# Conditional Mean Models

## Apps

Econometric Modeler | Analyze and model econometric time series |

## Functions

## 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.