Tests of time-invariance

Quantiles provide a comprehensive description of the properties of a variable and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how stationarity tests can be generalized to test the null hypothesis that a particular quantile is constant over time by using weighted indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy-tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. We report Monte Carlo experiments investigating the effectiveness of the proposed tests and then move on to consider how to test for relative time invariance, based on residuals from fitting a time-varying level or trend. Empirical examples, using stock returns and U.S. inflation, provide an indication of the practical importance of the tests

A Multi-Level Choice Theory

The Great Recession has called into question many tenets of Neo-classical Microeconomics. Neo-classical theory allows each agent only one fixed type, homo economicus, while not denying other possible types as in adverse selection. We propose that economic agents not only choose their market basket but also their types. Agents are members of groups and each group has social norms to which the agent more or less conforms. His/her market behavior trades off private well being which responds to prices but also social well being which responds to norms. We show how deviation from norms are determined. We also discuss other anomalies in the light of this model.

Optimal Auctions for Correlated Buyers with Sampling

Cr\'emer and McLean [1985] showed that, when buyers' valuations are drawn from a correlated distribution, an auction with full knowledge on the distribution can extract the full social surplus. We study whether this phenomenon persists when the auctioneer has only incomplete knowledge of the distribution, represented by a finite family of candidate distributions, and has sample access to the real distribution. We show that the naive approach which uses samples to distinguish candidate distributions may fail, whereas an extended version of the Cr\'emer-McLean auction simultaneously extracts full social surplus under each candidate distribution. With an algebraic argument, we give a tight bound on the number of samples needed by this auction, which is the difference between the number of candidate distributions and the dimension of the linear space they span

Assessing T cell clonal size distribution: a non-parametric approach

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.Comment: 13 pages, 3 figures, 2 table

Range-Based Estimation of Stochastic Volatility Models or Exchange Rate Dynamics are More Interesting Than You Think

We propose using the price range, a recently-neglected volatility proxy with a long history in finance, in the estimation of stochastic volatility models. We show both theoretically and empirically that the log range is approximately Gaussian, in sharp contrast to popular volatility proxies, such as log absolute or squared returns. Hence Gaussian quasi-maximum likelihood estimation based on the range is not only simple, but also highly efficient. We illustrate and enrich our theoretical results with a Monte Carlo study and a substantive empirical application to daily exchange rate volatility. Our empirical work produces sharp conclusions. In particular, the evidence points strongly to the inadequacy of one-factor volatility models, favoring instead two-factor models with one highly persistent factor and one quickly mean reverting factor.

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain

Exact and asymptotic solutions of the call auction problem

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.Comment: 24 pages, 7 figure

Time Series Analysis

We provide a concise overview of time series analysis in the time and frequency domains, with lots of references for further reading.time series analysis, time domain, frequency domain, Research Methods/ Statistical Methods,