Assessing Granger-Causality in the Southern Humboldt Current Ecosystem Using Cross-Spectral Methods

Learned Practical Guidelines for Evaluating Conditional Entropy and Mutual Information in Discovering Major Factors of Response-vs.-Covariate Dynamics

We reformulate and reframe a series of increasingly complex parametric statistical topics into a framework of response-vs.-covariate (Re-Co) dynamics that is described without any explicit functional structures. Then we resolve these topics' data analysis tasks by discovering major factors underlying such Re-Co dynamics by only making use of data's categorical nature. The major factor selection protocol at the heart of Categorical Exploratory Data Analysis (CEDA) paradigm is illustrated and carried out by employing Shannon's conditional entropy (CE) and mutual information (I[Re;Co]) as the two key Information Theoretical measurements. Through the process of evaluating these two entropy-based measurements and resolving statistical tasks, we acquire several computational guidelines for carrying out the major factor selection protocol in a do-and-learn fashion. Specifically, practical guidelines are established for evaluating CE and I[Re;Co] in accordance with the criterion called [C1:confirmable]. Following the [C1:confirmable] criterion, we make no attempts on acquiring consistent estimations of these theoretical information measurements. All evaluations are carried out on a contingency table platform, upon which the practical guidelines also provide ways of lessening the effects of the curse of dimensionality. We explicitly carry out six examples of Re-Co dynamics, within each of which, several widely extended scenarios are also explored and discussed.

Coherence Coefficient for Official Statistics

One of the quality requirements in official statistics is coherence of statistical information across domains, in time, in national accounts, and internally. However, no measure of its strength is used. The concept of coherence is also met in signal processing, wave physics, and time series. In the current article, the definition of the coherence coefficient for a weakly stationary time series is recalled and discussed. The coherence coefficient is a correlation coefficient between two indicators in time indexed by the same frequency components of their Fourier transforms and shows a degree of synchronicity between the time series for each frequency. The usage of this coefficient is illustrated through the coherence and Granger causality analysis of a collection of numerical economic and social statistical indicators. The coherence coefficient matrix-based non-metric multidimensional scaling for visualization of the time series in the frequency domain is a newly suggested method. The aim of this article is to propose the use of this coherence coefficient and its applications in official statistics.

Categorical Nature of Major Factor Selection via Information Theoretic Measurements

Without assuming any functional or distributional structure, we select collections of major factors embedded within response-versus-covariate (Re-Co) dynamics via selection criteria [C1: confirmable] and [C2: irrepaceable], which are based on information theoretic measurements. The two criteria are constructed based on the computing paradigm called Categorical Exploratory Data Analysis (CEDA) and linked to Wiener–Granger causality. All the information theoretical measurements, including conditional mutual information and entropy, are evaluated through the contingency table platform, which primarily rests on the categorical nature within all involved features of any data types: quantitative or qualitative. Our selection task identifies one chief collection, together with several secondary collections of major factors of various orders underlying the targeted Re-Co dynamics. Each selected collection is checked with algorithmically computed reliability against the finite sample phenomenon, and so is each member’s major factor individually. The developments of our selection protocol are illustrated in detail through two experimental examples: a simple one and a complex one. We then apply this protocol on two data sets pertaining to two somewhat related but distinct pitching dynamics of two pitch types: slider and fastball. In particular, we refer to a specific Major League Baseball (MLB) pitcher and we consider data of multiple seasons.

Fuel Prediction and Reduction in Public Transportation by Sensor Monitoring and Bayesian Networks

We exploit the use of a controller area network (CAN-bus) to monitor sensors on the buses of local public transportation in a big European city. The aim is to advise fleet managers and policymakers on how to reduce fuel consumption so that air pollution is controlled and public services are improved. We deploy heuristic algorithms and exhaustive ones to generate Bayesian networks among the monitored variables. The aim is to describe the relevant relationships between the variables, to discover and confirm the possible cause–effect relationships, to predict the fuel consumption dependent on the contextual conditions of traffic, and to enable an intervention analysis to be conducted on the variables so that our goals are achieved. We propose a validation technique using Bayesian networks based on Granger causality: it relies upon observations of the time series formed by successive values of the variables in time. We use the same method based on Granger causality to rank the Bayesian networks obtained as well. A comparison of the Bayesian networks discovered against the ground truth is proposed in a synthetic data set, specifically generated for this study: the results confirm the validity of the Bayesian networks that agree on most of the existing relationships.

The Response of Housing Construction to a Copper Price Shock in Chile (2009–2020)

The copper price is a leading indicator of real estate activity. Price increases are statistically related to increasing numbers of applications for residential building permits. However, this reciprocity is not instantaneous as permit numbers lag price rises by 9 to 10 months. This dynamic is implicit in various transmission channels: from the first effects on investment plans and demand for durable goods due to better expectations from investors and consumers to the real impact of higher copper revenues on the economy’s aggregate production and demand (multiplier or second-round effect). In this paper, we proposed the impulse-response functions of a vector autoregressive model to capture the dynamic between the copper price and house building permits. Therefore, it would be expected that the recent copper price increase will boost construction and real estate activity. The effects could materialize this year and extend into early 2022.

A Note on Causation versus Correlation in an Extreme Situation

Recently, it has been shown that the information flow and causality between two time series can be inferred in a rigorous and quantitative sense, and, besides, the resulting causality can be normalized. A corollary that follows is, in the linear limit, causation implies correlation, while correlation does not imply causation. Now suppose there is an event A taking a harmonic form (sine/cosine), and it generates through some process another event B so that B always lags A by a phase of π/2. Here the causality is obviously seen, while by computation the correlation is, however, zero. This apparent contradiction is rooted in the fact that a harmonic system always leaves a single point on the Poincaré section; it does not add information. That is to say, though the absolute information flow from A to B is zero, i.e., TA→B=0, the total information increase of B is also zero, so the normalized TA→B, denoted as τA→B, takes the form of 00. By slightly perturbing the system with some noise, solving a stochastic differential equation, and letting the perturbation go to zero, it can be shown that τA→B approaches 100%, just as one would have expected.

Distributed Deep Fusion Predictor for a Multi-Sensor System Based on Causality Entropy

Trend prediction based on sensor data in a multi-sensor system is an important topic. As the number of sensors increases, we can measure and store more and more data. However, the increase in data has not effectively improved prediction performance. This paper focuses on this problem and presents a distributed predictor that can overcome unrelated data and sensor noise: First, we define the causality entropy to calculate the measurement's causality. Then, the series causality coefficient (SCC) is proposed to select the high causal measurement as the input data. To overcome the traditional deep learning network's over-fitting to the sensor noise, the Bayesian method is used to obtain the weight distribution characteristics of the sub-predictor network. A multi-layer perceptron (MLP) is constructed as the fusion layer to fuse the results from different sub-predictors. The experiments were implemented to verify the effectiveness of the proposed method by meteorological data from Beijing. The results show that the proposed predictor can effectively model the multi-sensor system's big measurement data to improve prediction performance.