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October 27th, 2009, 12:18 AM
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| |  Relationship between mean reversion constant and period of oscillating series
Hi,
I am creating a series by:
1) Multiplying the previous value in the series by a negative constant. For example 100.857 * -0.1 = -10.086, where 100.857 is the previous value and -0.1 is the constant.
2) Calculating the difference between the last value in the series and the value before that. For example, 100.857 - 92.948 = 7.909
3) Summing the last value in the series with the results from steps 1) and 2) to arrive at the next value in the series. For example, 100.857 -10.086 + 7.909 = 98.680.
Repeating this process produces an oscillating series that I think is a sine wave. There is a relationship between the constant and the period of the resulting series. For example, if the constant is -0.1 then the period is approximately 19 iterations. My problem is that I would like to know the formula that relates the constant to the period.
I have attached a spreadsheet that has sample values.
Sincere Thanks,
James |
October 27th, 2009, 01:24 AM
|  | Grand Panjandrum | | Join Date: Nov 2005 Location: South of England
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Quote:
Originally Posted by jalsck  Hi,
I am creating a series by:
1) Multiplying the previous value in the series by a negative constant. For example 100.857 * -0.1 = -10.086, where 100.857 is the previous value and -0.1 is the constant.
2) Calculating the difference between the last value in the series and the value before that. For example, 100.857 - 92.948 = 7.909
3) Summing the last value in the series with the results from steps 1) and 2) to arrive at the next value in the series. For example, 100.857 -10.086 + 7.909 = 98.680.
Repeating this process produces an oscillating series that I think is a sine wave. There is a relationship between the constant and the period of the resulting series. For example, if the constant is -0.1 then the period is approximately 19 iterations. My problem is that I would like to know the formula that relates the constant to the period.
I have attached a spreadsheet that has sample values.
Sincere Thanks,
James | Write out the recurence and post that here.
CB
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October 27th, 2009, 02:31 AM
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The recurrence relation is:
Y(i) = Y(i-1) - k * Y(i-1) + Y(i-1) - Y(i-2)
simplified:
Y(i) = (2 - k) * Y(i - 1) - Y(i - 2)
where -k is the constant (eg. -0.10)
The (i), (i - 1) and (i - 2) should be in subscript, but I'm not sure how to do that.
Thanks,
James |
October 27th, 2009, 04:21 PM
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I have found what appears to be very close to the answer via simple harmonic motion:
Period = (2 * Pi) / (k^0.5)
James
Last edited by jalsck; October 27th, 2009 at 04:32 PM.
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