# Testing normality for unconditionally heteroscedastic macroeconomic variables

## TL;DR

This paper evaluates methods for testing normality in macroeconomic time series with heteroscedasticity, proposing a bootstrap approach to improve accuracy over traditional tests like Jarque-Bera.

## Contribution

It introduces a bootstrap-based method to address size distortions in normality testing of heteroscedastic macroeconomic data, improving reliability.

## Key findings

- Kernel smoothing approach can suffer from size distortion in macroeconomic samples.
- Bootstrap methodology effectively corrects size distortions in normality tests.
- Analysis of inflation data from US, Korea, and Australia demonstrates the method's practical utility.

## Abstract

In this paper the testing of normality for unconditionally heteroscedastic macroeconomic time series is studied. It is underlined that the classical Jarque-Bera test (JB hereafter) for normality is inadequate in our framework. On the other hand it is found that the approach which consists in correcting the heteroscedasticity by kernel smoothing for testing normality is justified asymptotically. Nevertheless it appears from Monte Carlo experiments that such methodology can noticeably suffer from size distortion for samples that are typical for macroeconomic variables. As a consequence a parametric bootstrap methodology for correcting the problem is proposed. The innovations distribution of a set of inflation measures for the U.S., Korea and Australia are analyzed.