Autocorrelated and Heteroscedastic Disturbances

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.

For conditional mean model tools that support ARIMA model creation and analysis, see Conditional Mean Models.

Apps

Econometric Modeler

Analyze and model econometric time series

Functions

expand all

Create Model

`regARIMA`	Create regression model with ARIMA time series errors
`arima`	Convert regression model with ARIMA errors to ARIMAX model

Fit Model to Data

`hac`	Heteroscedasticity and autocorrelation consistent covariance estimators
`fgls`	Feasible generalized least squares
`estimate`	Fit univariate regression model with ARIMA errors to data
`infer`	Infer residuals of univariate regression model with ARIMA time series errors
`summarize`	Display estimation results of regression model with ARIMA errors

Generate Simulations and Impulse Responses

`simulate`	Monte Carlo simulation of univariate regression model with ARIMA time series errors
`filter`	Filter disturbances through regression model with ARIMA errors
`impulse`	Generate regression model with ARIMA errors impulse response function (IRF)

Generate Minimum Mean Square Error Forecasts

forecast Forecast responses of univariate regression model with ARIMA time series errors

Topics

Interactive Workflows

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.
Estimate Regression Model with ARMA Errors Using Econometric Modeler App
Interactively specify and estimate a regression model with ARMA errors.
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.

Create Model

Regression Models with Time Series Errors
Learn about regression models with ARIMA errors.
Time Series Regression Models
Define different types of time series regression models.
Create Regression Models with ARIMA Errors
Create regression models with autoregressive integrated moving average errors using regARIMA or the Econometric Modeler app.
Specify 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.
Nonspherical Models
Learn about innovations that exhibit autocorrelation and heteroscedasticity.
Alternative ARIMA Model Representations
Convert between ARMAX and regression models with ARMA errors.

Fit Model to Data

Estimate 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.
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.
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.

Generate Simulations or Impulse Responses

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.
Plot Impulse Response of Regression Model with ARIMA Errors
Plot impulse response functions of various regression models with ARIMA errors.
Impulse Response of Regression Models with ARIMA Errors
Learn about impulse response functions of regression models with ARIMA errors.
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.

Generate Minimum Mean Square Error Forecasts

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.
MMSE Forecasting Regression Models with ARIMA Errors
Learn about minimum mean square error forecasts.
Monte Carlo Forecasting of regARIMA Models
Learn about forecasting a regression model with ARIMA errors using many simulated paths.