX and X.…”

Section: Proofsmentioning

confidence: 99%

“…The bounds permit derivation of asymptotic moments and asymptotic normality for the model estimators. In connection with the estimation of higher-order spectral densities, we should point out that a non-parametric approach has been mainly followed, resulting in periodograms of higher orders and their modifications with the use of smoothing, tapering, shift-in-time methods (see, for example, [19,1,8]). Estimation of parametric models using higher-order information has been developed in the time domain for some particular cases such as AR and ARMA models based on a generalization of the Yule-Walker method (see, for example, [48]).…”

Section: Introductionmentioning

confidence: 99%

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Statistical inference using higher-order information

Anh

Leonenko

Sakhno

2007

Journal of Multivariate Analysis

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show abstract

Section: Remarkmentioning

confidence: 97%

Section: Theorem 2 Let Conditions Iv-xii Be Satisfied Then As T → ∞mentioning

confidence: 99%

“…w (1) Further, to prove the consistency of the estimator T given by (3.9), we need to show that the convergence (5.5) holds uniformly in ∈ . Here, we use the conditions IX and X.…”

Section: Proofsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical inference using higher-order information

Anh

Leonenko

Sakhno

2007

Journal of Multivariate Analysis

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“…For a linear series with a symmetric error distribution, we have that ; therefore, both and are also useful for testing whether or not a series is Gaussian white noise. The advantage of the frequency-bicoherence as a test statistic for nonlinearity is that the two quantities and are asymptotically independent at a rate for a linear series when using the so-called direct bispectrum estimate [3]. As these independent quantities also have an asymptotic complex Gaussian distribution (under the null hypothesis of linearity), a test can be formed with a desired size.…”

Section: Etmentioning

confidence: 99%

A time-domain test for some types of nonlinearity

Barnett

Wolff

2005

IEEE Trans. Signal Process.

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Abstract-The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

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Forecasting bubbles with mixed causal-noncausal autoregressive models

Hecq

Voisin

2021

Econometrics and Statistics

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This paper investigates one-step ahead density forecasts of mixed causalnoncausal models. We compare the sample-based and the simulations-based approaches respectively developed by Gouriéroux and Jasiak (2016) and Lanne, Luoto, and Saikkonen (2012). We focus on explosive episodes and therefore on predicting turning points of bubbles bursts. We suggest the use of both methods to construct investment strategies based on how much probabilities are induced by the assumed model and by past behaviours. We illustrate our analysis on Nickel prices series.

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Asymptotic Properties of Higher-Order Periodograms

Cited by 6 publications

References 13 publications

Statistical inference using higher-order information

Statistical inference using higher-order information

A time-domain test for some types of nonlinearity

Forecasting bubbles with mixed causal-noncausal autoregressive models

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