McLeod, A.I., and Hipel, K.W. (1978), "Preservation of the Rescaled Adjusted Range. 1. A Reassessment of the Hurst Phenomenon," Water Resources Research, 14, 491-- 508.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....flow data has remained an innovating research area. Novel statistical models for simulation, forecasting and diagnostic analysis have been introduced for river flow data and other new methods have been tried on river flow data soon after their introduction, see e.g. Lawrance and Kottegada (1977) McLeod and Hipel (1978), and Hipel and McLeod (1978ab) Noakes, Hipel, McLeod, Jimenez and Yakowitz (1988) compared the one yearahead forecasting ability of ARMA models, fractional Gaussian noise models, Fractional ARMA models, Markov type models and nonparametric regression models for four yearly river flow series. ....

....area. Novel statistical models for simulation, forecasting and diagnostic analysis have been introduced for river flow data and other new methods have been tried on river flow data soon after their introduction, see e.g. Lawrance and Kottegada (1977) McLeod and Hipel (1978) and Hipel and McLeod (1978ab) Noakes, Hipel, McLeod, Jimenez and Yakowitz (1988) compared the one yearahead forecasting ability of ARMA models, fractional Gaussian noise models, Fractional ARMA models, Markov type models and nonparametric regression models for four yearly river flow series. These series were analyzed ....

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McLeod, A.I., and Hipel, K.W. (1978), "Preservation of the Rescaled Adjusted Range. 1. A Reassessment of the Hurst Phenomenon," Water Resources Research, 14, 491-- 508.

....regression, Smoothed periodogram regression, Block size. 2 1 Introduction During the last two decades there has been considerable interest in the application of long memory time series processes in many fields, such as economics, hydrology and geology. Hurst (1951) Mandelbort (1971) and McLeod and Hipel (1978) among others, observed the long memory property in time series while working with different data sets. They observed the persistence of the observed autocorrelation function, that is, where the autocorrelations take far longer to decay than that of the same associated ARMA class. Granger (1978) ....

....the persistence of the observed autocorrelation function, that is, where the autocorrelations take far longer to decay than that of the same associated ARMA class. Granger (1978) was one of the first authors who considered fractional differencing in time series analysis. Based on studies by McLeod and Hipel (1978) which are related to the original studies of Hurst (1951) a simple method for estimating d based on re scaled adjusted range known as the Hurst coefficient method, was considered by various authors. However, Hosking (1984) concluded that this estimator of d cannot be recommended because the ....

McLeod, A. I. and Hipel, K. W. (1978) Preservation of the rescaled adjusted range 1: A reassessment of the Hurst phenomenon. Water Resource Research 14, 491-508.

....differenced noise. For this case, an explicit autocovariance function is given by fl( Gamma1) Gamma(1 Gamma 2d) Gamma( Gamma d 1) Gamma(1 Gamma Gamma d) oe 2 : 7) This formula is used in various generation methods of pure fractionally differenced noise, e.g. the method of McLeod and Hipel (1978) which we use in our Monte Carlo experiments. 2.2 Estimation In our estimations we employ the approximate Whittle estimator that is obtained by maximizing an approximation of the likelihood function in the frequency domain. In this procedure, the parameter vector 0 = ff 0 ; d; fi 0 ) is ....

....500 replications. Not all estimations of models with higher order converged. The numbers in parentheses denote the mean of the estimated standard errors. The last column reports the number of convergent simulations N used to calculate the means. All time series were generated with the method of McLeod and Hipel (1978) and all estimations use the approximate Whittle estimator (8) 3 The Selection Experiments 3.1 The Monte Carlo Study Our Monte Carlo experiments assess the performance of various model selection criteria when the true model is fractionally integrated and the alternatives of inter8 est are ARMA ....

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McLeod, A.I. and Hipel, K.W. (1978). `Preservation of the rescaled adjusted range. 1. a reassessment of the Hurst phenomen', Water Resources Research, Vol. 14,pp. 491 -- 508.

....time series models is only able to capture short memory processes. Consequently, ARMA models are unable to model stochastic dependence between distant observations. Processes of the latter kind are said to exhibit long memory and are defined by a non absolutely summable autocovariance function (McLeod and Hipel (1978)) Indeed, using the R S analysis, Booth, Kaen, and Koveos (1982) present evidence for long memory in daily changes of the US Dollar spot rates of the British Pound, the French Franc, and the Deutsche Mark for the period from July 1, 1973 until June 30, 1979. Using the modified R S test suggested ....

McLeod, A.I. and Hipel, K.W.. "Preservation of the rescaled adjusted range. 1. A reassessment of the Hurst phenomenon.", Water Resources Research, 14 (1978): 491 -- 508.

....5.5 log(m) Figure 4.2: Pox plot of Ethernet traffic data the discrepancy between the estimates of H obtained using the two methods. 4.1. 3 Stochastic Modeling of Self Similar Phenomenon Self similarity is not a new phenomenon, and has been studied extensively in several fields including hydrology [MH78] and economics [M69] Because of this, several formal mathematical models have already been developed which exhibit self similarity. However, because of the abstract nature of these models, it is often difficult to find a physical interpretation for the self similarity. Two such models are ....

A. I. McLeod, K. W. Hippel, "Preservation of the Rescaled Adjusted Range 1: A Reassessment of the Hurst Phenomenon," Water Resources Research 14, 491-508, 1978.

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A. I. McLeod, K. W. Hippel, "Preservation of the Rescaled Adjusted Range 1: A Reassessment of the Hurst Phenomenon", Water Resources Research 14, 491-508, 1978.

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