Analyzing Multiple Nonlinear Time Series with Extended Granger Causality

Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure called the Granger causality to detect such relations. In this work we consider nonlinear extensions of Granger's idea and refer to the result as Extended Granger Causality. A simple approach implementing the Extended Granger Causality is presented and applied to multiple chaotic time series and other types of nonlinear signals. In addition, for situations with three or more time series we propose a conditional Extended Granger Causality measure that enables us to determine whether the causal relation between two signals is direct or mediated by another process.Comment: 16 pages, 6 figure

MEĐUOVISNOST INDEKSA INDUSTRIJSKE PROIZVODNJE I TRŽIŠTA KAPITALA U HRVATSKOJ: VAR MODEL

Industrial production is an important indicator of future trends in each of the economy including the Croatian economy. On the other hand, as a preceding factor of the economy dynamics changes, the equity indices of the capital market can be used. Due to different considerations and interpretations of their mutual initial causation, the paper analyzes the interdependence between the main index Croatian capital market CROBEX and indicators of total industrial production of the Republic of Croatian. Also, in the model was introduced exchange parity euro dollar as an additional variable rate which is considered to have a significant influence on the competitiveness of the Croatian economy, as well as the capital market. The theoretical premise about the interaction of the foreign exchange rate and capital markets has been considered in the context of the "flow-oriented" and "stock-oriented" model. Aiming to determine the interdependence between aforementioned variables, the analysis was carried out using the vector autoregression model (VAR). The Granger causality test was conducted as part of the VAR model, as well as the decomposition of variance in future periods and the impulse response function of relevant variables. The results of analysis indicate the existence of causality of the exchange rate to the index of industrial production, as well as the existence of causality of the index of industrial production to CROBEX index.Industrijska je proizvodnja važan pokazatelj budućeg kretanja svakog gospodarstva pa tako i gospodarstva Republike Hrvatske. S druge strane, kao prethodeći faktor promjena dinamike kretanja gospodarstva mogu se koristiti i dionički indeksi tržišta kapitala. S obzirom na različita razmatranja i tumačenja njihove međusobne inicijalne uzročnosti, u radu se ispituje međuovisnost između glavnog indeksa hrvatskog tržišta kapitala CROBEX-a i pokazatelja ukupne industrijske proizvodnje Republike Hrvatske. Kao dodatna varijabla, u model se uvodi i devizni paritet eura prema kuni za kojeg se smatra da ima značajan utjecaj na konkurentnost hrvatskog gospodarstva, kao i na tržište kapitala. Teorijska pretpostavka o interakciji deviznog tečaja i tržišta kapitala razmatrana je u kontekstu „flow oriented“ i „stock oriented“ modela. S ciljem utvrđivanja međuovisnosti između navedenih varijabli, analiza je provedena primjenom modela vektorske autoregresije (VAR). U sklopu VAR modela, proveden je Grangerov test uzročnosti, dekompozicija varijanci u narednim razdobljima, kao i test impulsnog odaziva relevantnih varijabli. Dobiveni rezultati ukazuju na postojanje uzročnosti u smjeru od deviznog tečaja prema indeksu industrijske proizvodnje, kao i postojanje uzročnosti u smjeru od indeksa industrijske proizvodnje prema CROBEX indeksu

