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# Topic: Random walk

###### In the News (Thu 19 Apr 18)

 Random Walk A random walk is a simple type of discrete stochastic process whose increments form a white noise. In finance, an arithmetic random walk is a random walk with increments that are a Gaussian white noise. A geometric random walk is technically not a random walk, at least according to the general definition given above. www.riskglossary.com /articles/random_walk.htm   (517 words)

 NationMaster - Encyclopedia: Random walk Random walks have interesting mathematical properties that vary greatly depending on the number of dimensions in which the walk takes place and whether it is confined to a lattice. The same is true for a random walk in the plane, moving on the integer lattice points, with probability 1/4 in each of the coordinate directions: the probability of ending up back at the starting point is 1. The random thermal perturbations in a liquid are responsible for a random walk phenomenon known as Brownian motion, and the collisions of molecules in a gas are a random walk responsible for diffusion. www.nationmaster.com /encyclopedia/Random_walk   (506 words)

 Random Walk Model This is the so-called "random walk" model: it assumes that, from one period to the next, the original time series merely takes a random "step" away from its last recorded position. However, the intercept of the out-of-sample forecasts of the random walk model is always reanchored so that that the forecasts extend from the last observed data point, rather some point fixed in the past. Model Comparison report for the three models (linear trend, random walk, and random walk with constant), we see that the last model is indeed the best, both in-sample and out-of-sample. www.duke.edu /~rnau/411rand.htm   (899 words)

 random walk Random walks have interesting mathematical properties that vary greatly depending on the number of dimensions in which the walk takes place and whether it is confined to a lattice. The same is true for a random walk in the plane, moving on the integer lattice points, with probability 1/4 in each of the coordinate directions: the probability of ending up back at the starting point is 1. The random thermal perturbations in a liquid are responsible for a random walk phenomenon known as Brownian motion, and the collisions of molecules in a gas are a random walk responsible for diffusion. www.daviddarling.info /encyclopedia/R/random_walk.html   (366 words)

 Random Walks and Anomalous Diffusion The variance is sort of a typical size of the blob of random walkers, and is mathematically defined as the (average of the squares of the distance moved by a random walkers) minus (square of the average of the distance moved by random walkers). If you consider random walks where the walker goes to the left or to the right, the steps to the left can be considered as steps of a negative length. If you follow a normal random walk for a very long time, you start seeing "normal" behavior -- the small steps cannot be seen, and the overall motion is determined by the average affect of all of the steps. chaos.ph.utexas.edu /research/annulus/rwalk.html   (1702 words)

 PlanetMath: random walk Intuitively, a random walk can be viewed as movement in space where the length and the direction of each step are random. Cross-references: martingale, walk, mean, satisfy, Brownian motion, length, series, partial sums, sequence, natural numbers, random variables, iid, stochastic process, probability space This is version 4 of random walk, born on 2005-01-31, modified 2006-10-22. planetmath.org /encyclopedia/RandomWalk.html   (211 words)

 Financial Risk Management arithmetic random walk A random walk with increments that are a Gaussian white noise. arithmetic random walk with drift An arithmetic random walk with a constant drift. In 2002, accounting firm Arthur Andersen was convicted on a single charge related to its auditing of Enron. www.riskglossary.com   (519 words)

 Geometric random walk The stationary and random appearance of this graph suggests that the random walk model is appropriate for the logged series, and it should include a constant term (i.e., positive growth) to account for the trend in the original series. The random walk hypothesis was first formalized by the French mathematician (and stock analyst) Louis Bachelier in 1900, and in the past century it has been exhaustively studied and debated. The intuition for the random walk hypothesis is a variation on the economist's classical efficiency argument, which holds that a \$100 bill will never be found lying on the sidewalk because someone else would have picked it up first. www.duke.edu /~rnau/411georw.htm   (1967 words)

 Measuring Index Quality Using Random Walks on the Web Random walks are usually Markovian, which means that the transition at each step is independent of the previous steps and depends only on the current state. This is because if the states are highly connected in a random walk (i.e, if from each state you can get to ``many other'' states in a few steps), then bounds on the number of steps required to achieve a distribution very close to the equilibrium distribution are known. First, at a high level, our random walk yields a measure different than the actual PageRank measure, both because of bias from the initial starting point, and because our walk chooses a ``random'' URL to jump to in a non-uniform way (that is effective in practice). www8.org /w8-papers/2c-search-discover/measuring/measuring.html   (7297 words)

