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
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 usingregARIMAor the Econometric Modeler app. - Specify Default Regression Model with ARIMA Errors
Create a default regression model with ARIMA errors usingregARIMA. - Create Regression Models with AR Errors
Create regression models with AR errors usingregARIMA. - Create Regression Models with MA Errors
Create regression models with MA errors usingregARIMA. - Create Regression Models with ARMA Errors
Create regression models with ARMA errors usingregARIMAor the Econometric Modeler app. - Create Regression Models with ARIMA Errors
Create regression models with ARIMA errors usingregARIMA. - Create Regression Models with SARIMA Errors
Create regression models with SARIMA errors usingregARIMA. - 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) usingestimate. - Estimate a Regression Model with Multiplicative ARIMA Errors
Fit a regression model with multiplicative ARIMA errors to data usingestimate. - 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 usingforecastandsimulate. - 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 usingforecastandsimulate. - Forecast a Regression Model with Multiplicative Seasonal ARIMA Errors
Forecast a multiplicative seasonal ARIMA model usingforecast. - 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.
