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Conditional Mean Models

Autoregressive (AR), moving average (MA), ARMA, ARIMA, ARIMAX, and seasonal models

In time series econometrics, the dynamic behavior of a variable over time is often of interest. A dynamic conditional mean model specifies the expected value of a response process yt as a function of historical information.

To model the dynamic behavior of a univariate linear conditional mean model, use the Econometrics Toolbox™ arima function at the command line or you can create models interactively with the Econometric Modeler app. By using arima, you can create a wide variety of autoregressive integrated moving average (ARIMA) models, including optionally specifying seasonal components for a SARIMA model, linearly adjusting for exogenous predictors for an ARIMAX model, or specifying a GARCH variance model, for example, to create a composite conditional mean and variance model. For more details on programmatic and interactive ARIMA model creation, see Creating Univariate Conditional Mean Models.

For multivariate conditional mean models, see Vector Autoregression Models, and, for linear regression models that assume an ARIMA error process, see Autocorrelated and Heteroscedastic Disturbances.


Econometric ModelerAnalyze and model econometric time series


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arimaCreate univariate autoregressive integrated moving average (ARIMA) model
LagOpCreate lag operator polynomial
arma2arConvert ARMA model to AR model
arma2maConvert ARMA model to MA model
estimateFit univariate ARIMA or ARIMAX model to data
inferInfer univariate ARIMA or ARIMAX model residuals or conditional variances
summarizeDisplay univariate ARIMA or ARIMAX model estimation results
simulateMonte Carlo simulation of univariate ARIMA or ARIMAX models
filterFilter disturbances using univariate ARIMA or ARIMAX model
impulseGenerate univariate ARIMA model impulse response function (IRF)
armairfGenerate or plot ARMA model impulse responses
forecastForecast univariate ARIMA or ARIMAX model responses or conditional variances


Interactive Workflows

Create Model

Fit Model to Data

Generate Simulations or Impulse Responses

Generate Minimum Mean Square Error Forecasts