ccgarch for R.pdf

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Aug. 12 2008, useR!2008 in Dortmund, Germany. ccgarch: An R package for modelling multivariate GARCH models with conditional correlations Tomoaki Nakatani Department of Agricultural Economics Hokkaido University, Japan and Department of Economic Statistics Stockholm School of Economics, Sweden

1 Multivariate GARCH models Involve covariance estimation † Direct: – VEC representation – BEKK representation – GARCH part † Indirect: through conditional correlations ⁄ Volatility spillovers, asymmetry etc. ⁄ Constant Conditional Correlation (CCC) ⁄ Dynamic Conditional Correlation (DCC) ⁄ Smooth Transition Conditional Correlation (STCC) – Correlation part

Conditional Correlation GARCH models

2 GARCH part: with/without spillovers A vector GARCH(1, 1) equation: ht = a + Aε(2) t−1 + Bht−1, εi,t = h1/2 i,t zi,t, The diagonal speciﬁcation (no volatility spillovers) ht = a10 a20 + a11 0 0 a22 1,t−1 ε2 2,t−1 ε2 + b11 0 The extended speciﬁcation (allowing for volatility spillovers) ht = a10 a20 + a11 a12 a21 a22 1,t−1 ε2 2,t−1 ε2 + b11 b21 b12 b22 h1,t−1 h2,t−1 [ [ ] ] [ [ ][ ][ ] ] [ [ zt » ID(0, Pt) ] ][ 0 b22 h1,t−1 h2,t−1 ][ ]

3 Conditional Correlation Part CCC and ECCC of Bollerslev(1990) and Jeantheau (1998) Pt = P (constant over time) DCC of Engle (2002) and Engle and Sheppard (2001) Pt = (Qt ﬂ IN )−1/2Qt(Qt ﬂ IN )−1/2 Qt = (1 ¡ α ¡ β)Q + αzt−1z and α, β > 0 α + β < 1 0 t−1 + βQt−1 where Q is a sample covariance matrix of zt. STCC of Silvennoinen and Ter¨asvirta(2005) Pt = (1 ¡ Gt)P(1) + GtP(2) Gt = [1 + expf¡γ(st ¡ c)g]−1, γ > 0

The package

4 Description of the package Name: ccgarch Version: 0.1.0 (continuously updated) Author: Tomoaki Nakatani hnaktom2@gmail.comi Depends: R 2.6.1 or later Description: Functions for estimating and simulating the family of the CC-GARCH models. Simulating: the ﬁrst order (E)CCC-GARCH, (E)DCC-GARCH, (E)STCC-GARCH Estimating: the ﬁrst order (E)CCC-GARCH, (E)DCC-GARCH Availability: Not yet submitted to CRAN. Available upon request.

5 Functions for simulation CCC-GARCH and Extended CCC-GARCH models eccc.sim(nobs, a, A, B, R, d.f=Inf, cut=1000, model) DCC-GARCH and Extended DCC-GARCH models dcc.sim(nobs, a, A, B, R, dcc.para, d.f=Inf, cut=1000, model) STCC-GARCH and Extended STCC-GARCH models stcc.sim(nobs, a, A, B, R1, R2, tr.par, st.par, d.f=Inf, cut=1000, model)

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