Conditional Mean Models

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

Apps

Analyze and model econometric time series

Functions

Create Model

`arima`	Create univariate autoregressive integrated moving average (ARIMA) model
`LagOp`	Create lag operator polynomial
`arma2ar`	Convert ARMA model to AR model
`arma2ma`	Convert ARMA model to MA model

Fit Model to Data

`estimate`	Fit autoregressive integrated moving average (ARIMA) model to data
`infer`	Infer ARIMA or ARIMAX model residuals or conditional variances
`summarize`	Display ARIMA model estimation results

Generate Simulations or Impulse Responses

`simulate`	Monte Carlo simulation of ARIMA or ARIMAX models
`filter`	Filter disturbances using ARIMA or ARIMAX model
`impulse`	Generate univariate autoregressive integrated moving average (ARIMA) model impulse response function (IRF)
`armairf`	Generate or plot ARMA model impulse responses

Generate Minimum Mean Square Error Forecasts

forecast Forecast univariate autoregressive integrated moving average (ARIMA) model responses or conditional variances

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 App
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

Time Base Partitions for ARIMA Model Estimation
When you fit a time series model to data, lagged terms in the model require initialization, usually with observations at the beginning of the sample.
Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App
Interactively implement the Box-Jenkins methodology to select the appropriate number of lags for a univariate 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 App
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 ARIMAX Model Using Econometric Modeler App
Interactively specify and estimate an ARIMAX model.
Estimate Conditional Mean and Variance Model
Estimate a composite conditional mean and variance model.
Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App
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 App Session
Export variables to the MATLAB^® Workspace, generate plain text and live functions that return a model estimated in an app session, 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 of Conditional Mean Model
Plot the impulse response function of univariate autoregressive moving average 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 from ARX Model
Forecast an ARIMAX model by computing MMSE forecasts or using Monte Carlo simulation.
Specify Presample and Forecast Period Data to Forecast ARIMAX Model
This example shows how to partition a timeline into presample, estimation, and forecast periods, and it shows how to supply the appropriate number of observations to initialize a dynamic model for estimation and forecasting.

Concepts

Analyze Time Series Data Using Econometric Modeler
Interactively visualize and analyze univariate or multivariate time series data.
Specifying Univariate Lag Operator Polynomials Interactively
Specify univariate 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.
MMSE Forecasting of Conditional Mean Models
Learn about MMSE forecasting.

Related Information

Creating ARIMA Models Using Econometric Modeler App

Featured Examples

Model and Simulate Electricity Spot Prices Using the Skew-Normal Distribution

Simulate the future behavior of electricity spot prices from a time series model fitted to historical data. Because electricity spot prices can exhibit large deviations, the example models the innovations using a skew-normal distribution. The data set in this example contains simulated, daily electricity spot prices from January 1, 2010 through November 11, 2013.

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