MEĐUOVISNOST INDEKSA INDUSTRIJSKE PROIZVODNJE I TRŽIŠTA KAPITALA U HRVATSKOJ: VAR MODEL

Industrial production is an important indicator of future trends in each of the economy including the Croatian economy. On the other hand, as a preceding factor of the economy dynamics changes, the equity indices of the capital market can be used. Due to different considerations and interpretations of their mutual initial causation, the paper analyzes the interdependence between the main index Croatian capital market CROBEX and indicators of total industrial production of the Republic of Croatian. Also, in the model was introduced exchange parity euro dollar as an additional variable rate which is considered to have a significant influence on the competitiveness of the Croatian economy, as well as the capital market. The theoretical premise about the interaction of the foreign exchange rate and capital markets has been considered in the context of the "flow-oriented" and "stock-oriented" model. Aiming to determine the interdependence between aforementioned variables, the analysis was carried out using the vector autoregression model (VAR). The Granger causality test was conducted as part of the VAR model, as well as the decomposition of variance in future periods and the impulse response function of relevant variables. The results of analysis indicate the existence of causality of the exchange rate to the index of industrial production, as well as the existence of causality of the index of industrial production to CROBEX index.Industrijska je proizvodnja važan pokazatelj budućeg kretanja svakog gospodarstva pa tako i gospodarstva Republike Hrvatske. S druge strane, kao prethodeći faktor promjena dinamike kretanja gospodarstva mogu se koristiti i dionički indeksi tržišta kapitala. S obzirom na različita razmatranja i tumačenja njihove međusobne inicijalne uzročnosti, u radu se ispituje međuovisnost između glavnog indeksa hrvatskog tržišta kapitala CROBEX-a i pokazatelja ukupne industrijske proizvodnje Republike Hrvatske. Kao dodatna varijabla, u model se uvodi i devizni paritet eura prema kuni za kojeg se smatra da ima značajan utjecaj na konkurentnost hrvatskog gospodarstva, kao i na tržište kapitala. Teorijska pretpostavka o interakciji deviznog tečaja i tržišta kapitala razmatrana je u kontekstu „flow oriented“ i „stock oriented“ modela. S ciljem utvrđivanja međuovisnosti između navedenih varijabli, analiza je provedena primjenom modela vektorske autoregresije (VAR). U sklopu VAR modela, proveden je Grangerov test uzročnosti, dekompozicija varijanci u narednim razdobljima, kao i test impulsnog odaziva relevantnih varijabli. Dobiveni rezultati ukazuju na postojanje uzročnosti u smjeru od deviznog tečaja prema indeksu industrijske proizvodnje, kao i postojanje uzročnosti u smjeru od indeksa industrijske proizvodnje prema CROBEX indeksu

Energy and Economic Growth

Physical theory shows that energy is necessary for economic production and therefore growth but the mainstream theory of economic growth, except for specialized resource economics models, pays no attention to the role of energy. This paper reviews the relevant biophysical theory, mainstream and resource economics models of growth, the critiques of mainstream models, and the various mechanisms that can weaken the links between energy and growth. Finally we review the empirical literature that finds that energy used per unit of economic output has declined, but that this is to a large extent due to a shift from poorer quality fuels such as coal to the use of higher quality fuels, and especially electricity. Furthermore, time series analysis shows that energy and GDP cointegrate and energy use Granger causes GDP when additional variables such as energy prices or other production inputs are included. As a result, prospects for further large reductions in energy intensity seem limited.

Finding the direction of disturbance propagation in a chemical process using transfer entropy

Published versio

Evaluation of Granger causality measures for constructing networks from multivariate time series

Granger causality and variants of this concept allow the study of complex dynamical systems as networks constructed from multivariate time series. In this work, a large number of Granger causality measures used to form causality networks from multivariate time series are assessed. These measures are in the time domain, such as model-based and information measures, the frequency domain and the phase domain. The study aims also to compare bivariate and multivariate measures, linear and nonlinear measures, as well as the use of dimension reduction in linear model-based measures and information measures. The latter is particular relevant in the study of high-dimensional time series. For the performance of the multivariate causality measures, low and high dimensional coupled dynamical systems are considered in discrete and continuous time, as well as deterministic and stochastic. The measures are evaluated and ranked according to their ability to provide causality networks that match the original coupling structure. The simulation study concludes that the Granger causality measures using dimension reduction are superior and should be preferred particularly in studies involving many observed variables, such as multi-channel electroencephalograms and financial markets.Comment: 24 pages, 5 figures, to be published in Entrop

RELATIVE PRICE DYNAMICS AND MONETARY POLICY: EVIDENCE FROM DIRECTED GRAPHS

This paper examines the dynamic relationship between monetary policy variables and agricultural prices using alternative VAR-type model specifications. Time series techniques as currently specified in most studies raises issues of misspecification and inferential adequacy because observational (non-experimental) data are being analyzed by estimations techniques better suited for experimental data. Directed graph theory is proposed as an alternative modeling approach to supplement current methods of analyzing agricultural time series.Financial Economics,

On the Dynamics of Exports and FDI: The Spanish Internationalization Process

This paper provides further insights into the dynamics of exports and outward foreign direct investment (FDI) flows in Spain from a time-series approach. The contribution of the paper is twofold: i) the existence of either substitution or a complementary relationship between Spanish outward investments and exports is empirically tested using a multivariate cointegrated model (VECM). The evolution in exchange flows (1993-2008) and country-specific variables (such as world demand - including Spain’s main recently growing foreign markets - for trade flows and the relative price of exports in order to proxy new global competitors) are taken into account for the first time. And ii) the growth in the trade of services in recent decades leads us to test a specific causality relationship by disaggregating between goods and services flows. Our results provide evidence of a positive (Granger) causality relationship running from FDI to exports of goods (stronger) and to exports of services (weaker) in the long run, the complementarity relation of which is consistent with vertical FDI strategies. In the short run, however, only exports of goods are affected (positively) by FDIs.Foreign Direct Investment, Exports, Granger-Causality. JEL classification:F21, F40