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Regression models with nonspherical errors, and HAC and FGLS
estimators

To explicitly model for serial correlation in the disturbance series,
create a regression model with ARIMA errors (`regARIMA`

model object). Alternatively, to acknowledge the presence of
nonsphericality, you can estimate a
heteroscedastic-and-autocorrelation-consistent (HAC) coefficient
covariance matrix, or implement feasible generalized least squares
(FGLS). For more details on HAC and FGLS estimators, see Time Series Regression X: Generalized Least Squares and HAC Estimators.

Econometric Modeler | Analyze and model econometric time series |

**Create Regression Models with ARIMA Errors**

Create regression models with autoregressive integrated moving average errors
using `regARIMA`

or the Econometric Modeler app.

**Specify the Default Regression Model with ARIMA Errors**

Create a default regression model with ARIMA errors using
`regARIMA`

.

**Create Regression Models with AR Errors**

Create regression models with AR errors using
`regARIMA`

.

**Create Regression Models with MA Errors**

Create regression models with MA errors using
`regARIMA`

.

**Create Regression Models with ARMA Errors**

Create regression models with ARMA errors using `regARIMA`

or
the Econometric Modeler app.

**Create Regression Models with ARIMA Errors**

Create regression models with ARIMA errors using
`regARIMA`

.

**Create Regression Models with SARIMA Errors**

Create regression models with SARIMA errors using
`regARIMA`

.

**Specify ARIMA Error Model Innovation Distribution**

Choose between Gaussian- or t-distributed innovations.

**Specify Regression Model with SARIMA Errors**

Create a regression model with multiplicative seasonal ARIMA errors.

**Modify regARIMA Model Properties**

Change aspects of an existing model.

**Plot Impulse Response of Regression Model with ARIMA Errors**

Plot impulse response functions of various regression models with ARIMA errors.

**Alternative ARIMA Model Representations**

Convert between ARMAX and regression models with ARMA errors.

**Estimate Regression Model with ARMA Errors Using Econometric Modeler App**

Interactively specify and estimate a regression model with ARMA errors.

**Estimate a Regression Model with ARIMA Errors**

Estimate the sensitivity of the US Gross Domestic Product (GDP) to changes in
the Consumer Price Index (CPI) using `estimate`

.

**Estimate a Regression Model with Multiplicative ARIMA Errors**

Fit a regression model with multiplicative ARIMA errors to data using
`estimate`

.

**Alternative ARIMA Model Representations**

Convert between ARMAX and regression models with ARMA errors.

**Choose Lags for ARMA Error Model**

To select the nonseasonal autoregressive and moving average lag polynomial degrees for a regression model with ARMA errors, use Akaike Information Criterion (AIC).

**Plot a Confidence Band Using HAC Estimates**

Plot corrected confidence bands using Newey-West robust standard errors.

**Change the Bandwidth of a HAC Estimator**

Change the bandwidth when estimating a HAC coefficient covariance, and compare estimates over varying bandwidths and kernels.

**Compare Robust Regression Techniques**

Address influential outliers using regression models with ARIMA errors, bags of regression trees, and Bayesian linear regression.

**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.

**Simulate Regression Models with ARMA Errors**

Simulate observations from various regression models with ARMA errors.

**Simulate Regression Models with Nonstationary Errors**

Simulate regression model with nonstationary and exponential errors.

**Simulate Regression Models with Multiplicative Seasonal Errors**

Simulate regression model with stationary and difference stationary errors.

**Forecast a Regression Model with ARIMA Errors**

Forecast a regression model with ARIMA(3,1,2) errors using
`forecast`

and `simulate`

.

**Forecast a Regression Model with ARIMA Errors**

Forecast a regression model with ARIMA(3,1,2) errors using
`forecast`

and `simulate`

.

**Forecast a Regression Model with Multiplicative Seasonal ARIMA Errors**

Forecast a multiplicative seasonal ARIMA model using
`forecast`

.

**Verify Predictive Ability Robustness of a regARIMA Model**

Forecast a regression model with ARIMA errors, and check the model predictability robustness.

**Econometric Modeler App 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.

**Impulse Response of Regression Models with ARIMA Errors**

Learn about impulse response functions of regression models with ARIMA errors.

Learn about innovations that exhibit autocorrelation and heteroscedasticity.

**Regression Models with Time Series Errors**

What are regression models with ARIMA errors?

Define different types of time series regression models.

**Initial Values for regARIMA Model Estimation**

Learn how MATLAB uses initial parameter values during estimation.

**Intercept Identifiability in Regression Models with ARIMA Errors**

Learn about intercept identifiability in regression model with ARIMA errors.

**Select Regression Model with ARIMA Errors**

Learn how to select an appropriate regression model with ARIMA errors.

**Maximum Likelihood Estimation of regARIMA Models**

Learn about maximum likelihood estimation for regression models with ARIMA errors.

**Optimization Settings for regARIMA Model Estimation**

Learn about optimization settings for regression model with ARIMA errors estimation.

**Presample Values for regARIMA Model Estimation**

Learn how MATLAB uses presample values during estimation.

**regARIMA Model Estimation Using Equality Constraints**

Estimate regression model with ARIMA errors with equality constraints.

**Monte Carlo Simulation of Regression Models with ARIMA Errors**

Learn about generating independent, random draws from a regression model with ARIMA errors.

**Presample Data for regARIMA Model Simulation**

Learn about the presample data required to simulate a regression model with ARIMA errors.

**Transient Effects in regARIMA Model Simulations**

Learn about how presample data affects a simulated path.

**Monte Carlo Forecasting of regARIMA Models**

Learn about forecasting a regression model with ARIMA errors using many simulated paths.

**MMSE Forecasting Regression Models with ARIMA Errors**

Learn about minimum mean square error forecasts.