Definition Of Granger Causality Research Articles

Granger causality from quantized measurements

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, a characterization of Granger causality in terms of the rank of a matrix involving the covariances is presented. We call this the causality matrix. The smallest singular value of the causality matrix gives a lower bound on the distance between the two conditional Gaussian distributions appearing in the definition of Granger causality and yields a new measure of causality. Then, conditions are derived under which Granger causality between jointly Gaussian processes can be reliably inferred from the second order moments of quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform or high resolution quantizers. Apart from the assumed partial Markov order and joint Gaussianity, this approach does not require the parameters of a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.

Investigation of the Granger Causal Relationship Between Macroeconomic Variables and Stock Prices in Kenya

The aim of this paper was to analyze the causal relationship between macroeconomic variables and stock prices in the VAR(Vector Autoregressive) modeling framework using secondary time series annual data from 1980 to 2012. Sim's causality test based on Granger definition of causality was used to test the causality relationship while OLS (Ordinary Least Squares) is used to test for any significant relationship. According to Granger causality test results, it is evident that movement in the macroeconomic variables had no significant effect on stock prices except for inflation rate; exchange rate and change in stock prices also seem to be an insignificant factor explaining part of the movement in the macroeconomic variables except for market interest rates. Also, the regression test result shows that all the macroeconomic variables are jointly significant in explaining the variations in stock prices. Hence, the findings imply that the causality between macroeconomic variables and stock prices runs unilaterally or entirely in one direction from inflation rate and exchange rate to stock prices and from stock prices to market interest rates. Thus, there is evidence to show that inflation rate and exchange rate are the cause of movement on stock prices and stock prices are the cause of movement of interest rates in Kenya.

Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions

The Partial Directed Coherence (PDC) and its generalized formulation (gPDC) are popular tools for investigating, in the frequency domain, the concept of Granger causality among multivariate (MV) time series. PDC and gPDC are formalized in terms of the coefficients of an MV autoregressive (MVAR) model which describes only the lagged effects among the time series and forsakes instantaneous effects. However, instantaneous effects are known to affect linear parametric modeling, and are likely to occur in experimental time series. In this study, we investigate the impact on the assessment of frequency domain causality of excluding instantaneous effects from the model underlying PDC evaluation. Moreover, we propose the utilization of an extended MVAR model including both instantaneous and lagged effects. This model is used to assess PDC either in accordance with the definition of Granger causality when considering only lagged effects (iPDC), or with an extended form of causality, when we consider both instantaneous and lagged effects (ePDC). The approach is first evaluated on three theoretical examples of MVAR processes, which show that the presence of instantaneous correlations may produce misleading profiles of PDC and gPDC, while ePDC and iPDC derived from the extended model provide here a correct interpretation of extended and lagged causality. It is then applied to representative examples of cardiorespiratory and EEG MV time series. They suggest that ePDC and iPDC are better interpretable than PDC and gPDC in terms of the known cardiovascular and neural physiologies.

Financial Stock Market and Economic Growth in Developing Countries: The Case of Douala Stock Exchange in Cameroon

In this article Sims’ causality test based on Granger definition of causality was used to examine causalityrelationships between stock markets and economic growth in Cameroon based on the time series data from 2006to 2010. Our findings suggest that the Douala Stock Exchange still doesn’t affect Cameroonian economic growth.Research has been made in this topic and found positive relationship between financial stock marketdevelopment and economic growth, but in Cameroon the purpose of the government to develop economy, bycreating the Douala Stock Exchange is still not reached. After running variance decomposition test of Cholesky,we found systematic evidence that the market capitalization affects positively the GDP. Our paper comes up withthe opportunity given to the Cameroonian government to understand that it is time to find financial policies, toencourage companies and develop financial stock market culture, and enhance to push companies to initiate IPOinstead of bank loans when money is needed to increase their investment.

Velocity effects of anticipated and unanticipated money growth and its variability

The purpose of this paper is to empirically test the relationship between velocity growth and anticipated and unanticipated money growth and its variability. In particular, by decomposing actual monetary growth into anticipated and unanticipated components, the study investigates whether knowledge of past variability of anticipated and unanticipated monetary growth improves the prediction of future velocity growth beyond predictions that are based on past velocity growth alone. This is the empirical definition of Granger causality. Comparasions are made, in all tests, among simple sum and Divisia aggregates (of M1, M2, M3, and L) and with Spindt's monetary velocity (MQ) aggregate.

The Casual Causal Relationship Between Money and Income: Some Caveats for Time Series Analysis

T HE investigation of causal relationships between economic variables is the bread and butter of econometric analysis. It is therefore not surprising that Granger's (1969) contribution of an operational definition of in a time series context has stimulated great interest among econometric theorists and applied practitioners. The nexus between Granger's definition of causality based on a criterion of forecasting value and the philosophers of science notion of causality has yet to be clearly established.1 Nevertheless, the Granger definition is now widely used and has been shown to have some very appealing properties. Heuristically, Granger's notion of causality states that X Y if the past history of X can be used to predict Y more accurately than simply using the past history of Y. While this definition differs from traditional conceptions, it has several attractive applications. First, as shown by Sims (1972), Granger-type causality is equivalent to econometric exogeneity so that unidirectional causality from the independent to the dependent variable is a necessary condition for the consistent estimation of distributed lag models involving variables other than lagged dependent variables. Hence testing for the direction of causality may allow the researcher to avoid the problems discussed by Goldfeld and Blinder (1972) which result from incorrectly assuming that a policy variable is exogenously determined. Reduced form distributed lag models such as the St. Louis model of Anderson and Jordan (1968) must first pass the causality test in order for the estimation and interpretation of these models to be meaningful.2 A second implication of Granger's causality notion is concerned with leading indicators and rational expectations. Pierce (1975) has suggested characterizing a variable as a leading indicator of another variable if the first causes the second, in the sense defined above. Similarly, Feige and Pearce (1976) have argued that, under certain assumptions about the relative costs of information, testing for Granger-type causality is a useful way to evaluate what information can be usefully employed in forming economically rational expectations.3 Moreover, Caves and Feige (1977) have demonstrated the equivalence between the Granger definition of causality and the concept of incremental efficiency which has direct applications for testing the efficient market hypothesis. Perhaps most importantly, the Granger definition has given rise to a set of procedures for testing the direction of causality between economic variables that avoids the problem of spurious regression described by Granger and Newbold (1974). The purpose of this paper is to examine the alternative procedures that have been proposed as practical tests for the presence and direction of causality and to investigate the robustness of substantive economic results when alternative test procedures are employed. We focus our attention on three test procedures now employed in the literature: a crosscorrelation technique suggested by Haugh (1972, 1976) and Pierce (1977), which is essentially a Received for publication May 6, 1974. Revision accepted for publication September 25, 1978. * University of Wisconsin and University of MissouriColumbia, respectively. This is a much revised version of an earlier paper given at the meetings of the Mid-West Economic Association, April 1974. We wish to thank John Geweke, David Pierce, and Christopher Sims for many helpful comments, Douglas Caves, Robert McGee and Spence Hilton for very able computation assistance. Financial support from the Graduate School of the University of Wisconsin-Madison and the National Science Foundation Grant SOC76-21439 is gratefully acknowledged. Any remaining errors in the paper are the sole responsibility of the authors. See Davidson and Weintraub (1973) and Zellner (1977). 2 Anderson and Jordan explicitly assume that their measure of fiscal policy is exogenously determined. I The basic assumption is that information on past inflation rates has the least cost.