This example shows how to use the shorthand `arima(p,D,q)`

syntax to specify the default ARMA(*p*, *q*) model,

By default, all parameters in the created model object have unknown values, and the innovation distribution is Gaussian with constant variance.

Specify the default ARMA(1,1) model:

model = arima(1,0,1)

model = ARIMA(1,0,1) Model: -------------------- Distribution: Name = 'Gaussian' P: 1 D: 0 Q: 1 Constant: NaN AR: {NaN} at Lags [1] SAR: {} MA: {NaN} at Lags [1] SMA: {} Variance: NaN

The output shows that the created model object, `model`

, has `NaN`

values for all model parameters: the constant term, the AR and MA coefficients, and the variance. You can modify the created model object using dot notation, or input it (along with data) to `estimate`

.

This example shows how to specify an ARMA(*p*, *q*) model with constant term equal to zero. Use name-value syntax to specify a model that differs from the default model.

Specify an ARMA(2,1) model with no constant term,

where the innovation distribution is Gaussian with constant variance.

model = arima('ARLags',1:2,'MALags',1,'Constant',0)

model = ARIMA(2,0,1) Model: -------------------- Distribution: Name = 'Gaussian' P: 2 D: 0 Q: 1 Constant: 0 AR: {NaN NaN} at Lags [1 2] SAR: {} MA: {NaN} at Lags [1] SMA: {} Variance: NaN

The `ArLags`

and `MaLags`

name-value pair arguments specify the lags corresponding to nonzero AR and MA coefficients, respectively. The property `Constant`

in the created model object is equal to `0`

, as specified. The model has default values for all other properties, including `NaN`

values as placeholders for the unknown parameters: the AR and MA coefficients, and scalar variance.

You can modify the created model using dot notation, or input it (along with data) to `estimate`

.

This example shows how to specify an ARMA(*p*, *q*) model with known parameter values. You can use such a fully specified model as an input to `simulate`

or `forecast`

.

Specify the ARMA(1,1) model

where the innovation distribution is Student's *t* with 8 degrees of freedom, and constant variance 0.15.

tdist = struct('Name','t','DoF',8); model = arima('Constant',0.3,'AR',0.7,'MA',0.4,... 'Distribution',tdist,'Variance',0.15)

model = ARIMA(1,0,1) Model: -------------------- Distribution: Name = 't', DoF = 8 P: 1 D: 0 Q: 1 Constant: 0.3 AR: {0.7} at Lags [1] SAR: {} MA: {0.4} at Lags [1] SMA: {} Variance: 0.15

Because all parameter values are specified, the created model has no `NaN`

values. The functions `simulate`

and `forecast`

don't accept input models with `NaN`

values.

`arima`

| `estimate`

| `forecast`

| `simulate`

| `struct`

- Specify Conditional Mean Models Using arima
- Modify Properties of Conditional Mean Model Objects
- Specify Conditional Mean Model Innovation Distribution

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