Page 135 - Special Topic Session (STS) - Volume 2

STS474 Hideatsu T.

A copula approach to spatial econometrics with
applications to finance
Hideatsu Tsukahara
Faculty of Economics, Seijo University, Tokyo, Japan

Abstract
Traditional models in spatial econometrics utilize a spatial weight matrix as a
means to express spatial dependence, but its choice is quite arbitrary. Besides,
it imposes a linear structure between dependent variables; in its simplest form,
a dependent variable at one spatial unit is a linear combination of dependent
variables at other spatial units. When the underlying disturbance distribution
is assumed to be Gaussian or elliptical in general, the model does not allow
asymmetry in dependence structure and tail dependence for spatial
interactions. These restrictions are too strict in some applications, for example,
to financial data. In this study, therefore, we generalize existent models to
allow for some nonlinear and tail dependence in disturbance distribution by
applying the copula approach which somehow reflects the spatial dependence
indicated by spatial weight matrix. After discussing some properties of the
resulting model, we develop an estimation method assuming (semi)parametric
copula. Simulation results illustrate the applicability of our procedure, and
some real applications to financial data will be given.

Keywords
Spatial dependence; tail dependence; asymmetry

1. Introduction
Suppose that there are N spatial units. Let
1 1 11 12 … 1
21 22 … 2
= ( ⋮ 2 ) , = ( ⋮ 2 ), = ( ⋮ ⋮ ⋱ ⋮ )
1 1 …
For = 1, … , , is a dependent variable at spatial unit , and " denote a

disturbance term. Components of a spatial weight matrix satisfies ≥ 0

for all , {1, … , } and = 0 for all {1, … , }. The rows and columns

correspond to the cross-sectional observations. Its (, ) -element

represents the prior strength of the interaction between spatial units and .
This can be interpreted as the presence and strength of a link between nodes
(the observations) in a network representation that matches the spatial
weights structure (Anselin et al., 2008). As such, pairwise dependence structure
is of special importance in spatial econometrics.
The simplest model in this field is the spatial autoregressive process:

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