Estimation of Irregularly Sampled Random Processes
Generate a realization of an irregularly sampled OrnsteinUhlenbeckProcess.
In[1]:=
![Click for copyable input](assets.en/estimation-of-irregularly-sampled-random-processes/In_81.png)
sample = TimeSeriesResample[
RandomFunction[
OrnsteinUhlenbeckProcess[0, .1, .3], {0, 100, .1}], {Sort[
RandomReal[100, 1000]]}]
Out[1]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_60.png)
show complete Wolfram Language input
Out[2]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_61.png)
Estimate the process parameters from irregularly sampled data.
In[3]:=
![Click for copyable input](assets.en/estimation-of-irregularly-sampled-random-processes/In_83.png)
EstimatedProcess[sample,
OrnsteinUhlenbeckProcess[\[Mu], \[Sigma], \[Theta]]]
Out[3]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_62.png)
Retrieve the stock prices for GE since January 1, 2013, and convert them to TemporalData .
In[4]:=
![Click for copyable input](assets.en/estimation-of-irregularly-sampled-random-processes/In_84.png)
price = TemporalData[FinancialData["GE", "Jan. 1, 2013"]]
Out[4]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_63.png)
show complete Wolfram Language input
Out[5]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_64.png)
The time stamp of the stock price data is nonuniform.
In[6]:=
![Click for copyable input](assets.en/estimation-of-irregularly-sampled-random-processes/In_86.png)
MinMax[Differences[price["Times"]]]
Out[6]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_65.png)
Assume the log price satisfies FractionalBrownianMotionProcess and estimate the parameters.
In[7]:=
![Click for copyable input](assets.en/estimation-of-irregularly-sampled-random-processes/In_87.png)
EstimatedProcess[Log[price],
FractionalBrownianMotionProcess[\[Mu], \[Sigma], h]]
Out[7]=
![](assets.en/estimation-of-irregularly-sampled-random-processes/O_66.png)