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A model created by arima has values assigned to all model properties. To change any of these property values, you do not need to reconstruct the whole model. You can modify property values of an existing model using dot notation. That is, type the model name, then the property name, separated by '.' (a period).
For example, start with this model specification:
Mdl = arima(2,0,0)
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 0 Constant: NaN AR: {NaN NaN} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
Modify the model to remove the constant term:
Mdl.Constant = 0
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 0 Constant: 0 AR: {NaN NaN} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
The updated constant term now appears in the model output.
Be aware that every model property has a data type. Any modifications you make to a property value must be consistent with the data type of the property. For example, AR, MA, SAR, and SMA are all cell vectors. This mean you must index them using cell array syntax.
For example, start with the following model:
Mdl = arima(2,0,0)
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 0 Constant: NaN AR: {NaN NaN} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
To modify the property value of AR, assign AR a cell array. Here, assign known AR coefficient values:
Mdl.AR = {0.8,-0.4}
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 0 Constant: NaN AR: {0.8 -0.4} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
The updated model now has AR coefficients with the specified equality constraints.
Similarly, the data type of Distribution is a data structure. The default data structure has only one field, Name, with value 'Gaussian'.
Distribution = Mdl.Distribution
Distribution = Name: 'Gaussian'
To modify the innovation distribution, assign Distribution a new name or data structure. The data structure can have up to two fields, Name and DoF. The second field corresponds to the degrees of freedom for a Student's t distribution, and is only required if Name has the value 't'.
To specify a Student's t distribution with unknown degrees of freedom, enter:
Mdl.Distribution = 't'
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 't', DoF = NaN P: 2 D: 0 Q: 0 Constant: NaN AR: {0.8 -0.4} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
The updated model has a Student's t distribution with NaN degrees of freedom. To specify a t distribution with eight degrees of freedom, say:
Mdl.Distribution = struct('Name','t','DoF',8)
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 't', DoF = 8 P: 2 D: 0 Q: 0 Constant: NaN AR: {0.8 -0.4} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
The degrees of freedom property of the model is updated. Note that the DoF field of Distribution is not directly assignable. For example, Mdl.Distribution.DoF = 8 is not a valid assignment. However, you can get the individual fields:
Mdl.Distribution.DoF
ans = 8
You can modify Mdl to include, for example, two coefficients and corresponding to two predictor series. Since Beta has not been specified yet, you have not seen it in the output. To include it, enter:
Mdl.Beta=[0.2 4]
Mdl = ARIMAX(2,0,0) Model: --------------------- Distribution: Name = 't', DoF = 8 P: 2 D: 0 Q: 0 Constant: NaN AR: {0.8 -0.4} at Lags [1 2] SAR: {} MA: {} SMA: {} Beta: [0.2 4] Variance: NaN
Not all model properties are modifiable. You cannot change these properties in an existing model:
P. This property updates automatically when any of p (degree of the nonseasonal AR operator), (degree of the seasonal AR operator), D (degree of nonseasonal differencing), or s (degree of seasonal differencing) changes.
Q. This property updates automatically when either q (degree of the nonseasonal MA operator), or (degree of the seasonal MA operator) changes.
Not all name-value pair arguments you can use for model creation are properties of the created model. Specifically, you can specify the arguments ARLags, MALags, SARLags, and SMALags during model creation. These are not, however, properties of arima models. This means you cannot retrieve or modify them in an existing model.
The nonseasonal and seasonal AR and MA lags update automatically if you add any elements to (or remove from) the coefficient cell arrays AR, MA, SAR, or SMA.
For example, specify an AR(2) model:
Mdl = arima(2,0,0)
Mdl = ARIMA(2,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 0 Constant: NaN AR: {NaN NaN} at Lags [1 2] SAR: {} MA: {} SMA: {} Variance: NaN
The model output shows nonzero AR coefficients at lags 1 and 2.
Add a new AR term at lag 12:
Mdl.AR{12} = NaN
Mdl = ARIMA(12,0,0) Model: -------------------- Distribution: Name = 'Gaussian' P: 12 D: 0 Q: 0 Constant: NaN AR: {NaN NaN NaN} at Lags [1 2 12] SAR: {} MA: {} SMA: {} Variance: NaN
The three nonzero coefficients at lags 1, 2, and 12 now display in the model output. However, the cell array assigned to AR returns twelve elements:
Mdl.AR
ans = Columns 1 through 10 [NaN] [NaN] [0] [0] [0] [0] [0] [0] [0] [0] Columns 11 through 12 [0] [NaN]
AR has zero coefficients at all the interim lags to maintain consistency with traditional MATLAB® cell array indexing.