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

Detecting finite bandwidth periodic signals in stationary noise using the signal coherence spectrum

: This is an introduction to the basic elements of Fourier analysis of a time series that is a sum of deterministic components and a stationary random process. The various mathematical concepts relating to Fourier analysis are presented in a basically intuitive manner. The intended audience consists of economists and data processors. (Author)

Introduction to fourier analysis of data

We use a new statistical test based on the signal coherence function to detect subtle periodicities in the Chilean exchange rate. We resort to a unique intraday data set that allows us to capture persistent cyclical movements during the day that challenge the random walk hypothesis. We provide a microstructural explanation for the observed behavior, and also look at the day-of-the-week effect for the Chilean peso and find that the different days of the week indeed have different behavior patterns. This is an important result for investment allocation and risk assessment.

Intraday patterns in exchange rate of return of the chilean peso: new evidence for day-of-the-week effect

In this article, we show how tests of nonlinear serial dependence can be applied to high-frequency time series data that exhibit high volatility, strong mean reversion, and leptokurtotis. Portmanteau correlation, bicorrelation, and tricorrelation tests are used to detect nonlinear serial dependence in the data. Trimming is used to control for the presence of outliers in the data. The data that are employed are 161,786 half-hourly spot electricity price observations recorded over nearly a decade in the wholesale electricity market in New South Wales, Australia. Strong evidence of nonlinear serial dependence is found and its implications for time series modeling are discussed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1365100509090543

Identifying nonlinear serial dependence in volatile, high-frequency time series and its implications for volatility modeling

The rise of China in the world economy has attracted a great deal of international attention. This paper investigates the performance of nonlinear self-exciting threshold autoregressive (SETAR) model-based trading rules in the Chinese stock market. We compare the performance of the SETAR model with the autoregressive (AR) model and the moving average (MA) trading rules. Our results indicate that trading rules are profitable in the B-share market, and that the nonlinear SETAR rule outperforms the other two linear rules in general.

Melvin J. Hinich

Papers

Detecting finite bandwidth periodic signals in stationary noise using the signal coherence spectrum

Introduction to fourier analysis of data

Intraday patterns in exchange rate of return of the chilean peso: new evidence for day-of-the-week effect

Identifying nonlinear serial dependence in volatile, high-frequency time series and its implications for volatility modeling

Are nonlinear trading rules profitable in the chinese stock market