Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator

Teverovsky, Vadim; Taqqu, Murad S.

doi:10.1111/1467-9892.00050

Cited by 129 publications

(99 citation statements)

References 4 publications

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“…A method for detecting long-range dependence even in the presence of these types of nonstationarity was recently proposed by Teverovsky and Taqqu [1997]. It is a variance-type …”

Section: Dilferenced Variance Methodsmentioning

confidence: 99%

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Montanari¹,

Rosso²,

Taqqu³

1997

Water Resources Research

267

199

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Abstract. Since Hurst [1951] detected the presence of long-term persistence in hydrologic data, new estimation methods and long-memory models have been developed. The lack of flexibility in representing the combined effect of short and long memory has been the major limitation of stochastic models used to analyze hydrologic time series. In the present paper a fractionally differenced autoregressive integrated moving average (FARIMA) model is considered. In contrast to using traditional ARIMA models, this approach allows the modeling of both short-and long-term persistence in a time series. A framework for identification and estimation is presented. The data do not have to be Gaussian. The resulting model, which replicates the sample probability density of the data, can be used for the generation of long synthetic series. An application to the monthly and daily inflows of Lake Maggiore, Italy, is presented. Once a suitable model is chosen, this method gives a more accurate estimate of H. In this paper, the fractionally differenced autoregressive integrated moving average models (FARIMA, see section 3) are considered because they account for both the short-and long-memory components that are present in many hydrologic long-memory processes. An identification procedure consisting of several steps is introduced in order to determine the most suitable model. This method is then applied to daily flows to Lake Maggiore, Italy. For purposes of comparison we also apply it to monthly flows to Lake Maggiore and to monthly rainfall in Genoa, Italy. A stochastic simulation of the non-Gaussian observations is also performed.In the next section the determination of the Hurst exponent from observed hydrologic time series is discussed. Although heuristic graphical methods can detect the presence of long memory, they are not capable of estimating its intensity with a sufficient degree of accuracy. Therefore, in section 3 a stochastic modeling framework is introduced in order to combine long-memory effects with the traditional identification and estimation approach of autoregressive integrated moving average (ARIMA) models. The application of the model to daily (and monthly) flows is discussed in the section 4. An application to monthly rainfall is also presented in order to assess the flexibility of the proposed approach when modeling data not affected by persistence. Detecting Long Memory in Hydrologic Time SeriesThe relative simplicity of the heuristic estimation methods for H has made them popular as diagnostic tools. Their purpose is only to detect long memory and to provide a rough estimate of the value of the H exponent; they are not able to supply any additional information concerning the spectral density function of the data. Among the methods found in the literature, the best known is the R/S statistic, which was introduced by Hurst [1951]. Other methods have been proposed. 1035

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“…A method for detecting long-range dependence even in the presence of these types of nonstationarity was recently proposed by Teverovsky and Taqqu [1997]. It is a variance-type …”

Section: Dilferenced Variance Methodsmentioning

confidence: 99%

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Montanari¹,

Rosso²,

Taqqu³

1997

Water Resources Research

267

199

View full text Add to dashboard Cite

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“…Reviews of long memory can be found in Palma (2007) or Beran et al (2013). Time domain H estimation methods include the R/S statistic (Mandelbrot and Taqqu 1979;Bhattacharya et al 1983); aggregate series variance estimators (Taqqu et al 1995;Teverovsky and Taqqu 1997;Giraitis et al 1999); least squares regression using subsampling in Higuchi (1990); variance of residuals estimators in Peng et al (1994).…”

Section: Review Of Long-range Dependence Its Estimation Wavelets Anmentioning

confidence: 99%

A wavelet lifting approach to long-memory estimation

2016

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Reliable estimation of long-range dependence parameters is vital in time series. For example, in environmental and climate science such estimation is often key to understanding climate dynamics, variability and often prediction. The challenge of data collection in such disciplines means that, in practice, the sampling pattern is either irregular or blighted by missing observations. Unfortunately, virtually all existing Hurst parameter estimation methods assume regularly sampled time series and require modification to cope with irregularity or missing data. However, such interventions come at the price of inducing higher estimator bias and variation, often worryingly ignored. This article proposes a new Hurst exponent estimation method which naturally copes with data sampling irregularity. The new method is based on a multiscale lifting transform exploiting its ability to produce wavelet-like coefficients on irregular data and, simultaneously, to effect a necessary powerful decorrelation of those coefficients. Simulations show that our method is accurate and effective, performing well against competitors

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“…This problem is considered for example by Giraitis et al (2000a). Teverovsky/Taqqu (1997) considered the behaviour of a variance-type estimator of the memory parameter by adding a model with shifts in the mean or a slowly decaying trend of the same type as in Bhattacharya et al (1983) andK unsch (1986) to the noise process. These trends are special cases of the model of Giraitis et al (2000a) and thus of the considerations below.…”

Section: Long-range Dependence and Non-monotonic Trendsmentioning

confidence: 99%

Long memory versus structural breaks: An overview

Sibbertsen

2004

Statistical Papers

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We discuss the increasing literature on misspecifying structural breaks or more general trends as long range dependence. We consider tests on structural breaks in the long-memory regression model as well as the behaviour of estimators of the memory parameter when structural breaks or trends are in the data but long-memory is not. It can be seen that it is hard to distinguish deterministic trends from long-range dependence.

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Testing for long‐range dependence in the presence of shifting means or a slowly declining trend, using a variance‐type estimator

Cited by 129 publications

References 4 publications

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation

A wavelet lifting approach to long-memory estimation

Long memory versus structural breaks: An overview

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