Estimation of Irregularly Sampled Random Processes

Generate a realization of an irregularly sampled OrnsteinUhlenbeckProcess.

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sample = TimeSeriesResample[ RandomFunction[ OrnsteinUhlenbeckProcess[0, .1, .3], {0, 100, .1}], {Sort[ RandomReal[100, 1000]]}]

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ListLinePlot[sample, Filling -> Axis, ImageSize -> Medium, PlotTheme -> "Detailed"]

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Estimate the process parameters from irregularly sampled data.

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EstimatedProcess[sample, OrnsteinUhlenbeckProcess[\[Mu], \[Sigma], \[Theta]]]

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Retrieve the stock prices for GE since January 1, 2013, and convert them to TemporalData .

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price = TemporalData[FinancialData["GE", "Jan. 1, 2013"]]

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DateListPlot[price, Filling -> Axis, ImageSize -> Medium, PlotTheme -> "Detailed"]

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The time stamp of the stock price data is nonuniform.

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MinMax[Differences[price["Times"]]]

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Assume the log price satisfies FractionalBrownianMotionProcess and estimate the parameters.

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EstimatedProcess[Log[price], FractionalBrownianMotionProcess[\[Mu], \[Sigma], h]]

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