Page 277 - Contributed Paper Session (CPS) - Volume 6

CPS1929 Takayuki M.
separate GARCH-MIDAS models for the stock returns for day i = 1,...,Nt in
month t as:

2
where the total stock variance σi,t is separated into a short-run component gi,t
2
and a long-run component τt such that σi,t = τtgi,t. A GARCH (1,1) process
describes the short-run component:

where α > 0 and β ≥ 0,α + β < 1. The long-run component is described by a

MIDAS regression where the lagged EPU shocks of the EPUt−k are included

over k = 1,...,24:

where the weighting scheme is described by a beta lag polynomial:

where the parameter θ1 measures the effects of the economic policy
uncertanity shocks on the long-run volatility. We fix w1 = 1 to ensure higher
weights to the most recent observations as with Asgharian et al. (2016).
Colacito et al. (2011) propose the DCC-MIDAS model which is a natural
extension of the GARCHMIDAS model to the Engle (2002) DCC model. Using
the standardized residuals , it is possible to obtain a matrix whose elements
are:

where we could have used simple cross-products of ξi,t in the above
formulation of ci,j,t. The normalization allow us to discuss regularity conditions
in terms of correlation matrices. Correlations can then be computed as:

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