Main Content

Nonspherical Models

Model or correct effects of heteroscedasticity and correlation


arimaCreate univariate autoregressive integrated moving average (ARIMA) 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
hacHeteroscedasticity and autocorrelation consistent covariance estimators
fglsFeasible generalized least squares

Examples and How To

Detect ARCH Effects Using Econometric Modeler App

Interactively assess whether a series has volatility clustering by inspecting correlograms of the squared residuals and by testing for significant ARCH lags.

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.