# A Vine-copula extension for the HAR model

## TL;DR

This paper extends the HAR model by incorporating a vine copula to model the joint distribution of volatility components, improving forecast accuracy for high-frequency stock data.

## Contribution

Introduces a vine-copula based extension to the HAR model, enhancing volatility forecasting by modeling joint distributions more flexibly.

## Key findings

- Vine-copula HAR outperforms standard HAR in forecasting accuracy.
- Model effectively captures dependencies among volatility components.
- Empirical results based on seven years of stock data demonstrate robustness.

## Abstract

The heterogeneous autoregressive (HAR) model is revised by modeling the joint distribution of the four partial-volatility terms therein involved. Namely, today's, yesterday's, last week's and last month's volatility components. The joint distribution relies on a (C-) Vine copula construction, allowing to conveniently extract volatility forecasts based on the conditional expectation of today's volatility given its past terms. The proposed empirical application involves more than seven years of high-frequency transaction prices for ten stocks and evaluates the in-sample, out-of-sample and one-step-ahead forecast performance of our model for daily realized-kernel measures. The model proposed in this paper is shown to outperform the HAR counterpart under different models for marginal distributions, copula construction methods, and forecasting settings.