 Random walk - EvoWiki   (Site not responding. Last check: 2007-11-05) A random walk is a mathematical model of a random process. Starting in point zero, then walking around in that way, the average distance from zero will be the square root of the walking time. At one time, the random walker will hit the precipice of extinction of one handedness and not be able to go back from there. wiki.cotch.net /index.php?title=Random_walk&printable=yes   (306 words)

 A random walk in one dimension Random walks are used to describe a variety of physical phenomena, ranging from diffusion (think of an ink drop spreading in water) to the conformation of polymers consisting of long molecular chains. The applet illustrates a random walk in one dimension. Because of the many random choices of the walker, the final position of the walker varies each time the simulation is done. webphysics.davidson.edu /WebTalks/clark/onedimensionalwalk.html   (513 words)

 Random Walk, statistics, statistical mechanics, physics, mathematics Tutorial The words, Random Walk, in their simplest incarnation, refer to this situation: The proverbial drunk is clinging to the lamppost. The next figure is a graph for one such random walk showing the position (the displacement) after having taken n steps. He is most likely to be where the color is deepest because many random walks have covered that terrain. www.physics.ucla.edu /~chester/TECH/RandomWalk/index.html   (332 words)

 Random Walk Theory - StockCharts.com   (Site not responding. Last check: 2007-11-05) Random walk theory jibes with the semi-strong efficient hypothesis in its assertion that it is impossible to outperform the market on a consistent basis. While there are some good points to be gleaned from the random walk theory, it appears to be a bit dated and does not accurately reflect the current investment climate. These rebuttals to random walk theory are not meant to suggest that the vast majority of individuals are going to suddenly start outperforming the market. www.stockcharts.com /education/Overview/randomWalk.html   (1588 words)

 Random walk on Percolation clusters Random walk is mathematical formulation of the intuitive idea of taking successive steps, each in a random direction. In this article we study the Random Walk on an invasion percolation cluster (and estimate the dimension parameters using its asymptotic behavior. We could calculate the various exponents from this simulation and established that the fracton and fractal dimension of such Random walks are different from the unconstrained walks in 2 Dimension. www.personal.psu.edu /saj169/PercolationRW/PercolationRw.html   (1447 words)

 Off-line n-step TD Prediction on the Random Walk Task First,repeated A->B,B->A n-step sequences in the random walk can lead to mutual "overcorrection" of the TD error in the n-step off-line TD update if they happen frequently enough and if α is high enough and γ is close enough to 1. Third,the highest probability of n-step resonance falls in the middle of the random walk state space.Since for n=1 it takes a larger number of episodes to propagate the non-zero reward back to the middle states,n=1 does not show this resonance anomaly for first 10 episodes as do other odd values of n. While it seems that a lot of the reason why off-line TD fails on this task has to do with rather unique conditions,it is possible that the problem of repeated state sequences is a general one and could lead to similar resonance effect in other situations.It is easy to combat with a reasonable discounting factor. www.cs.utexas.edu /~ikarpov/Classes/RL/RandomWalk   (2007 words)

 Random Walk Theory -- A complete definition The random walk theory also states that all methods of predicting stock prices are futile in the long run. The random walk theory also considers technical analysis undependable because, according to Malkiel, chartists buy only after price trends are established and sell only after price trends are broken; essentially, the chartists buy or sell too late and miss the boat. The random walk theory proclaims that it is impossible to consistently outperform the market, particularly in the short-term, because it is impossible to predict stock prices. www.streetauthority.com /terms/r/random-walk-theory.asp   (839 words)

 A Random Walk in Arithmetic That is: randomness lurks at the heart of that most traditional branch of pure mathematics, number theory. The answer is random because the only way to prove it is to postulate each answer as an additional independent axiom. Each bit of information in the random program is chosen by tossing a coin, an independent toss for each bit, so that a program containing so many bits of information, say, N bits, will have a probability of 2-N. We can now ask what is the total probability that those programs will halt. www.fortunecity.com /emachines/e11/86/randwalk.html   (2221 words)

