Gaussian Semiparametric Estimation of Non‐stationary Time Series

Velasco, Carlos

doi:10.1111/1467-9892.00127

Cited by 293 publications

(231 citation statements)

References 19 publications

(45 reference statements)

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“…Velasco (1999), Hurvich & Ray (2003), and Hurvich et al (2005) also assume this type of process. Since f P t s=1 x s g is nonstationary z t does not have a spectral density if d 2 [1=2; 1) but it has a pseudo spectral density, see e.g.…”

Section: Local Whittle Estimation Of Perturbed Fractional Processesmentioning

confidence: 99%

Local polynomial Whittle estimation of perturbed fractional processes

Frederiksen¹,

Nielsen

2012

Journal of Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in ‡ate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal for d 2 (0; 3=4), and if the spectral density is su¢ ciently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, p n. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator. Terms of use: Documents inJEL Classi…cations: C22.

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Section: Local Whittle Estimation Of Perturbed Fractional Processesmentioning

confidence: 99%

Local polynomial Whittle estimation of perturbed fractional processes

Frederiksen¹,

Nielsen

2012

Journal of Econometrics

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“…To extend the range of application of these semiparametric methods, data differencing and data tapering have been suggested [3,15]. These methods have the advantage that they are easy to implement and they make use of existing algorithms once the data filtering has been carried out.…”

Section: Introduction Semiparametric Estimation Of the Memory Paramementioning

confidence: 99%

“…Thus, the LW estimator is not a good general-purpose estimator when the value of d may take on values in the nonstationary zone beyond 3 4 . Similar comments apply in the case of LP estimation [4].To extend the range of application of these semiparametric methods, data differencing and data tapering have been suggested [3,15]. These methods have the advantage that they are easy to implement and they make use of existing algorithms once the data filtering has been carried out.…”

mentioning

confidence: 99%

“…This section reports some simulations that were conducted to examine the finite sample performance of the exact LW estimator (hereafter, exact estimator), the LW estimator (hereafter, untapered estimator) and the LW estimator with two types of tapering studied by Hurvich and Chen [3] and Velasco [15] with Bartlett's window [hereafter, tapered (HC) and tapered (V) estimator, resp.]. The tapered (HC) estimator and tapered (V) estimator are consistent and asymptotically normal for d ∈ (−0.5, 1.5) with limiting variances 1.5/(4m) and 2.1/(4m), respectively (see Remark 1).…”

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confidence: 99%

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Exact Local Whittle Estimation of Fractional Integration With Unknown Mean and Time Trend

Shimotsu¹

2009

Econom. Theory

187

209

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An exact form of the local Whittle likelihood is studied with the intent of developing a general-purpose estimation procedure for the memory parameter (d) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N(0, 1 4 ) limit distribution for all values of d if the optimization covers an interval of width less than 9 2 and the initial value of the process is known. Introduction. Semiparametric estimation of the memory parameter (d) in fractionally integrated (I (d))time series is appealing in empirical work because of the general treatment of the short-memory component that it affords. Two common statistical procedures in this class are log-periodogram (LP) regression [1,10] and local Whittle (LW) estimation [5,11]. LW estimation is known to be more efficient than LP regression in the stationary (|d| < 1 2 ) case, although numerical optimization methods are needed in the calculation. Outside the stationary region, it is known that the asymptotic theory for the LW estimator is discontinuous at d = 3 4 and again at d = 1, is awkward to use because of nonnormal limit theory and, worst of all, the estimator is inconsistent when d > 1 [8]. Thus, the LW estimator is not a good general-purpose estimator when the value of d may take on values in the nonstationary zone beyond 3 4 . Similar comments apply in the case of LP estimation [4].To extend the range of application of these semiparametric methods, data differencing and data tapering have been suggested [3,15]. These methods have the advantage that they are easy to implement and they make use of existing algorithms once the data filtering has been carried out. Differencing has the disadvantage that prior information is needed on the appropriate order of differencing. Tapering has the disadvantage that the filter distorts the trajectory of the data and inflates the asymptotic variance. As a consequence, there is presently

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“…Prefiltering and tapering were considered by [42] where they studied the performance of the local Whittle estimator with and without both preprocessing procedures. Consistency and the distribution of the local Whittle estimator in the nonstationary case were considered by [48] and [49] involving data tapers.…”

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confidence: 99%

Estimation methods for the LRD parameter under a change in the mean

2016

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When analyzing time series which are supposed to exhibit long-range dependence (LRD), a basic issue is the estimation of the LRD parameter, for example the Hurst parameter H ∈ (1/2, 1). Conventional estimators of H easily lead to spurious detection of long memory if the time series includes a shift in the mean. This defect has fatal consequences in change-point problems: Tests for a level shift rely on H, which needs to be estimated before, but this estimation is distorted by the level shift.We investigate two blocks approaches to adapt estimators of H to the case that the time series includes a jump and compare them with other natural techniques as well as with estimators based on the trimming idea via simulations. These techniques improve the estimation of H if there is indeed a change in the mean.In the absence of such a change, the methods little affect the usual estimation. As adaption, we recommend an overlapping blocks approach: If one uses a consistent estimator, the adaption will preserve this property and it performs well in simulations.

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Gaussian Semiparametric Estimation of Non‐stationary Time Series

Cited by 293 publications

References 19 publications

Local polynomial Whittle estimation of perturbed fractional processes

Local polynomial Whittle estimation of perturbed fractional processes

Exact Local Whittle Estimation of Fractional Integration With Unknown Mean and Time Trend

Estimation methods for the LRD parameter under a change in the mean

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