# Documentation

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# Nonspherical Models

Model or correct effects of heteroscedasticity and correlation

## Classes

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

## Functions

 `autocorr` Sample autocorrelation `lbqtest` Ljung-Box Q-test for residual autocorrelation `parcorr` Sample partial autocorrelation `archtest` Engle test for residual heteroscedasticity
 `arima` Convert regression model with ARIMA errors to ARIMAX model
 `hac` Heteroscedasticity and autocorrelation consistent covariance estimators `fgls` Feasible 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.

## Concepts

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.

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