Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related Field

A time series causal model

Cause-effect relations are central in economic analysis. Uncovering empirical cause-effect relations is one of the main research activities of empirical economics. In this paper we develop a time series casual model to explore casual relations among economic time series. The time series causal model is grounded on the theory of inferred causation that is a probabilistic and graph-theoretic approach to causality featured with automated learning algorithms. Applying our model we are able to infer cause-effect relations that are implied by the observed time series data. The empirically inferred causal relations can then be used to test economic theoretical hypotheses, to provide evidence for formulation of theoretical hypotheses, and to carry out policy analysis. Time series causal models are closely related to the popular vector autoregressive (VAR) models in time series analysis. They can be viewed as restricted structural VAR models identified by the inferred causal relations.Inferred Causation, Automated Learning, VAR, Granger Causality, Wage-Price Spiral

Causal Discovery from Temporal Data: An Overview and New Perspectives

Temporal data, representing chronological observations of complex systems, has always been a typical data structure that can be widely generated by many domains, such as industry, medicine and finance. Analyzing this type of data is extremely valuable for various applications. Thus, different temporal data analysis tasks, eg, classification, clustering and prediction, have been proposed in the past decades. Among them, causal discovery, learning the causal relations from temporal data, is considered an interesting yet critical task and has attracted much research attention. Existing casual discovery works can be divided into two highly correlated categories according to whether the temporal data is calibrated, ie, multivariate time series casual discovery, and event sequence casual discovery. However, most previous surveys are only focused on the time series casual discovery and ignore the second category. In this paper, we specify the correlation between the two categories and provide a systematical overview of existing solutions. Furthermore, we provide public datasets, evaluation metrics and new perspectives for temporal data casual discovery.Comment: 52 pages, 6 figure

Dynamic dependence networks: Financial time series forecasting and portfolio decisions (with discussion)

We discuss Bayesian forecasting of increasingly high-dimensional time series, a key area of application of stochastic dynamic models in the financial industry and allied areas of business. Novel state-space models characterizing sparse patterns of dependence among multiple time series extend existing multivariate volatility models to enable scaling to higher numbers of individual time series. The theory of these "dynamic dependence network" models shows how the individual series can be "decoupled" for sequential analysis, and then "recoupled" for applied forecasting and decision analysis. Decoupling allows fast, efficient analysis of each of the series in individual univariate models that are linked-- for later recoupling-- through a theoretical multivariate volatility structure defined by a sparse underlying graphical model. Computational advances are especially significant in connection with model uncertainty about the sparsity patterns among series that define this graphical model; Bayesian model averaging using discounting of historical information builds substantially on this computational advance. An extensive, detailed case study showcases the use of these models, and the improvements in forecasting and financial portfolio investment decisions that are achievable. Using a long series of daily international currency, stock indices and commodity prices, the case study includes evaluations of multi-day forecasts and Bayesian portfolio analysis with a variety of practical utility functions, as well as comparisons against commodity trading advisor benchmarks.Comment: 31 pages, 9 figures, 3 table

Causal Inference by Independent Component Analysis with Applications to Micro- and Macroeconomic Data

Structural vector-autoregressive models are potentially very useful tools for guiding both macro- and microeconomic policy. In this paper, we present a recently developed method for exploiting non-Gaussianity in the data for estimating such models, with the aim of capturing the causal structure underlying the data, and show how the method can be applied to both microeconomic data (processes of firm growth and firm performance) as well as macroeconomic data (effects of monetary policy).Causality, Structural VAR, Independent Components Analysis, Non-Gaussianity, Firm Growth, Monetary Policy

Brainwave nets: Are sparse dynamic models susceptible to brain manipulation experimentation?

© Copyright © 2020 Nascimento, Pinto-Orellana, Leite, Edwards, Louzada and Santos. Sparse time series models have shown promise in estimating contemporaneous and ongoing brain connectivity. This paper was motivated by a neuroscience experiment using EEG signals as the outcome of our established interventional protocol, a new method in neurorehabilitation toward developing a treatment for visual verticality disorder in post-stroke patients. To analyze the [complex outcome measure (EEG)] that reflects neural-network functioning and processing in more specific ways regarding traditional analyses, we make a comparison among sparse time series models (classic VAR, GLASSO, TSCGM, and TSCGM-modified with non-linear and iterative optimizations) combined with a graphical approach, such as a Dynamic Chain Graph Model (DCGM). These dynamic graphical models were useful in assessing the role of estimating the brain network structure and describing its causal relationship. In addition, the class of DCGM was able to visualize and compare experimental conditions and brain frequency domains [using finite impulse response (FIR) filter]. Moreover, using multilayer networks, the results corroborate with the susceptibility of sparse dynamic models, bypassing the false positives problem in estimation algorithms. We conclude that applying sparse dynamic models to EEG data may be useful for describing intervention-relocated changes in brain connectivity

Applied Data Science Approaches in FinTech: Innovative Models for Bitcoin Price Dynamics

Living in a data-intensive environment is a natural consequence to the continuous innovations and technological advancements, that created countless opportunities for addressing domain-specific challenges following the Data Science approach. The main objective of this thesis is to present applied Data Science approaches in FinTech, focusing on proposing innovative descriptive and predictive models for studying and exploring Bitcoin Price Dynamics and Bitcoin Price Prediction. With reference to the research area of Bitcoin Price Dynamics, two models are proposed. The first model is a Network Vector Autoregressive model that explains the dynamics of Bitcoin prices, based on a correlation network Vector Autoregressive process that models interconnections between Bitcoin prices from different exchange markets and classical assets prices. The empirical findings show that Bitcoin prices from different markets are highly interrelated, as in an efficiently integrated market, with prices from larger and/or more connected exchange markets driving other prices. The results confirm that Bitcoin prices are unrelated with classical market prices, thus, supporting the diversification benefit property of Bitcoin. The proposed model can predict Bitcoin prices with an error rate of about 11% of the average price. The second proposed model is a Hidden Markov Model that explains the observed time dynamics of Bitcoin prices from different exchange markets, by means of the latent time dynamics of a predefined number of hidden states, to model regime switches between different price vectors, going from "bear'' to "stable'' and "bear'' times. Structured with three hidden states and a diagonal variance-covariance matrix, the model proves that the first hidden state is concentrated in the initial time period where Bitcoin was relatively new and its prices were barely increasing, the second hidden state is mostly concentrated in a period where Bitcoin prices were steadily increasing, while the third hidden state is mostly concentrated in the last period where Bitcoin prices witnessed a high rate of volatility. Moreover, the model shows a good predictive performance when implemented on an out of sample dataset, compared to the same model structured with a full variance-covariance matrix. The third and final proposed model, falls within the area of Bitcoin Price Prediction. A Hybrid Hidden Markov Model and Genetic Algorithm Optimized Long Short Term Memory Network is proposed, aiming at predicting Bitcoin prices accurately, by introducing new features that are not usually considered in the literature. Moreover, to compare the performance of the proposed model to other models, a more traditional ARIMA model has been implemented, as well as a conventional Genetic Algorithm-optimized Long Short Term Memory Network. With a mean squared error of 33.888, a root mean squared error of 5.821 and a mean absolute error of 2.510, the proposed model achieves the lowest errors among all the implemented models, which proves its effectiveness in predicting Bitcoin prices