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FindProcessParameters

✖

finds the parameter estimates for the process proc from data.

✖
FindProcessParameters[data,proc,{{p,p0},{q,q0},…}]

finds the parameters p, q, … with starting values p0, q0, … .

Details and Options

  • FindProcessParameters returns a list of replacement rules for the parameters in proc.
  • The data can be given in the following forms:
  • {s0,…}a path with state si at time i
    {{t0,s0},…}a path with state si at time ti
    TemporalData[…]one or several paths
  • The times ti and states si must belong to the time and state domain of the process proc.
  • The process proc can be any parametric scalar- or vector-valued process.
  • The following options can be given:
  • AccuracyGoalAutomaticthe accuracy sought
    ProcessEstimator Automaticwhat process parameter estimator to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecision Automaticthe precision used in internal computations
  • The following basic settings can be used for ProcessEstimator:
  • Automaticautomatically choose the parameter estimator
    "MaximumLikelihood"maximize the log likelihood directly
    "MethodOfMoments"match covariance
  • Special settings for ProcessEstimator are documented under the individual random process reference pages.
  • Additional settings for time series processes include "MaximumConditionalLikelihood" and "SpectralEstimator".
  • Additional settings for HiddenMarkovProcess include "BaumWelch" and "ViterbiTraining".

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Estimate the parameter of a PoissonProcess:

In[1]:=1
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https://wolfram.com/xid/0fq46jwannkir-87m94z
In[2]:=2
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https://wolfram.com/xid/0fq46jwannkir-ntrd4p
Out[2]=2

Obtain the estimated process:

In[3]:=3
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https://wolfram.com/xid/0fq46jwannkir-bm24nr
Out[3]=3

Compare simulations of the estimated process to the original data:

In[4]:=4
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https://wolfram.com/xid/0fq46jwannkir-hb971p
In[5]:=5
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https://wolfram.com/xid/0fq46jwannkir-ijidg5
Out[5]=5

Find the parameters for an ARProcess:

In[1]:=1
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https://wolfram.com/xid/0fq46jwannkir-oul0zw
In[2]:=2
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https://wolfram.com/xid/0fq46jwannkir-kv3pzl
Out[2]=2

Obtain the estimated process:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-jchbvw
Out[3]=3

Compare correlation functions for data and the estimated process:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-crx03b
In[5]:=5
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https://wolfram.com/xid/0fq46jwannkir-f03fu8
In[6]:=6
✖
https://wolfram.com/xid/0fq46jwannkir-i2u3tg
Out[6]=6

Scope  (9)Survey of the scope of standard use cases

Parametric Processes  (3)

Estimate the parameter for a RandomWalkProcess:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-oy6ao1
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-ir45un
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-onmzof
Out[3]=3

Estimate the parameters for a RenewalProcess:

In[1]:=1
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https://wolfram.com/xid/0fq46jwannkir-b2qqzq
In[2]:=2
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https://wolfram.com/xid/0fq46jwannkir-zkzjr
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-ddwrlu
Out[3]=3

Estimate the parameters for a Wiener process:

In[1]:=1
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https://wolfram.com/xid/0fq46jwannkir-b4q52
In[2]:=2
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https://wolfram.com/xid/0fq46jwannkir-e93vf3
Out[2]=2

Time Series Processes  (3)

Estimate the parameters for an ARProcess:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-cvszuw
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-rfo3pl
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-l8kdsv
Out[3]=3

Compare covariance functions:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-c0klru
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0fq46jwannkir-ds1qpl
Out[5]=5

Estimate an ARMAProcess:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-c6smt7
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-ufs50l
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-ikoofc
Out[3]=3

Compare covariance functions:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-h55k41
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0fq46jwannkir-i1nooj
Out[5]=5

Provide initial values for the estimation of an ARProcess:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-mudo3o
In[2]:=2
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https://wolfram.com/xid/0fq46jwannkir-sy5tiy
Out[2]=2

Solve for repeated parameters:

In[3]:=3
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https://wolfram.com/xid/0fq46jwannkir-jq07g
In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-casyxt
Out[4]=4

Queueing Processes  (2)

Estimate the arrival and service rates for an M/M/1 queue:

In[1]:=1
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https://wolfram.com/xid/0fq46jwannkir-baqdm5
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-dw93n7
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-hwt1y2
Out[3]=3

Use the corresponding random path for the data:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-p9jw4
Out[4]=4

Estimate the arrival rate for an M/M/1 queue:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-cklfom
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-b2st24
Out[2]=2

