There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper proposes a very tractable approach to modeling changes in regime. The parameters of an autoregression are viewed as the outcome of a discrete-state Markov process. For example, the mean growth rate of a nonstationary series may be subject to occasional, discrete shifts. The econometrician is presumed not to observe these shifts directly, but instead must draw probabilistic inference about whether and when they may have occurred based on the observed behavior of the series. The paper presents an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter

A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Forecasting with artificial neural networks: the state of the art

Recurrence plots for the analysis of complex systems

This letter applies the Hinich portmanteau bicorrelation test jointly with the windowed testing procedure to detect nonlinear behaviour in the rate of returns series for seven Latin American stock market indices. Our results suggest that the nonlinear serial dependencies are episodic in nature. All the stock returns series are characterized by few brief periods of highly significant nonlinearity, followed by long time periods in which the returns follow a pure noise process. Our findings help explain why there are difficulties in forecasting asset returns.

/pdf/episodic-nonlinearity-in-latin-american-stock-market-indices-1m8daci7ay.pdf

Episodic nonlinearity in Latin American stock market indices

http://www.la.utexas.edu/hinich/files/Economics/Cross-bicors.pdf

Cross-correlations and cross-bicorrelations in Sterling exchange rates

We introduce a frequency-domain test of time reversibility, the REVERSE test. It is based on the bispectrum. We analytically establish the asymptotic distribution of the test and also explore its finite-sample properties through Monte-Carlo simulation. Following other researchers who demonstrated that the problem of business-cycle asymmetry can be stated as whether macroeconomic fluctuations are time irreversible, we use the REVERSE test as a frequency-domain test of business-cycle asymmetry. Our empirical results show that time irreversibility is the rule rather than the exception for a representative set of macroeconomic time series for five OECD countries.

Frequency-domain test of time reversibility

Time series test of nonlinear convergence and transitional dynamics

This study indicates that a probabilistic voting model allowing voters to abstain from alienation or indifference leads to a transitive ordering over candidate ideologies. Further, a weighted form of the mean most preferred ideology of the voters is the optimal ideology for both candidates in a two-candidate election. Centrist ideologies are attractive to the major parties in a two-party system, and probabilistic voting provides an important part of the explanation.

Melvin J. Hinich

Papers

Episodic nonlinearity in Latin American stock market indices

Cross-correlations and cross-bicorrelations in Sterling exchange rates

Frequency-domain test of time reversibility

Time series test of nonlinear convergence and transitional dynamics

Probabilistic Voting and the Importance of Centrist Ideologies in Democratic Elections