This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Nonspherical Models

Model or correct effects of heteroscedasticity and correlation


arimaCreate ARIMA or ARIMAX time series model
regARIMACreate regression model with ARIMA time series errors


autocorrSample autocorrelation
lbqtestLjung-Box Q-test for residual autocorrelation
parcorrSample partial autocorrelation
archtestEngle test for residual heteroscedasticity
arimaConvert regression model with ARIMA errors to ARIMAX model
hacHeteroscedasticity and autocorrelation consistent covariance estimators
fglsFeasible generalized least squares

Examples and How To

Detect ARCH Effects

Test for autocorrelation in the squared residuals, or conduct Engle’s ARCH test.

Detect Autocorrelation

Estimate the ACF and PACF, or conduct the Ljung-Box Q-test.

Time Series Regression X: Generalized Least Squares and HAC Estimators

This example shows how to estimate multiple linear regression models of time series data in the presence of heteroscedastic or autocorrelated (nonspherical) innovations.

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.

Alternative ARIMA Model Representations

Convert between ARMAX and regression models with ARMA errors.

Specify Conditional Mean and Variance Models

Create a composite conditional mean and variance model.


Select Regression Model with ARIMA Errors

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

Nonspherical Models

Learn about innovations that exhibit autocorrelation and heteroscedasticity.

Was this topic helpful?