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

The purpose of this article is to investigate the ability of bandpass filters commonly used in economics to extract a known periodicity. The specific bandpass filters investigated include a Discrete Fourier Transform (DFT) filter, together with those proposed by Hodrick and Prescott (1997) and Baxter and King (1999). Our focus on the cycle extraction properties of these filters reflects the lack of attention that has been given to this issue in the literature, when compared, for example, to studies of the trend removal properties of some of these filters. The artificial data series we use are designed so that one periodicity deliberately falls within the passband while another falls outside. The objective of a filter is to admit the ‘bandpass’ periodicity while excluding the periodicity that falls outside the passband range. We find that the DFT filter has the best extraction properties. The filtered data series produced by both the Hodrick-Prescott and Baxter-King filters are found to admit low frequency components that should have been excluded.

/pdf/an-investigation-of-the-cycle-extraction-properties-of-53h6v1msf3.pdf

An Investigation of the Cycle Extraction Properties of Several Bandpass Filters Used to Identify Business Cycles

The fractional integrated process has been widely studied since the seminal work of Granger and Joyeux (1980). However, most of the tests for fractional integration are time-domain tests. This article develops a Cramer–von Mises type frequency-domain test for fractional integration. Our test is shown to have high power against a wide variety of alternatives. The test is applied to U.S. real disposable income and the quarterly real GDP data of the G7 countries. It is found that most of the series are fractionally integrated at the 5% level. The result is in line with Hinich and Chong (2007).

/pdf/an-omnibus-test-for-time-series-model-i-d-3rabtq30de.pdf

An Omnibus Test for Time Series Model I(d)

https://espace.library.uq.edu.au/view/UQ:218117/UQ218117_Partial.pdf

A statistical uncertainty principle for estimating the time of a discrete shift in the mean of a continuous time random process

Least-squares estimation of the lag coefficients of a distributed lag model is not a straightforward regression problem when the sample has missed or distorted observations. Even though the normal equations can be computed using sums of the available cross products, the asymptotic properties of a solution of these equations are unknown. Since a special computer program is required to compute these normal equations when observations are missed, it is practical to consider another approach to the problem.

A Hilbert Transform Method for Estimating Distributed Lag Models With Randomly Missed or Distorted Observations

The nine papers in this volume are a diverse set of quality contributions to the field in economics that is called political economy. It is important to understand that social scientists hold different interpretations of the term political economy. Most mainstream economists expect a paper in the field to use the same models as are used in neoclassical economics, be it micro or macro. The field of political economy is seen by most economists to be exclusively the purview of their field. However, the political system of a country determines the nature of its economics system. The economy feeds back to the political system but the rules of the game are determined by the political system.The study of politics is the hardest task in the social sciences. The political system defines the scope of the economics system while taking resources from the economy in order to run campaigns and produce the types of compromises that are required of a stable political system that allows economic agents to make sensible investments. The interaction between the highly inter-dependant yet very different fields of politics and economics forms the basis of this volume. It contains a collection of key papers on the topic of analytical political economy. The papers authored by some of the foremost experts in the field. It is part of the "ISETE" series.

/pdf/topics-in-analytical-political-economy-56lbfa30eb.pdf

Melvin J. Hinich

Papers

An Investigation of the Cycle Extraction Properties of Several Bandpass Filters Used to Identify Business Cycles

An Omnibus Test for Time Series Model I(d)

A statistical uncertainty principle for estimating the time of a discrete shift in the mean of a continuous time random process

A Hilbert Transform Method for Estimating Distributed Lag Models With Randomly Missed or Distorted Observations

Topics in analytical political economy