({{, (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel])[…] 
represents the symbolic time series model obtained from (RefLink[TimeSeriesModelFit, paclet:ref/TimeSeriesModelFit]).}})

OpenersNotesSection(Spacer1)Details and Options

Properties of a time series model are obtained from (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel])[…]["property"].

The value of the model at time t can be obtained by giving model[t]. If t is in the range of the input data, then the data at time t is returned; otherwise, a forecasted value is given.

Forecast prediction limits at a time t can be obtained using model["PredictionLimits"][t].

(RefLink[Normal, paclet:ref/Normal]) gives the underlying time series process for the time series model.

(RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel])[…][prop,ann] gives the annotation ann associated with the property prop.

Possible time series model properties are listed on the page for (RefLink[TimeSeriesModelFit, paclet:ref/TimeSeriesModelFit]).

OpenersPrimaryExamplesSection(Spacer1)Examples  (8)

OpenersExampleSection0(Spacer1)Basic Examples  (1)

Create a (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel]) from some data:

data=RandomFunction[ARMAProcess[{.1},{.2},1],{1,10^4}];

mod=TimeSeriesModelFit[data]

Extract a property from the model:

mod["AIC"]

Evaluate the time series model at time 100:

mod[100]

Use (RefLink[Normal, paclet:ref/Normal]) to obtain the underlying time series process:

Normal[mod]

Obtain a list of available properties:

mod["Properties"]

OpenersExampleSection1(Spacer1)Scope  (7)

Extract a property from a (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel]):

mod=TimeSeriesModelFit[RandomReal[{-1,1},10^4]]

The BIC value for the model:

mod["BIC"]

Obtain a list of properties:

mod=TimeSeriesModelFit[RandomReal[{-1,1},10^4]]

mod[{"AIC","BIC"}]

Evaluate the time series model at a point:

mod=TimeSeriesModelFit[RandomReal[{-1,1},100]];

mod[102]

Map over several points:

mod/@{1,2,3,4}

Evaluate the time series model at a date:

mod=TimeSeriesModelFit[TemporalData[RandomReal[{-1,1},100],{"January 24 1982",Automatic,"Month"}]];

mod["March 15th 1989"]

Obtain the underlying time series process:

mod=TimeSeriesModelFit[RandomReal[{-1,1},100]];

Normal[mod]

Annotate a property:

mod=TimeSeriesModelFit[RandomFunction[ARMAProcess[{.1},{.2},1],{1,10^4}]];

propAnnotate[p_]:=(Column[Join[{Row[{"Property:\n\t",#1}]},Table[Row[{i,":\n\t",mod[#1,i]}],{i,{"Description","LongDescription","Value"}}]]]&)[p]

propAnnotate["BestFit"]

Use the original data to simulate future observations with (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel]):

data=TemporalData[RandomFunction[ARProcess[{.8},1],{100}]["Values"],{"January 24 1982",Automatic,"Month"}]

Fit a model using (RefLink[TimeSeriesModelFit, paclet:ref/TimeSeriesModelFit]):

model=TimeSeriesModelFit[data]

Use the best fit process to simulate 10 future observations:

process=model["Process"]

No information about time stamps or initial values is passed to (RefLink[RandomFunction, paclet:ref/RandomFunction]):

SeedRandom["TSM"];BlockRandom[sim1=RandomFunction[process,{10},4]]

Simulate using (RefLink[TimeSeriesModel, paclet:ref/TimeSeriesModel]) to use information given by the original data:

SeedRandom["TSM"];BlockRandom[sim2=RandomFunction[model,{10},4]]

{ListLinePlot[sim1],DateListPlot[sim2]}

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[TimeSeriesModelFit, paclet:ref/TimeSeriesModelFit])  ▪  (RefLink[TimeSeriesForecast, paclet:ref/TimeSeriesForecast])  ▪  (RefLink[UnitRootTest, paclet:ref/UnitRootTest])  ▪  (RefLink[AutocorrelationTest, paclet:ref/AutocorrelationTest])  ▪  (RefLink[ARProcess, paclet:ref/ARProcess])  ▪  (RefLink[MAProcess, paclet:ref/MAProcess])  ▪  (RefLink[ARMAProcess, paclet:ref/ARMAProcess])  ▪  (RefLink[ARIMAProcess, paclet:ref/ARIMAProcess])  ▪  (RefLink[SARIMAProcess, paclet:ref/SARIMAProcess])  ▪  (RefLink[RandomFunction, paclet:ref/RandomFunction])  ▪  (RefLink[SequencePredictorFunction, paclet:ref/SequencePredictorFunction])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Time Series Processes, paclet:guide/TimeSeriesProcesses])}})}})