Estimate the service rate:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-clw5hv
In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-j2sft6
Out[4]=4

Finite Markov Processes  (1)

Estimate the parameters for a discrete Markov process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-c5f4g4
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-3xogo
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-zumc0
Out[3]=3

Options  (5)Common values & functionality for each option

WorkingPrecision  (1)

Estimate process parameters using default machine precision:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-hy8xm1
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-fm09r4
Out[2]=2

Use higher precision:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-cxgk21
In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-bje0vl
Out[4]=4

ProcessEstimator  (4)

Maximum likelihood for a parametric process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-2s6tu4
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-78ksl6
Out[2]=2

Time series process:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-uhijoi
In[5]:=5
✖
https://wolfram.com/xid/0fq46jwannkir-w76fg5
Out[5]=5

Method of moments for a parametric process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-fclfcl
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-sghs27
Out[2]=2

Time series process:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-qfbb8d
In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-2qssm8
Out[4]=4

Maximize conditional likelihood for a time series process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-0a5hy1
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-n9momy
Out[2]=2

Spectral estimator for a time series process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-tsq7b4
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-ghncbm
Out[2]=2

Applications  (2)Sample problems that can be solved with this function

Model the mean daily temperature for Champaign in August 2012:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-cz01f1
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-k66ryv
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-nhqqqg
Out[3]=3

Find process parameters:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-4c4xkj
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0fq46jwannkir-ezwc4f
Out[5]=5

Compare CorrelationFunction of the model and the data:

In[6]:=6
✖
https://wolfram.com/xid/0fq46jwannkir-dbor6k
Out[6]=6

The daily exchange rates of the euro to the dollar from May 2012 through September 2012:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-z0cz9j
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-ksytjw
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-jm5uvi
Out[3]=3

Fit an AR process to the exchange rates:

In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-1lkzx3
Out[4]=4
In[5]:=5
✖
https://wolfram.com/xid/0fq46jwannkir-ctn5nr
Out[5]=5

Forecast for 20 business days ahead:

In[6]:=6
✖
https://wolfram.com/xid/0fq46jwannkir-3da2v4
Out[6]=6

Plot the forecast with original data:

In[7]:=7
✖
https://wolfram.com/xid/0fq46jwannkir-x82zye
Out[7]=7

Properties & Relations  (2)Properties of the function, and connections to other functions

FindProcessParameters returns a list of parameter estimates for a process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-fi0nv6
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-nuv6dg
Out[2]=2

EstimatedProcess estimates the parametric process:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-g1wonv
Out[3]=3

FindProcessParameters returns a list of parameter estimates for a process:

In[1]:=1
✖
https://wolfram.com/xid/0fq46jwannkir-fa9tm0
In[2]:=2
✖
https://wolfram.com/xid/0fq46jwannkir-wtkc3
Out[2]=2

FindDistributionParameters returns a list of parameter estimates for a distribution:

In[3]:=3
✖
https://wolfram.com/xid/0fq46jwannkir-1dde8
In[4]:=4
✖
https://wolfram.com/xid/0fq46jwannkir-yq9vm
Out[4]=4
Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.
✖
Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.

Text

Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.

✖
Wolfram Research (2012), FindProcessParameters, Wolfram Language function, https://reference.wolfram.com/language/ref/FindProcessParameters.html.

CMS

Wolfram Language. 2012. "FindProcessParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindProcessParameters.html.

✖
Wolfram Language. 2012. "FindProcessParameters." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindProcessParameters.html.

APA

Wolfram Language. (2012). FindProcessParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindProcessParameters.html

✖
Wolfram Language. (2012). FindProcessParameters. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindProcessParameters.html

BibTeX

@misc{reference.wolfram_2025_findprocessparameters, author="Wolfram Research", title="{FindProcessParameters}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FindProcessParameters.html}", note=[Accessed: 02-June-2025 ]}

✖
@misc{reference.wolfram_2025_findprocessparameters, author="Wolfram Research", title="{FindProcessParameters}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/FindProcessParameters.html}", note=[Accessed: 02-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_findprocessparameters, organization={Wolfram Research}, title={FindProcessParameters}, year={2012}, url={https://reference.wolfram.com/language/ref/FindProcessParameters.html}, note=[Accessed: 02-June-2025 ]}

✖
@online{reference.wolfram_2025_findprocessparameters, organization={Wolfram Research}, title={FindProcessParameters}, year={2012}, url={https://reference.wolfram.com/language/ref/FindProcessParameters.html}, note=[Accessed: 02-June-2025 ]}