*Article* **Parsimonious Heterogeneous ARCH Models for High Frequency Modeling**

#### **Juan Carlos Ruilova 1 and Pedro Alberto Morettin 2,\***


Received: 6 January 2020; Accepted: 8 February 2020; Published: 20 February 2020

**Abstract:** In this work we study a variant of the GARCH model when we consider the arrival of heterogeneous information in high-frequency data. This model is known as HARCH(*n*). We modify the HARCH(*n*) model when taking into consideration some market components that we consider important to the modeling process. This model, called parsimonious HARCH(*m,p*), takes into account the heterogeneous information present in the financial market and the long memory of volatility. Some theoretical properties of this model are studied. We used maximum likelihood and Griddy-Gibbs sampling to estimate the parameters of the proposed model and apply it to model the Euro-Dollar exchange rate series.

**Keywords:** GARCH model; HARCH model; PHARCH model; Griddy-Gibs; Euro-Dollar
