Page 275 - Contributed Paper Session (CPS) - Volume 6

CPS1929 Takayuki M.
Meanwhile, Engle et al. (2013) use the MIDAS approach to link
macroeconomic variables to the long-term component of volatility. They
incorporate a mean reverting unit daily heteroscedastic volatility process with
a MIDAS polynomial that applies to long-term macroeconomic variables,
which is called the generalized autoregressive conditional heteroscedasticity
model with MIDAS (GARCH-MIDAS) approach. Now we replace a
macroeconomic variable with a monthly EPU in GARCH-MIDAS model
following Asgharian et al. (2016). Furthermore, Colacito et al. (2011) introduce
a novel component model for dynamic correlations which is called the
dynamic conditional correlation model with MIDAS (DCC-MIDAS) approach.
DCC-MIDAS model is a natural extension of GARCH-MIDAS model to DCC
model advocated by Engle (2002). We also use DCC-MIDAS model to capture
the dynamic correlation of volatilities between the market index and individual
stocks in TSE.
The EPU index of Japan which can be downloaded on the web site:
www.policyuncertainty.com is based on frequency counts of articles in Japan's
newspapers, Asahi and Yomiuri. It counts the number of news articles
containing the terms uncertain or uncertainty, and one or more policy terms.
Policy terms are the Japanese equivalents of `tax', `policy', `spending',
`regulation', etc. To capture `spending' by the government, they use a set of
four terms: `saishutsu', `kokyo jigyohi', `kokyo toushi', and `kokuhi', see the
web site for more details. Our specification employs monthly EPU index of
Japan as an explanatory variable in the variance equation of a unit daily
GARCH-MIDAS model, which we refer to the model as GARCH-MIDAS-EPU. In
our empirical analysis, we first estimate the parameters the GARCH-MIDAS-
EPU model pair of two stock returns. After that, we obtain the estimated DCC-
MIDAS parameters with the standardized residuals from the GARCH-MIDAS-
EPU model using the quasi-likelihood method.

2. Models
In this section, we briefly introduce GARCH-MIDAS-EPU and DCC-MIDAS
models which are mentioned above, following Colacito et al. (2011), Asgharian
et al. (2016) and Conrad et al. (2014). Let us assume that the vector of returns
′
rt = [r1,t,...,rn,t] follows the process:

where µ is the vector of unconditional means, Ht is the conditional covariance

matrix and Dt is a diagonal matrix with standard deviations on the diagonal.

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