Long memory monthly streamflow simulation by a broken line model

Garcia, Luis E.; Dawdy, David R.; Mej­ía, José

doi:10.1029/wr008i004p01100

Cited by 22 publications

(7 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most developed type of such models are the fractional noise models of Mandelbrot andWallis (1968, 1969a, b, c). Also there are the so-called brokenline models of Mejia et al (1972 and Garcia et al (1972) following Ditlevson (1969); a further type are certain ARlMA models, as proposed by O'Connell (1971O'Connell ( , 1974. An initial problem with the fractional noise models was difficulty of implementation, not to mention comprehension, and this held up their application.…”

Section: Long Memory Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic Modelling of Riverflow Time Series

Lawrance¹,

Kottegoda²

1977

Journal of the Royal Statistical Society. Series A (General)

202

100

View full text Add to dashboard Cite

Statistical work in hydrology on the topic of riverflow time series is discussed. The theme is the "data-generation method" which in the present situation aims to produce simulations corresponding to a chosen historical riverflow series; they are required to resemble the historical data in respect of hydrologically important properties, such as runs of low flows. In practice the simulations are then used as input to a projected water resources system, but this aspect is not treated here. Capture of statistical resemblence entails a thorough statistical analysis of the historical series, and the paper describes the distinctive non-Gaussian and periodic features of typical riverflow series; it emphasizes the hydrological importance of seasonality, marginal distribution, dependence and crossing properties. The paper then describes hydrological adaptions and use of some of the traditional time series and shot noise models. It discusses the hydrologically motivated long memory fractional noise and broken line models; here the aim is to bring them to the attention of statisticians for appraisal while at the same time making their theory more accessible to hydrologists. Places where the presently used methodology needs consolidating are mentioned, as are areas where further statistical and mathematical work would be of value.

show abstract

Section: Long Memory Modelsmentioning

confidence: 99%

“…Indeed further work is needed on constructing such non-Gaussian models. The models discussed here are stationary and so do not model seasonal behaviour; they may be used as input to the disaggregation process of Valencia and Schaake (1973) to produce seasonal series, and could model prewhitened seasonal series (Garcia et al, 1972).…”

Section: N=ojn-tmentioning

confidence: 99%

Stochastic Modelling of Riverflow Time Series

Lawrance¹,

Kottegoda²

1977

Journal of the Royal Statistical Society. Series A (General)

202

100

View full text Add to dashboard Cite

show abstract

“…However, by choosing parameters carefully, it can be shown that it is possible to replicate the observed Hurst phenomenon over a large range of n. O'Connell [33] was an early exponent of this idea; specifically, he used an ARMA(1, 1) model which could (roughly) preserve a given first-lag auto-correlation as well as h. For completeness, we mention that other modelling approaches were investigated to try and replicate the Hurst phenomenon. One such model was the so-called "broken-line" process detailed by Rodriguez-Iturbe et al [62], Garcia et al [63], and Mejia et al [64,65] which sought to preserve a twice differentiable spectrum. This was criticised by Mandelbrot [66] and did not prosper.…”

Section: Reactions To Mandelbrot's Modelmentioning

confidence: 99%

A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980

Graves

Gramacy

Watkins

et al. 2017

Entropy

111

View full text Add to dashboard Cite

Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is exhibiting long memory since that impacts the accuracy and confidence with which one may predict future events on the basis of a small amount of historical data. A major force in the development and study of long memory was the late Benoit B. Mandelbrot. Here, we discuss the original motivation of the development of long memory and Mandelbrot's influence on this fascinating field. We will also elucidate the sometimes contrasting approaches to long memory in different scientific communities.Keywords: long-range dependence; Hurst effect; fractionally differenced models; Mandelbrot IntroductionIn many fields, there is strong evidence that a phenomenon called "long memory" plays a significant role, with implications for forecast skill, low frequency variations, and trends. In a stationary time series, the term "long memory"-sometimes "long range dependence" (LRD) or "long term persistence"-implies that there is non-negligible dependence between the present and all points in the past. To dispense quickly with some technicalities, we clarify here that our presentation follows the usual convention in statistics [1,2] and define a stationary finite variance process to have long memory when its two-sided autocorrelation function (ACF) diverges:lim N→∞ ∑ N k=−N ρ(k) → ∞. This is equivalent to its power spectrum having a pole at zero frequency [1,2]. In practice, this means the ACF and the power spectrum both follow a power-law, because the underlying process does not have any characteristic decay timescale. This is in striking contrast to many standard (stationary) stochastic processes where the effect of each data point decays so fast that it rapidly becomes indistinguishable from noise. The study of long memory processes is important because they exhibit nonintuitive properties where many familiar mathematical results fail to hold, and because of the numerous datasets [1,2] where evidence for long memory has been found. In this paper, we will give a historical account of three key aspects of long memory: (1) The environmetric observations in the 1950s which first

show abstract

“…Another family of hydrologic models, the broken line model, has been suggested by Rodriguez-Iturbe, et a!. (1972), Mejia, et aL (1972), and Garcia, et aL (1972). These authors suggest that a number of different simple broken line processes be added together to form a more complicated general broken line process.…”

Section: Review Of Forecasting Methodsmentioning

confidence: 99%

FORECAST UNCERTAINTY IN WATER SUPPLY RESERVOIR OPERATION¹

Mishalani

Palmer

1988

J American Water Resour Assoc

View full text Add to dashboard Cite

This research investigates the benefits of forecasting in water supply systems. Questions relating operational losses to forecast period and accuracy are addressed. Some simple available forecasting techniques are assessed for their accuracy and applicability. These issues are addressed through the use of a simulation model of the Cedar and South Fork Tolt Rivers, where the system is modeled as a single purpose reservoir supplying municipal and industrial water to the Seattle metropolitan area. The following conclusions were made for this system: (1) reservoir operation deteriorates markedly with the loss of forecast accuracy; (2) the optimal length of forecasting period is five months; (3) reservoir operation may be improved by as much as 88 percent if perfect predictive abilities are available; (4) the mean of the historic data is not recommended to predict future flows because Markov methods are always superior; and (5) lag‐one autoregressive Markov schemes exhibit about a 9 percent improvement in operation over no forecasting.

show abstract

Long memory monthly streamflow simulation by a broken line model

Cited by 22 publications

References 2 publications

Stochastic Modelling of Riverflow Time Series

Stochastic Modelling of Riverflow Time Series

A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980

FORECAST UNCERTAINTY IN WATER SUPPLY RESERVOIR OPERATION¹

Contact Info

Product

Resources

About

Long memory monthly streamflow simulation by a broken line model

Cited by 22 publications

References 2 publications

Stochastic Modelling of Riverflow Time Series

Stochastic Modelling of Riverflow Time Series

A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951–1980

FORECAST UNCERTAINTY IN WATER SUPPLY RESERVOIR OPERATION1

Contact Info

Product

Resources

About

FORECAST UNCERTAINTY IN WATER SUPPLY RESERVOIR OPERATION¹