 Random Walk Model   (Site not responding. Last check: 2007-11-05) A random walk is a mathematical model for the movement of a particle that is under the influence of some random or stochastic mechanism that affects its direction of movement. The board is a two dimensional random walk model consisting of a hexagonal array of corks, The random walk begins from the center cork and the roll of a die determines which direction the particle moves (in a real random walk, any angle is possible; here we are limited to six directions). www.fas.harvard.edu /~scdiroff/lds/MathamaticalTopics/RandomWalkModel/RandomWalkModel.html   (212 words)

 Lo, A.W. and MacKinlay, A.C.: A Non-Random Walk Down Wall Street. For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. A particular highlight is their now-famous inquiry into the pitfalls of "data-snooping biases" that have arisen from the widespread use of the same historical databases for discovering anomalies and developing seemingly profitable investment strategies. It provides convincing evidence against the random walk as applied to stock markets, and at the same time warns us of the dangers of finding spurious anomalies. press.princeton.edu /titles/6558.html   (543 words)

 Financial Concepts: Random Walk Theory Random walk theory gained popularity in 1973 when Burton Malkiel wrote "A Random Walk Down Wall Street", a book that is now regarded as an investment classic. Random walk is a stock market theory that states that the past movement or direction of the price of a stock or overall market cannot be used to predict its future movement. Random walk has never been a popular concept with those on Wall Street, probably because it condemns the concepts on which it is based such as analysis and stock picking. www.investopedia.com /university/concepts/concepts5.asp   (475 words)

 Random Walk Theory Suggests Past Has No Effect On Future Stocks   (Site not responding. Last check: 2007-11-05) Random walk theory is used to model prices of shares. Random walk theory does promote the idea that traders should use a long-term buy and hold strategy, rather than trying to time the market’s movements. Random walk theory was never popular among those on Wall Street because it condemns stock picking and analysis, both of which are the heart-and-soul of Wall Street operation. www.stockdogma.com /market-theory-random.shtml   (353 words)

 Random Walk We here at Random Walk favor baseball to basketball, but the Houston Rockets have rebounded (heh, get it?) from an injury-riddled disaster of a season in 2005-2006 to an injury-riddled, pleasantly surprising start to this campaign. Having migrated the Random Wife to a Micro\$oft wireless optical mouse a year or so previous with great success, I picked up the successor version of her model a couple weeks back, and installed it on the new computer, relegating my old wired mouse to a dusty corner of my bookshelf. Both of the Random Kids had soccer tournaments this weekend; fortunately at the same location, so it wasn't quite the logistical nightmare it could have been, but a deluge on Saturday morning didn't help matters much. www.bretonconsulting.net /weblog/randomwalk.html   (2425 words)

 Walking The actual Average number of steps taken over all the walks performed so far is shown in the field above that. Until you change the starting position or path length, the program retains the average length of a walk thus far. Pressing STOP aborts the current walk but will pick up from there when you next press GO. www.math.sc.edu /~sumner/RandomWalk.html   (189 words)

 Bobsguide - RANDOM WALK OPENS BOSTON OFFICE; APPOINTS GENERAL MANAGER FOR NEW ENGLAND REGION Random Walk also appointed industry veteran William W. Riffert to spearhead its Boston regional operations, including business development and sales efforts. Random Walk from Reuters America where he was Vice President, Application Enterprise Solutions. "Random Walk is already winning business among the investment management community, which is increasingly looking to leverage the advanced technologies that Random Walk has brought to Wall Street," said Joel Scotkin, CEO of Random Walk. www.bobsguide.com /guide/news/2317.html   (281 words)

 Random Walk 2D A bounded random walk in two dimensions is shown to the left. In this simulation the boundaries of the plane are absorbing so when a random walk reaches one of the four borders on the plane it terminates and restarts from the center. For the duration of the entire simulation, the background displays how often each position in the plane was visited using a ``hot'' coloring (i.e., the hotter the color (i.e., redder), the more that point was visited). www.computing.armstrong.edu /FacNStaff/burge/java/random_walk_2d/random_walk_2d.html   (141 words)

 random walk theory Definition An investment theory which claims that market prices follow a random path up and down, without any influence by past price movements, making it impossible to predict with any accuracy which direction the market will move at any point. In other words, the theory claims that path a stock's price follows is a random walk that cannot be determined from historical price information, especially in the short term. Investors who believe in the random walk theory feel that it is impossible to outperform the market without taking on additional risk, and believe that neither fundamental analysis nor technical analysis have any validity. www.investorwords.com /4029/random_walk_theory.html   (257 words)

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