A B S T R A C T The dynamic conditional correlation (DCC) model by Engle (2002) is one of the most popular multivariate volatility models. This model is based solely on closing prices. It has been documented in the literature that the high and low prices of a given day can be used to obtain an efficient volatility estimation. We therefore suggest a model that incorporates high and low prices into the DCC framework. We conduct an empirical evaluation of this model on three datasets: currencies,

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... tocks, and commodity exchange traded funds. Regardless of whether we consider in-sample fit, covariance forecasts or value-at-risk forecasts, our model outperforms not only the standard DCC model, but also an alternative range-based DCC model. ✩ This research was supported by the National Science Centre project number 2016/21/B/HS4/00662 entitled "Multivariate volatility models -the application of low and high prices". The authors would like to thank anonymous reviewer for his/her constructive comments. low and high prices have already been proposed in the literature, including the range-based DCC by and the range-based regime-switching DCC by Su and Wu (2014) . These models, however, are based on modelling the time evolution of price range and it is not possible to compare them directly with the return-based DCC model. We propose a DCC model constructed using the Range-GARCH model by Molnár (2016) , which is formulated with the usage of low and high prices but also based on returns calculated from closing prices. Our contribution is threefold. First, we construct a new specification of the DCC model based on the Range-GARCH model by Molnár (2016) , which we refer to as the DCC-Range-GARCH model (denoted by DCC-RGARCH). The model itself is very similar to the DCC model by Engle (2002) . Squared errors in the univariate GARCH model are replaced by the Parkinson (1980) volatility estimator, but the parametrization of the covariance matrix remains the same. Second, we show using low and high prices in the formulation of the DCC model improves the estimation of the covariance matrix of returns and increases the accuracy of covariance and VaR forecasts based on this model, compared with the standard DCC model based on closing prices. Since both models, DCC and DCC-RGARCH, share the same structure in the correlation component, achieving more precise volatility estimates improves the covariance forecasts. Third, we demonstrate that covariance forecasts based on our proposed model are more accurate than those obtained using the range-based DCC model by . That is an important conclusion, because the range-based DCC model is also formulated using low and high prices and is the main competitor for the DCC-RGARCH model in this class of models. The rest of the paper is organized in the following way. Section 2 provides a description of applied models and methods. Section 3 presents data: three currency pairs -EUR/USD, USD/JPY and GBP/USD, three commodity exchange traded funds (ETFs) -United States Oil Fund, United States Natural Gas Fund and Energy Select Sector SPDR Fund and five U.S. stocks -Amazon, Apple, Goldman Sachs, Google and IBM. In Section 4.1 the parameters of the return-based DCC, range-based DCC and DCC-RGARCH models are estimated and compared. Section 4.2 evaluates the forecasts of the variance of returns from the GARCH, CARR and RGARCH models. In Section 4.3 the accuracy of covariance forecasts based on the DCC-GARCH and DCC-CARR models is compared with the forecasts from the DCC-RGARCH model. Section 4.4 evaluates the VaR forecasts based on all considered DCC models. Section 5 concludes. Theoretical background The DCC-GARCH model In this paper we extend the DCC model by Engle (2002) by introducing the range (the difference between low and high prices) to the model. First, we present the standard DCC model based on closing prices. In order to better distinguish this model from its competitors used in the paper, which are based on different univariate models, we will refer to it as the DCC-GARCH model. Let us assume that ϵ ( × 1 vector) is the innovation process for the conditional mean (or in a particular case the multivariate return process) and can be written as: