On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

Distinguishing Cause and Effect via Second Order Exponential Models

We propose a method to infer causal structures containing both discrete and continuous variables. The idea is to select causal hypotheses for which the conditional density of every variable, given its causes, becomes smooth. We define a family of smooth densities and conditional densities by second order exponential models, i.e., by maximizing conditional entropy subject to first and second statistical moments. If some of the variables take only values in proper subsets of R^n, these conditionals can induce different families of joint distributions even for Markov-equivalent graphs. We consider the case of one binary and one real-valued variable where the method can distinguish between cause and effect. Using this example, we describe that sometimes a causal hypothesis must be rejected because P(effect|cause) and P(cause) share algorithmic information (which is untypical if they are chosen independently). This way, our method is in the same spirit as faithfulness-based causal inference because it also rejects non-generic mutual adjustments among DAG-parameters.Comment: 36 pages, 8 figure

New permutation algorithms for causal discovery using ICA

Abstract. Causal discovery is the task of finding plausible causal relationships from statistical dat

Causal Discovery of Dynamic Systems

Recently, several philosophical and computational approaches to causality have used an interventionist framework to clarify the concept of causality [Spirtes et al., 2000, Pearl, 2000, Woodward, 2005]. The characteristic feature of the interventionist approach is that causal models are potentially useful in predicting the effects of manipulations. One of the main motivations of such an undertaking comes from humans, who seem to create sophisticated mental causal models that they use to achieve their goals by manipulating the world.Several algorithms have been developed to learn static causal models from data that can be used to predict the effects of interventions [e.g., Spirtes et al., 2000]. However, Dash [2003, 2005] argued that when such equilibrium models do not satisfy what he calls the Equilibration-Manipulation Commutability (EMC) condition, causal reasoning with these models will be incorrect, making dynamic models indispensable. It is shown that existing approaches to learning dynamic models [e.g., Granger, 1969, Swanson and Granger, 1997] are unsatisfactory, because they do not perform a necessary search for hidden variables.The main contribution of this dissertation is, to the best of my knowledge, the first provably correct learning algorithm that discovers dynamic causal models from data, which can then be used for causal reasoning even if the EMC condition is violated. The representation that is used for dynamic causal models is called Difference-Based Causal Models (DBCMs) and is based on Iwasaki and Simon [1994]. A comparison will be made to other approaches and the algorithm, called DBCM Learner, is empirically tested by learning physical systems from artificially generated data. The approach is also used to gain insights into the intricate workings of the brain by learning DBCMs from EEG data and MEG data

Causal Connection Search and Structural Demand Modeling on Retail-Level Scanner Data

Many researchers would be interested in one question: If a change of X is made, will Y be influenced in response? However, while a lot of statistical methods are developed to analyze association between variables, how to find a causal relationship among variables is relatively neglected. The PC algorithm, developed on the basis of Pearl, Sprites, Glymour, and Scheines‟s studies, is used to find the causal pattern of the real-world observed data. However, PC in Tetrad produces a class of directed acyclic graphs (DAGs) that are statistically equivalent under a normal distribution, and therefore such a distributional assumption causes a series of unidentifiable DAGs because of the same joint probability. In 2006 Shimizu, Hoyer, Hyvärinen, and Kerminen developed the Linear Independent Non-Gaussian Model (LiNGAM) to do a causal search based on the independently non-Gaussian distributed disturbances by applying higher-order moment structures. The research objective of this dissertation is to examine whether the LiNGAM is helpful relative to the PC algorithm, to detect the causal relation of non-normal data. The LiNGAM algorithm is implemented by first doing independent component analysis (ICA) estimation and then discovering the correct ordering of variables. Thus, the procedures of ICA estimation and the process of finding the correct causal orderings in LiNGAM are illustrated. Next, we do a causal search on the retail-level scanner data to investigate the pricing interaction between the manufacturer and the retailer by applying these two algorithms. While PC generates the set of indistinguishable DAGs, LiNGAM gives more exact causal patterns. This work demonstrates the algorithm based on the non-normal distribution assumption makes causal associations clearer. In Chapter IV, we apply a classical structural demand model to investigate the consumer purchase behavior in the carbonated soft drink market. Unfortunately, when further restrictions are imposed, we cannot get reasonable results as most researchers require. LiNGAM is applied to prove the existence of endogeneity for the brand‟s retail price and verify that the brand‟s wholesale price is not a proper instrument for its retail price. Therefore, consistent estimates cannot be derived as the theories suggest. These results imply that economic theory is not always found in restriction applied to observational data

Three Essays on Time Series Analysis of Chinese Financial Markets

This dissertation studies three important issues in Chinese financial markets. The interdependence structure and information transmission among Chinese cross-listed stocks in Shanghai, Hong Kong and New York is examined. Results indicate that the home bias hypothesis, which suggests the dominant role of home market in pricing information transmission, is strongly supported in contemporaneous time, modestly supported at the short horizon and not supported at the long horizon. The Shanghai market as the home market is highly exogenous at all horizons. Moreover, the Hong Kong market leads the New York market in contemporaneous time. Whether interest rates help to forecast stock returns in China is studied using the prequential approach. With respect to calibration (reliability), it is found that including interest rates in the model improves the model’s ability to issue realistic probability forecasts of stock returns – a model of stock returns that does not include interest rates as an explanatory variable is not as well calibrated as a model that does include interest rates in the stock returns equation. With regard to sorting (resolution), results suggest that the model that includes interest rates performs better in distinguishing stock returns that actually occur and stock returns that do not occur when compared to a model that does not include interest rates in the stock returns equation. Overall, the interest rates help in forecasting stock returns in China in terms of both calibration and sorting. Two factor analysis methods are investigated through forecasting Chinese interest rate based on a factor-augmented vector autoregression (FAVAR). Factors are estimated from 288 Chinese security series to reflect the common forces that drive the movements and dynamics in the Chinese equity market. As a result, the factor estimation method by Lam and Yao outperforms the traditional principal components analysis (PCA) in terms of forecasting accuracy, especially at the short horizons