# random walk

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## random walk

n. Statistics
A sequence of changes, either in the value of a random variable or in a process (as in the price of a share of stock), in which the direction and size of each change is randomly determined, subject to some specified rules.

## random walk

n
1. (General Physics) a mathematical model used to describe physical processes, such as diffusion, in which a particle moves in straight-line steps of constant length but random direction
2. (Statistics) statistics a route consisting of successive and connected steps in which each step is chosen by a random mechanism uninfluenced by any previous step

## ran′dom walk′

n.
the path of a point or quantity that moves or changes in a stepwise manner, where the direction of each step is statistically random.
[1900–05]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 random walk - a stochastic process consisting of a sequence of changes each of whose characteristics (as magnitude or direction) is determined by chancestochastic process - a statistical process involving a number of random variables depending on a variable parameter (which is usually time)
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Second part of Table 8 compares the difference in the forecasting performance of the structural models to the benchmark random walk with drift model.
In Pakistan there is a need to stabilize production of wheat in order to sustain food security the main crop models used for wheat in our country are APSIM DSSAT SWAT CROPWAT Random Walk with Drift Linear Trend Simple Exponential Smoothing ARIMAand IFSM.
The trend component is flexibly specified such that it nests a random walk with drift model, a smooth trend model, and a deterministic trend model.
(A) Random walk with drift = 196.165###(B) Constant mean = 6761.69
A series of rolling forecasts are created for each modeling approach and then compared to random walk benchmarks and random walk with drift benchmarks.
Equation (2) indicates the "Random Walk with Drift" model; the series has a nonzero mean.
In this case, the [dS.sub.t] process in equation (4) includes a constant corresponding to the average annual increment, and the expenditures series is a random walk with drift. This type of spending behavior is captured by:
After testing several specifications, they found that a random walk with drift was the most appropriate model for their data.
Both unsophisticated models (random walk and random walk with drift) and more complex models (Box-Jenkins ARIMA and vector autoregressive models) are developed for the line items.
In particular, Watson's model assumed that the trend component of log GDP was a random walk with drift.
The left-hand panel presents results from the drift-less random walk benchmark while the right-hand panel presents results from the random walk with drift. Contrasting the results, using a drift in the benchmark eliminates any evidence of predictability for the JPY case but increases the predictability in the CAD and CHF, especially at short horizons.

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