MATLAB Examples

Compute and plot the impulse response function for an autoregressive (AR) model. The AR ( p ) model is given by

Estimate a seasonal ARIMA model:

Use arima to specify a multiplicative seasonal ARIMA model (for monthly data) with no constant term.

Specify an ARIMAX model using arima .

Specify an AR ( p ) model with nonzero coefficients at nonconsecutive lags.

Use the shorthand arima(p,D,q) syntax to specify the default AR ( p ) model,

Specify an MA ( q ) model with nonzero coefficients at nonconsecutive lags.

Specify an AR ( p ) model with a Student's t innovation distribution.

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

Not all model properties are modifiable. You cannot change these properties in an existing model:

Use the shorthand arima(p,D,q) syntax to specify the default MA

Use the shorthand arima(p,D,q) syntax to specify the default ARIMA ( p , D , q ) model,

Estimate an ARIMA model with nonseasonal integration using estimate . The series is not differenced before estimation. The results are compared to a Box-Jenkins modeling strategy, where

Specify a multiplicative seasonal ARIMA model (for quarterly data) with known parameter values. You can use such a fully specified model as an input to simulate or forecast .

Specify an ARIMA ( p , D , q ) model with known parameter values. You can use such a fully specified model as an input to simulate or forecast .

Simulate sample paths from a stationary AR(2) process without specifying presample observations.

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 .

Plot the impulse response function for an autoregressive moving average (ARMA) model. The ARMA ( p , q ) model is given by

The property Distribution in a model stores the distribution name (and degrees of freedom for the t distribution). The data type of Distribution is a struct array. For a Gaussian innovation

Simulate sample paths from a multiplicative seasonal ARIMA model using simulate . The time series is monthly international airline passenger numbers from 1949 to 1960.

Forecast responses and conditional variances from a composite conditional mean and variance model.

Specify an MA ( q ) model with known parameter values. You can use such a fully specified model as an input to simulate or forecast .

Forecast an ARIMAX model two ways.

Simulate responses and conditional variances from a composite conditional mean and variance model.

Specify an AR ( p ) model with constant term equal to zero. Use name-value syntax to specify a model that differs from the default model.

Calculate and plot the impulse response function for a moving average (MA) model. The MA ( q ) model is given by

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 MA ( q ) model with a Student's t innovation distribution.

Forecast a multiplicative seasonal ARIMA model using forecast . The time series is monthly international airline passenger numbers from 1949 to 1960.

Simulate sample paths from a stationary MA(12) process without specifying presample observations.

Forecast a stationary AR(12) process using forecast . Evaluate the asymptotic convergence of the forecasts, and compare forecasts made with and without using presample data.

After a model exists in the Workspace, you can modify its Distribution property using dot notation. You cannot modify the fields of the Distribution data structure directly. For example,

Use the shorthand arima(p,D,q) syntax to specify the default ARMA ( p , q ) model,

Simulate trend-stationary and difference-stationary processes. The simulation results illustrate the distinction between these two nonstationary process models.

Specify an MA ( q ) model with constant term equal to zero. Use name-value syntax to specify a model that differs from the default model.

Specify a stationary ARMAX model using arima .

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