Dynamic Copula-Based GARCH Model Analysis China Outbound Tourism Demand - Innovative Management in Information and Production - page 115

and the asymmetric effect of shocks in two of the four countries. Seo et al. ( 2009 )
applied the multivariate GARCH model to analyses of the relationships in Korea
outbound tourism demand. It found that conditional correlation among tourism
demand was time-varying.
However, multivariate GARCH models such as the CCC-GARCH, DCC-
GARCH, or VARMA-GARCH models are somewhat restrictive due to their
requirements of normality for the joint distribution and linear relationships among
variables. To account for nonlinear and time-dependent dependence, the parameters
of the copula functions were assumed to follow dynamic processes conditional to
the available information. This study applied four kinds of copula-based GARCH
to estimate the conditional dependence structure as a measure of analyzing the
time-varying relationship of tourism demand for the leading destinations. Recently,
the copula-based GARCH model becomes popular in analyzing economic studies,
especially in financial ( Patton 2006 ; Ane and Labidi 2006 ; Ning and Wirjanto 2009 ;
Wang et al. 2011 ; Wu et al. ( 2011 ); Reboredo 2011 ). As far as we know, there is no
study applying copula-based GARCH model to investigate the dependence among
tourism demands. Thus, in this study, we fill in the gap in literature by employing
the copula-basedGARCH model to examine dependence among tourism demands.

3 Econometrics Models

3.1 The Model for the Marginal Distribution

The GARCH (1, 1) model can be described as follows:

2
i = 1 ϕ i D i , t + e i , t

y i , t = c 0 + c 1 y i , t − 1 + c 2 e i , t − 1 + (1)

h i , t x i , t ,

e i , t = x i , t ∼ SkT ( x i | η i , λ i ) (2)

h i , t = ω i , t + α i e 2 i , t − 1 + β i h i , t − 1

(3)

where D i , t are seasonal dummies ( D 1 , t and D 2 , t are Chinese Spring Festival and
summer holiday, respectively) and capture the impact of the seasonal effects. The
condition in the variance equation are 1. In order

to capture the possible asymmetric and heavy-tailed characteristics of the tourism
demand returns, the error term of e i , t is assumed to be a skewed-t distribution. The
density function is followed by Hansen ( 1994 ):

ω i > 0 , α i , β i ≥ 0and α i + β i <

⎧
⎨

nd 1

2 − ( η + 1 ) / 2

2 nx + m

1
η −

m
n

+ , x < −

1 − λ

skewed − t ( x | η , λ )= (4)

nd 1

2 − ( η + 1 ) / 2

η − 2 nx + m

⎩

1 m

n

+ , x ≥−

1 + λ