阅读Realized GARCH相关论文，试图理解以下几方面问题：
1. Realized GARCH的主要模型，以及MEM和HEAVY模型。
主要论文整理：
1. A multiple indicators model for volatility using intra-daily data Robert F. Engle, Giampiero M. Galloc
2. Multivariate High-Frequency-Based Volatility (HEAVY) Models Diaa Noureldin, Neil Shephard
2. Realized GARCH模型的衍生和扩展。
1. Realized Beta GARCH:A Multivariate GARCH Model with Realized Measures of Volatility Peter Reinhard Hansen, Asger Lunde, Valeri Voev
3. Realized GARCH和XGBoost or RNN。
REALIZED GARCH: A JOINT MODEL FOR RETURNS AND REALIZED MEASURES OF VOLATILITY
INTRODUCTION
High-frequency financial data are now widely available and the literature has recently introduced a number of realized measures of volatility, including realized variance, bipower variation, the realized kernel, and many related quantities (see Andersen and Bollerslev, 1998; Andersen et al., 2001; Barndorff-Nielsen and Shephard, 2002, 2004; Andersen et al., 2008; Barndorff-Nielsen et al., 2008; Hansen and Horel, 2009; and references therein).
Estimating a GARCH model that includes a realized measure in the GARCH equation (known as a GARCH-X model) provides a good illustration of this point. Such models were estimated by Engle (2002), who used the realized variance (see also Forsberg and Bollerslev, 2002). Within the GARCH-X framework no effort is paid to explain the variation in the realized measures, so these GARCH-X models are partial (incomplete) models that have nothing to say about returns and volatility beyond a single period into the future.
Engle and Gallo (2006) introduced the first ‘complete’ model in this context. Their model specifies a GARCH structure for each of the realized measures, so that an additional latent volatility process is introduced for each realized measure in the model. The model by Engle and Gallo (2006) is known as the multiplicative error model (MEM), because it builds on the MEM structure proposed by Engle (2002). Another complete model is the HEAVY model by Shephard and Sheppard (2010), which, in terms of its mathematical structure, is nested in the MEM framework. Unlike the traditional GARCH models, these models operate with multiple latent volatility processes. For instance, the MEM by Engle and Gallo (2006) has a total of three latent volatility processes and the HEAVY model by Shephard and Sheppard (2010) has two (or more) latent volatility processes.Within the context of stochastic volatility models, Takahashi et al. (2009) proposed a joint model for returns and a realized measure of volatility. Importantly, the economic and statistical gains from incorporating realized measures in volatility models are typically found to be large (see, for example, Christoffersen et al., 2010; Dobrev and Szerszen, 2010).
REALIZED GARCH
The General Formulation
The general structure of the RealGARCH(p, q) model is given by
（1）
(2)
(3)
We refer to the first two equations as the return equation and the GARCH equation.
We shall refer to (3) as the measurement equation, because the realized measure,, can often be interpreted as a measurement of
Realized GARCH with a Log-Linear Specification
(4)
(5)