Hypothesis testing for long-term memory in hydrologic series

Rao, A. Ramachandra; Bhattacharya, Debarati

doi:10.1016/s0022-1694(99)00005-0

Cited by 26 publications

(16 citation statements)

References 11 publications

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“…Thus, the rescaled range is a proper method for the time series of the long term memory but it is not for the short term memory. [13], developed the modified rescaled range method like the Equations (15) to (17) and [14,15] applied the method.…”

Section: (2) Rescaled Rangementioning

confidence: 99%

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Kim¹,

Kim²,

Min³

2014

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Hurst's memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent (H). However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, rescaled range (RR) analysis, modified rescaled range (MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation (MLE), detrended fluctuations analysis (DFA), and aggregated variance time (AVT) method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then, this study discusses the advantages and disadvantages of the techniques and also the limitations of them. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the short term memory and long term memory. We analyze the SOI (Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H = 0.92. Contrary to earlier work, all the tree ring series are not random from our analysis. A certain tree ring series show a long term memory of H = 0.97 and nonlinear property. Therefore, we can say that the SOI series has the properties of long memory and nonlinearity and tree ring series could also show long memory and non-linearity.

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Section: (2) Rescaled Rangementioning

confidence: 99%

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Kim¹,

Kim²,

Min³

2014

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“…Montanari et al (1997) applied the ARFIMA model to the monthly and daily inflows of Lake Maggiore, Italy. Rao and Bhattacharya (1999) explored some monthly and annual hydrologic time series, including average monthly streamflow, maximum monthly streamflow, average monthly temperature and monthly precipitation, at various stations in the mid-western United States. They stated that there is little evidence of long-term memory in monthly hydrologic series, and for annual series the evidence for lack of long-term memory is inconclusive.…”

Section: Introductionmentioning

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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“…And the rescaled range analysis (R/S) method is one of the most common methods to calculate the Hurst index (Rao and Bhattachary 1999;Han and Tang 2004); the basic principles are as follows: for a time series, t is the temporal range and R (t) and S (t) are the range deviation sequence and the standard deviation sequence, respectively, c is a constant number, and H is the Hurst index. There is an exponential equation as follows:…”

Section: Hurst Indexmentioning

confidence: 99%

Spatial–temporal dynamics of NDVI and Chl-a concentration from 1998 to 2009 in the East coastal zone of China: integrating terrestrial and oceanic components

Hou

Gao

et al. 2012

Environ Monit Assess

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Annual normalized difference vegetation index (NDVI) and chlorophyll-a (Chl-a) concentration are the most important large-scale indicators of terrestrial and oceanic ecosystem net primary productivity. In this paper, the Sea-viewing Wide Field-of-view Sensor level 3 standard mapped image annual products from 1998 to 2009 are used to study the spatial-temporal characters of terrestrial NDVI and oceanic Chl-a concentration on two sides of the coastline of China by using the methods of mean value (M), coefficient of variation (CV), the slope of unary linear regression model (Slope), and the Hurst index (H). In detail, we researched and analyzed the spatial-temporal dynamics, the longitudinal zonality and latitudinal zonality, the direction, intensity, and persistency of historical changes. The results showed that: (1) spatial patterns of M and CV between NDVI and Chl-a concentration from 1998 to 2009 were very different. The dynamic variation of terrestrial NDVI was much mild, while the variation of oceanic Chl-a concentration was relatively much larger; (2) distinct longitudinal zonality was found for Chl-a concentration and NDVI due to their hypersensitivity to the distance to shoreline, and strong latitudinal zonality existed for Chl-a concentration while terrestrial NDVI had a very weak latitudinal zonality; (3) overall, the NDVI showed a slight decreasing trend while the Chla concentration showed a significant increasing trend in the past 12 years, and both of them exhibit strong self-similarity and long-range dependence which indicates opposite future trends between land and ocean.

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Hypothesis testing for long-term memory in hydrologic series

Cited by 26 publications

References 11 publications

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

Hurst’s Memory for Chaotic, Tree Ring, and SOI Series

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

Spatial–temporal dynamics of NDVI and Chl-a concentration from 1998 to 2009 in the East coastal zone of China: integrating terrestrial and oceanic components

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