1,721,018 research outputs found
On the Hsiao definition of non-causality
No full textGranger (Granger, C.W.J., 1969. Investigating causal relations by econometric models and cross-spectral
methods. Econometrica 37, 424–438.) defined causality between two variables X and Y in terms of
predictability. A difficulty with this definition is that it is restricted to one-step ahead prediction. In the presence
of a third environment variable Z the non-causality properties depend on the horizon of the involved prediction.
Hsiao (Hsaio, C., 1982. Autoregressive modelling and causal ordering of economic variables. Journal of
Economic Dynamic and Control 4, 243–259.) proposed a generalization of the Granger notion of causality. The
main purpose of this paper is to show that the Hsiao non-causality properties do not depend on the horizon of
involved prediction
Is a subspace containing a splitting subspace a splitting subspace?
No full textIf V, A and B are three closed subspaces of L2.
; F ; P/ we say that V is a splitting subspace
for A; B if and only if A and B are conditionally orthogonal given V. If V is a splitting subspace
for A; B, we shall say that V splits A; B. Rozanov [Rozanov, Y.A., 1979. Stochastic Markovian
Fields. In: Developments in Statistics, vol. 2. Academic Press, New York, p. 205] observes
that A ? BjV does not imply that the closed subspace W V splits A; B. However, no
example is provided. In this note we provide one
A Pitfall in Using the Characterization of Granger Non-Causality in Vector Autoregressive Models
Full text linkThe partial autocorrelation function of a first order non-invertible moving average process
No full textSelection of the Relevant Information Set for Predictive Relationships Analysis between Time Series
No full textIn time series analysis, a vector Y is often called causal for another vector
X if the former helps to improve the k-step-ahead forecast of the latter. If
this holds for k D 1, vector Y is commonly called Granger-causal for X.
It has been shown in several studies that the finding of causality between
two (vectors of) variables is not robust to changes of the information set.
In this paper, using the concept of Hilbert spaces, we derive a condition
under which the predictive relationships between two vectors are invariant
to the selection of a bivariate or trivariate framework. In more detail, we
provide a condition under which the finding of causality (improved predictability
at forecast horizon 1) respectively non-causality of Y for X is
unaffected if the information set is either enlarged or reduced by the information
in a third vector Z. This result has a practical usefulness since it
provides a guidance to validate the choice of the bivariate system fX,Yg in
place of fX,Y, Zg. In fact, to test the ‘goodness’ of fX,Yg we should test
whether Z Granger cause X not requiring the joint analysis of all variables in
fX,Y,Zg
On the use of Granger causality to investigate the human influence on climate
No full textA paper recently published in ``Nature'' ®nds that there is
suf®cient evidence to identify the effects of human activity
on global temperature. The study is based on northern and
southern hemispheres' time series temperature from 1865 to
1994 and the econometric technique applied is Granger
causality analysis. In this note, we make some critical
remarks on the conclusions of this study which seem to be
rather inconsistent from a methodological point of view. It is
shown that a more accurate application of Granger causality
analysis to this problem may not allow the same strong and
unambiguous conclusions
Granger causality between vectors of time series: A puzzling property
No full textLet us consider a discrete-time n-dimensional stochastic process z, with components x=(x1,...,xm1)′and y=(y1,...,ym2)′, m1+m2=n. We want to study causality relationships between the variables in x andy. Suppose that we find that y Granger causes x. Then we would expect to be able to pick out at least one of these variables, say yj, having a causal impact on x. It turns out that, when we consider the conditioning information set defined by the past observations of x and all the yi, i≠j, it may be that yjhas no causal impact on x, irrespective of the particular j=1,2,...,m2that we tried to pick out. This is a puzzling property. The paper provides a condition under which this property cannot hold
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