Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Series With Long‐range Dependence

Giraitis, Liudas; Robinson, Peter; Samarov, Alexander

doi:10.1111/1467-9892.00038

Cited by 59 publications

(69 citation statements)

References 7 publications

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“…Our point is that the extreme closeness of such models to fGn must ultimately manifest in simpler asymptotic behaviour which will, in general, translate to improved estimation. Indeed, in the spectral domain, the importance of the degree of smoothness at the origin for the ultimate limits on estimator performance has already been noted Giraitis et al (1997). Note that the above observations in no way put into question the findings of prior work on estimation of fractional processes in noise.…”

Section: Discussionmentioning

confidence: 78%

Why Farima Models Are Brittle

2013

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The FARIMA models, which have long-range-dependence (LRD), are widely used in many areas.Through deriving a precise characterisation of the spectrum, autocovariance function, and variance time function, we show that this family is very atypical among LRD processes, being extremely close to the fractional Gaussian noise in a precise sense. Furthermore, we show that this closeness property is not robust to additive noise. We argue that the use of FARIMA, and more generally fractionally differenced time series, should be reassessed in some contexts, in particular when convergence rate under rescaling is important and noise is expected.

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Section: Discussionmentioning

confidence: 78%

Why Farima Models Are Brittle

2013

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“…One possible solution could be to choose the number of frequencies used in the regression Eq. (7) more carefully (Giraitis et al, 1997;Hurvich and Deo, 1999). But the effectiveness of these methods seems to be limited.…”

Section: Results Of Simulationsmentioning

confidence: 99%

Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

Wang

Gelder

Vrijling

et al. 2007

Hydrol. Earth Syst. Sci.

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Abstract. The Lo's modified rescaled adjusted range test (R/S test) (Lo, 1991), GPH test (Geweke and Porter-Hudak, 1983) and two approximate maximum likelihood estimation methods, i.e., Whittle's estimator (W-MLE) and another one implemented in S-Plus (S-MLE) based on the algorithm of Haslett and Raftery (1989) are evaluated through intensive Monte Carlo simulations for detecting the existence of longmemory. It is shown that it is difficult to find an appropriate lag q for Lo's test for different short-memory autoregressive (AR) and fractionally integrated autoregressive and moving average (ARFIMA) processes, which makes the use of Lo's test very tricky. In general, the GPH test outperforms the Lo's test, but for cases where a strong short-range dependence exists (e.g., AR(1) processes with φ=0.95 or even 0.99), the GPH test gets useless, even for time series of large data size. On the other hand, the estimates of dgiven by S-MLE and W-MLE seem to give a good indication of whether or not the long-memory is present. The simulation results show that data size has a significant impact on the power of all the four methods because the availability of larger samples allows one to inspect the asymptotical properties better. Generally, the power of Lo's test and GPH test increases with increasing data size, and the estimates of d with GPH method, S-MLE method and W-MLE method converge with increasing data size. If no large enough data set is available, we should be aware of the possible bias of the estimates.The four methods are applied to daily average discharge series recorded at 31 gauging stations with different drainage areas in eight river basins in Europe, Canada and USA to detect the existence of long-memory. The results show that the presence of long-memory in 29 daily series is confirmed by at least three methods, whereas the other two series are indicated to be long-memory processes with two methods. The intensity of long-memory in daily streamflow processes has only a very weak positive relationship with the scale of watershed.

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“…This is an advantage of the LPW estimator over the bias-reduced estimator considered in AG, which is shown to attain the optimal rate for Gaussian processes. The optimal rate established in AG is related to, and relies on, results of Giraitis, Robinson, and Samarov (1997).…”

Section: Optimal Rate Of Convergencementioning

confidence: 99%

“…Results of Andrews and Guggenberger (2003) (AG), which in turn rely on results of Giraitis, Robinson, and Samarov (1997), show that the optimal choices of r and m (in terms of the rate of convergence of the estimator of d 0 ) depend on the smoothness of ϕ(λ) at zero. We provide an adaptive estimator of d 0 , denoted the ALPW estimator, based on the method of Lepskii (1990), that uses the data to select r and m. This estimator is shown to obtain the optimal rate of convergence, up to a logarithmic factor.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

Andrews¹,

Sun²

2004

Econometrica

114

118

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The local Whittle (or Gaussian semiparametric) estimator of long range dependence, proposed by Künsch (1987) and analyzed by Robinson (1995a), has a relatively slow rate of convergence and a finite sample bias that can be large. In this paper, we generalize the local Whittle estimator to circumvent these problems. Instead of approximating the short-run component of the spectrum, ϕ(λ), by a constant in a shrinking neighborhood of frequency zero, we approximate its logarithm by a polynomial. This leads to a "local polynomial Whittle" (LPW) estimator. We specify a data-dependent adaptive procedure that adjusts the degree of the polynomial to the smoothness of ϕ(λ) at zero and selects the bandwidth. The resulting "adaptive LPW" estimator is shown to achieve the optimal rate of convergence, which depends on the smoothness of ϕ(λ) at zero, up to a logarithmic factor.

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Rate Optimal Semiparametric Estimation of the Memory Parameter of the Gaussian Time Series With Long‐range Dependence

Cited by 59 publications

References 7 publications

Why Farima Models Are Brittle

Why Farima Models Are Brittle

Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes

Adaptive Local Polynomial Whittle Estimation of Long-range Dependence

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