WOLFRAM|DEMONSTRATIONS PROJECT

Mean-Reverting Random Walks

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annual trend rate
annual standard deviation
mean start
months
months to trend
24
sample ending values
th
90
percentile end value
102.979
th
70
percentile end value
94.5259
th
50
percentile end value
88.0195
th
30
percentile end value
82.6403
th
10
percentile end value
73.2783
geometric mean of end values
87.926
arithmetic mean of end values
88.5932
standard deviation of end values
10.9619
Many financial or economic processes can be modeled as mean-reverting random walks. Mean-reverting walks differ from simple diffusion by the addition of a central expectation, usually growing with time, and a restoring force that pulls subsequent values toward that expectation. The random term is lognormally distributed, and the initial value of the mean can be above or below the series start. The strength of the restoring force is given in terms of the time to return to the mean. The plot shows sample paths which result in the
th
90
,
th
70
,
th
50
,
th
30
, and
th
10
percentiles in endpoint value, out of a larger sample.