Kummer's function

Long-range dependency (abbreviated as LRD, also addressed as long memory or long-range persistence) is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence, with the implication that this decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields. LRD has been used in various fields such as internet traffic modelling, econometrics, hydrology, linguistics and the earth sciences. Different mathematical definitions of LRD are used for different contexts and purposes. Some references are

Short-range dependence vs. long-range dependence

One way of characterising long-range and short-range dependent stationary process is in terms of their autocovariance functions. For a short-range dependent process, the coupling between values at different times decreases rapidly as the time difference increases. Either the autocovariance drops to zero after a certain time-lag, or it eventually has an exponential decay. In the case of LRD, there is much stronger coupling. The decay of the autocovariance function is power-like and so decays slower than exponentially.

A second way of characterizing long- and short-range dependence is in terms of the variance of partial sum of consecutive values. For short-range dependence, the variance grows typically proportionally to the number of terms. As for LRD, the variance of the partial sum increases more rapidly which is often a power function with the exponent greater than 1. A way of examining this behavior uses the rescaled range. This aspect of long-range dependence is important in the design of dams on rivers for water resources, where the summations correspond to the total inflow to the dam over an extended period.

The above two ways are mathematically related to each other, but they are not the only ways to define LRD. In the case where the autocovariance of the process does not exist (heavy tails), one has to find other ways to define what LRD means, and this is often done with the help of self-similar processes.

The Hurst parameter H is a measure of the extent of long-range dependence in a time series (while it has another meaning in the context of self-similar processes). H takes on values from 0 to 1. A value of 0.5 indicates the absence of long-range dependence. The closer H is to 1, the greater the degree of persistence or long-range dependence. H less that 0.5 corresponds to anti-persistency, which as the opposite of LRD indicates strong negative correlation so that the process fluctuates violently.

Relation to self-similar processes

Given a stationary LRD sequence, the partial sum if viewed as a process indexed by the number of terms after a proper scaling, is a self-similar process with stationary increments asymptotically. In the converse, given a self-similar process with stationary increments with Hurst index H>0.5, its increments (consecutive differences of the process) is a stationary LRD sequence. This also holds true if the sequence is short-range dependent, but in this case the self-similar process resulting from the partial sum can only be Brownian motion (H=0.5), while in the LRD case the self-similar process is a self-similar process with H>0.5, the most typical one being fractional Brownian motion.

Models

Among stochastic models that are be used for long-range dependence, some popular ones are autoregressive fractionally integrated moving average models, which are defined for discrete-time processes, while continuous-time models might start from fractional Brownian motion.

See also

• Long-tail traffic
• Traffic generation model
• Detrended fluctuation analysis
• Tweedie distributions

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

• Beran, J. (1994) Statistics for Long-Memory Processes, Chapman & Hall. ISBN 0-412-04901-5.

Further reading

• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• Ledesma, S. and Liu, D. (2000) "Synthesis of fractional Gaussian noise using linear approximation for generating self-similar network traffic", Computer Communication Review, 30, 4–17.
• Ledesma, S., Liu, D. and Hernandez D. (2007) "Two Approximation Methods to Synthesize the Power Spectrum of Fractional Gaussian Noise",Computational Statistics and Data Analysis Journal, 52 (2), 1047–1062.
• Witt, A. and Malamud, B. D. (2013) "Quantification of long-range persistence in geophysical time series: Conventional and benchmark-based improvement techniques" Surveys in Geophysics, 34(5), 541–651. Available online at: http://link.springer.com/article/10.1007/s10712-012-9217-8