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Conditional Mean Models

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

Apps

Econometric ModelerAnalyze and model econometric time series

Functions

expand all

arimaCreate ARIMA or ARIMAX time series model
LagOpCreate lag operator polynomial (LagOp) object
arma2arConvert ARMA model to AR model
arma2maConvert ARMA model to MA model
estimateEstimate ARIMA or ARIMAX model parameters
inferInfer ARIMA or ARIMAX model residuals or conditional variances
summarizeDisplay ARIMA model estimation results
simulateMonte Carlo simulation of ARIMA or ARIMAX models
filterFilter disturbances using ARIMA or ARIMAX model
impulseImpulse response function
armairfGenerate ARMA model impulse responses
forecastForecast ARIMA or ARIMAX process

Examples and How To

Create Model

Specify Conditional Mean Models

Create conditional mean models using arima or the Econometric Modeler app.

Modify Properties of Conditional Mean Model Objects

Change modifiable model properties using dot notation.

Specify Conditional Mean Model Innovation Distribution

Specify Gaussian or t distributed innovations process, or a conditional variance model for the variance process.

Specify t Innovation Distribution Using Econometric Modeler

Interactively specify a t innovation distribution for an ARIMA model.

AR Model Specifications

Create stationary autoregressive models using arima or the Econometric Modeler app.

MA Model Specifications

Create invertible moving average models using arima or the Econometric Modeler app.

ARMA Model Specifications

Create stationary and invertible autoregressive, moving average models using arima or the Econometric Modeler app.

ARIMA Model Specifications

Create autoregressive integrated moving average models using arima or the Econometric Modeler app.

ARIMAX Model Specifications

Create ARIMAX models using arima or the Econometric Modeler app.

Multiplicative ARIMA Model Specifications

Create multiplicative ARIMA models using arima or the Econometric Modeler app.

Specify Multiplicative ARIMA Model

Create a seasonal ARIMA model.

Specify Conditional Mean and Variance Models

Create a composite conditional mean and variance model.

Fit Model to Data

Box-Jenkins Model Selection and Estimation Using Econometric Modeler

Interactively apply the Box-Jenkins methodology to select the appropriate number of lags for a conditional mean model. Then, fit the model to data and export the estimated model to the command line to generate forecasts.

Box-Jenkins Differencing vs. ARIMA Estimation

Compare Box-Jenkins and ARIMA estimation.

Choose ARMA Lags Using BIC

Select ARMA model using information criteria.

Estimate Multiplicative ARIMA Model Using Econometric Modeler

Interactively estimate a multiplicative seasonal ARIMA model.

Estimate Multiplicative ARIMA Model

Estimate a multiplicative seasonal ARIMA model.

Model Seasonal Lag Effects Using Indicator Variables

Estimate a seasonal ARIMA model by specifying a multiplicative model or using seasonal dummies.

Estimate Conditional Mean and Variance Models

Estimate a composite conditional mean and variance model.

Perform ARIMA Model Residual Diagnostics Using Econometric Modeler

Interactively evaluate model assumptions after fitting data to an ARIMA model by performing residual diagnostics.

Infer Residuals for Diagnostic Checking

Infer residuals from a fitted ARIMA model.

Share Results of Econometric Modeler Session

Export variables to the MATLAB® Workspace, generate a MATLAB function that creates variables, or generate a report recording your activities on time series and estimated models in an Econometric Modeler app session.

Generate Simulations or Impulse Responses

Simulate Stationary Processes

Simulate stationary autoregressive models and moving average models.

Simulate Trend-Stationary and Difference-Stationary Processes

Illustrate the distinction between trend-stationary and difference-stationary processes by simulation.

Simulate Multiplicative ARIMA Models

Simulate sample paths from a multiplicative seasonal ARIMA model.

Simulate Conditional Mean and Variance Models

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

Plot the Impulse Response Function

Plot the impulse response function for various models.

Generate Minimum Mean Square Error Forecasts

Compare Predictive Performance After Creating Models Using Econometric Modeler

Interactively choose lags for an ARIMA model by comparing the AIC values of estimated models, then export several models to the command line to compare their predictive performance.

Forecast Multiplicative ARIMA Model

Forecast a multiplicative seasonal ARIMA model.

Convergence of AR Forecasts

Evaluate the asymptotic convergence of forecasts from an AR model, and compare forecasts made with and without using presample data.

Forecast Conditional Mean and Variance Model

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

Forecast IGD Rate Using ARIMAX Model

Forecast an ARIMAX model by computing MMSE forecasts or using Monte Carlo simulation.

Concepts

Econometric Modeler Overview

The Econometric Modeler app is an interactive tool for visualizing and analyzing univariate time series data.

Specifying Lag Operator Polynomials Interactively

Specify lag operator polynomial terms for time series model estimation using Econometric Modeler.

Conditional Mean Models

Learn about the characteristics and forms of conditional mean models.

Autoregressive Model

Learn about autoregressive models.

Moving Average Model

Learn about moving average models.

Autoregressive Moving Average Model

Learn about autoregressive, moving average models.

ARIMA Model

Learn about autoregressive integrated moving average models.

Multiplicative ARIMA Model

Learn about addressing seasonality and potential seasonal unit roots using multiplicative ARIMA models.

ARIMA Model Including Exogenous Covariates

Learn about ARIMA models that include a linear term for exogenous variables.

Maximum Likelihood Estimation for Conditional Mean Models

Learn how maximum likelihood is carried out for conditional mean models.

Conditional Mean Model Estimation with Equality Constraints

Constrain the model during estimation using known parameter values.

Presample Data for Conditional Mean Model Estimation

Specify presample data to initialize the model.

Initial Values for Conditional Mean Model Estimation

Specify initial parameter values for estimation.

Optimization Settings for Conditional Mean Model Estimation

Troubleshoot estimation issues by specifying alternative optimization options.

Monte Carlo Simulation of Conditional Mean Models

Learn about Monte Carlo simulation.

Presample Data for Conditional Mean Model Simulation

Learn about presample requirements for simulation.

Transient Effects in Conditional Mean Model Simulations

Learn how to minimize transient effects.

Monte Carlo Forecasting of Conditional Mean Models

Learn about Monte Carlo forecasting.

Impulse Response Function

Learn about impulse response functions.

MMSE Forecasting of Conditional Mean Models

Learn about MMSE forecasting.

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