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A note on the Hiemstra-Jones test for Granger non-causality
Cees Diks & Valentyn Panchenko
Center for Nonlinear Dynamics in Economics and Finance
Department of Economics, University of Amsterdam, Roetersstraat 11
1018 WB Amsterdam, The Netherlands

November 17, 2004
Abstract
We address a consistency problem in the commonly used nonparametric test for Granger
causality developed by Hiemstra and Jones (1994). We show that the relationship tested is not implied by the null hypothesis of Granger non-causality. Monte Carlo simulations using processes
satisfying the null hypothesis show that, for a given nominal size, the actual rejection rate may
tend to one as the sample size increases. Our results imply that evidence for nonlinear Granger
causality reported in the applied empirical literature should be re-interpreted.
Keywords: Granger causality; Hypothesis tests; Nonparametric tests
JEL classification: C12, C22, C52

1

Introduction

Consider a strictly stationary and weakly dependent bivariate time series process {(Xt , Yt )}, t ∈ Z.
By definition, Y is strictly Granger (1969) causing X if the conditional distribution of Xt , given the
past observations Xt−1 , Xt−2 , . . . and Yt−1 , Yt−2 , . . ., differs from the conditional distribution of Xt ,
given the past observations Xt−1 , Xt−2 , . . . only. Intuitively, Y is a Granger cause of X if adding past
observations of Y to the information set increases the knowledge on the distribution of current values
of X. Note that although the definition concerns conditional distributions given an infinite number of
past observations, in practice tests are usually confined to finite orders in X and Y .
Several recent empirical studies report results for the Hiemstra and Jones (1994) test; a nonparametric test for Granger non-causality against general (linear and non-linear) alternatives. Evidence for causality is reported by e.g. Abhyankar (1998), Silvapulla and Moosa (1999), and Asimakopoulos et al. (2000). Okunev et al. (2002) report inefficiencies in Australian real estate and
stock market prices. In this note we argue that the Hiemstra-Jones test does not provide a solid basis
for conclusions of this type.
Initially, our interest was raised by the fact that, for some data sets, counter-intuitive results are
obtained from the Hiemstra-Jones test and conventional tests of the same null hypothesis against linear
Granger causality. Even if there is strong evidence for linear Granger causality, the Hiemstra-Jones
test c...
A note on the Hiemstra-Jones test for Granger non-causality
Cees Diks & Valentyn Panchenko
Center for Nonlinear Dynamics in Economics and Finance
Department of Economics, University of Amsterdam, Roetersstraat 11
1018 WB Amsterdam, The Netherlands
November 17, 2004
Abstract
We address a consistency problem in the commonly used nonparametric test for Granger
causality developed by Hiemstra and Jones (1994). We show that the relationship tested is not im-
plied by the null hypothesis of Granger non-causality. Monte Carlo simulations using processes
satisfying the null hypothesis show that, for a given nominal size, the actual rejection rate may
tend to one as the sample size increases. Our results imply that evidence for nonlinear Granger
causality reported in the applied empirical literature should be re-interpreted.
Keywords: Granger causality; Hypothesis tests; Nonparametric tests
JEL classification: C12, C22, C52
1 Introduction
Consider a strictly stationary and weakly dependent bivariate time series process {(X
t
, Y
t
)}, t Z.
By definition, Y is strictly Granger (1969) causing X if the conditional distribution of X
t
, given the
past observations X
t1
, X
t2
, . . . and Y
t1
, Y
t2
, . . ., differs from the conditional distribution of X
t
,
given the past observations X
t1
, X
t2
, . . . only. Intuitively, Y is a Granger cause of X if adding past
observations of Y to the information set increases the knowledge on the distribution of current values
of X. Note that although the definition concerns conditional distributions given an infinite number of
past observations, in practice tests are usually confined to finite orders in X and Y .
Several recent empirical studies report results for the Hiemstra and Jones (1994) test; a non-
parametric test for Granger non-causality against general (linear and non-linear) alternatives. Ev-
idence for causality is reported by e.g. Abhyankar (1998), Silvapulla and Moosa (1999), and Asi-
makopoulos et al. (2000). Okunev et al. (2002) report inefficiencies in Australian real estate and
stock market prices. In this note we argue that the Hiemstra-Jones test does not provide a solid basis
for conclusions of this type.
Initially, our interest was raised by the fact that, for some data sets, counter-intuitive results are
obtained from the Hiemstra-Jones test and conventional tests of the same null hypothesis against linear
Granger causality. Even if there is strong evidence for linear Granger causality, the Hiemstra-Jones
test can fail to detect causality, or suggest that there is less causality than under the null hypothesis of
no Granger causality (c.f. large negative values of test statistics reported in Brooks and Henry, 2000).
As an illustration we consider the test results presented in Table 1. We simulated 10000 obser-
vations from a bivariate data generating process (to be described in more detail later) with strong
linear Granger causality from Y to X and applied linear and nonlinear Granger causality tests in both
1
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