Multiscale Granger causality analysis by \`a trous wavelet transform

Since interactions in neural systems occur across multiple temporal scales, it is likely that information flow will exhibit a multiscale structure, thus requiring a multiscale generalization of classical temporal precedence causality analysis like Granger's approach. However, the computation of multiscale measures of information dynamics is complicated by theoretical and practical issues such as filtering and undersampling: to overcome these problems, we propose a wavelet-based approach for multiscale Granger causality (GC) analysis, which is characterized by the following properties: (i) only the candidate driver variable is wavelet transformed (ii) the decomposition is performed using the \`a trous wavelet transform with cubic B-spline filter. We measure GC, at a given scale, by including the wavelet coefficients of the driver times series, at that scale, in the regression model of the target. To validate our method, we apply it to publicly available scalp EEG signals, and we find that the condition of closed eyes, at rest, is characterized by an enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the standard Granger causality is not significantly different in the two conditions.Comment: 4 pages, 3 figure

Multiscale Bayesian State Space Model for Granger Causality Analysis of Brain Signal

Modelling time-varying and frequency-specific relationships between two brain signals is becoming an essential methodological tool to answer heoretical questions in experimental neuroscience. In this article, we propose to estimate a frequency Granger causality statistic that may vary in time in order to evaluate the functional connections between two brain regions during a task. We use for that purpose an adaptive Kalman filter type of estimator of a linear Gaussian vector autoregressive model with coefficients evolving over time. The estimation procedure is achieved through variational Bayesian approximation and is extended for multiple trials. This Bayesian State Space (BSS) model provides a dynamical Granger-causality statistic that is quite natural. We propose to extend the BSS model to include the \`{a} trous Haar decomposition. This wavelet-based forecasting method is based on a multiscale resolution decomposition of the signal using the redundant \`{a} trous wavelet transform and allows us to capture short- and long-range dependencies between signals. Equally importantly it allows us to derive the desired dynamical and frequency-specific Granger-causality statistic. The application of these models to intracranial local field potential data recorded during a psychological experimental task shows the complex frequency based cross-talk between amygdala and medial orbito-frontal cortex. Keywords: \`{a} trous Haar wavelets; Multiple trials; Neuroscience data; Nonstationarity; Time-frequency; Variational methods The published version of this article is Cekic, S., Grandjean, D., Renaud, O. (2018). Multiscale Bayesian state-space model for Granger causality analysis of brain signal. Journal of Applied Statistics. https://doi.org/10.1080/02664763.2018.145581

Interest rate changes and stock returns in Spain: A wavelet analysis

This paper investigates the relationship between changes in interest rates and the Spanish stock market at the industry level over the period from January 1993 to December 2012 using a wavelet-based approach. The empirical results indicate that Spanish industries exhibit, in general, a significant interest rate sensitivity, although the degree of interest rate exposure differs considerably across industries and depending on the time horizon under consideration. Inparticular,regulated industries such as Utilities, highly indebted industries such as Real Estate, Utilities or Technology and Telecommunications, and the Banking industry emerge as the most vulnerable to interest rates. Further, the link between movements in interest rates and industry equity returns is stronger at the coarsest scales. This finding is consistent with the idea that investors with long-term horizons are more likely to follow macroeconomic fundamentals, such as interest rates, in their investmen decisions

An intuitive guide to wavelets for economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.statistical methodology, multiresolution analysis, wavelets, business cycles, economic growth

An intuitive guide to wavelets for economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.statistical methodology, multiresolution analysis, wavelets, business cycles, economic growth

An intuitive guide to wavelets for economists

Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not yet fully entered the economics discipline. In this discussion paper, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilises wavelets is explored. Extensive examples of exploratory wavelet analysis are given, many using Canadian, US and Finnish industrial production data. Finally, potential future applications for wavelet analysis in economics are also discussed and explored.statistical methodology; multiresolution analysis; wavelets; business cycles; economic growth

Uncovering hidden information and relations in time series data with wavelet analysis: three case studies in finance

This thesis aims to provide new insights into the importance of decomposing aggregate time series data using the Maximum Overlap Discrete Wavelet Transform. In particular, the analysis throughout this thesis involves decomposing aggregate financial time series data at hand into approximation (low-frequency) and detail (high-frequency) components. Following this, information and hidden relations can be extracted for different investment horizons, as matched with the detail components. The first study examines the ability of different GARCH models to forecast stock return volatility in eight international stock markets. The results demonstrate that de-noising the returns improves the accuracy of volatility forecasts regardless of the statistical test employed. After de-noising, the asymmetric GARCH approach tends to be preferred, although that result is not universal. Furthermore, wavelet de-noising is found to be more important at the key 99% Value-at-Risk level compared to the 95% level. The second study examines the impact of fourteen macroeconomic news announcements on the stock and bond return dynamic correlation in the U.S. from the day of the announcement up to sixteen days afterwards. Results conducted over the full sample offer very little evidence that macroeconomic news announcements affect the stock-bond return dynamic correlation. However, after controlling for the financial crisis of 2007-2008 several announcements become significant both on the announcement day and afterwards. Furthermore, the study observes that news released early in the day, i.e. before 12 pm, and in the first half of the month, exhibit a slower effect on the dynamic correlation than those released later in the month or later in the day. While several announcements exhibit significance in the 2008 crisis period, only CPI and Housing Starts show significant and consistent effects on the correlation outside the 2001, 2008 and 2011 crises periods. The final study investigates whether recent returns and the time-scaled return can predict the subsequent trading in ten stock markets. The study finds little evidence that recent returns do predict the subsequent trading, though this predictability is observed more over the long-run horizon. The study also finds a statistical relation between trading and return over the long-time investment horizons of [8-16] and [16-32] day periods. Yet, this relation is mostly a negative one, only being positive for developing countries. It also tends to be economically stronger during bull-periods

Fuzzy-wavelet method for time series analysis

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)

Analyzing Granger causality in climate data with time series classification methods

Attribution studies in climate science aim for scientifically ascertaining the influence of climatic variations on natural or anthropogenic factors. Many of those studies adopt the concept of Granger causality to infer statistical cause-effect relationships, while utilizing traditional autoregressive models. In this article, we investigate the potential of state-of-the-art time series classification techniques to enhance causal inference in climate science. We conduct a comparative experimental study of different types of algorithms on a large test suite that comprises a unique collection of datasets from the area of climate-vegetation dynamics. The results indicate that specialized time series classification methods are able to improve existing inference procedures. Substantial differences are observed among the methods that were tested