Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series

We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested.Comment: submitte

An Information-Theoretic Test for Dependence with an Application to the Temporal Structure of Stock Returns

Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that time series data can usefully be studied as information -- by noting the relationship between statistical redundancy and dependence, we are able to use the results of information theory to construct a test for joint dependence of random variables. The test is in the same spirit of those developed by Ryabko and Astola (2005, 2006b,a), but differs from these in that we add extra randomness to the original stochatic process. It uses data compression to estimate the entropy rate of a stochastic process, which allows it to measure dependence among sets of random variables, as opposed to the existing econometric literature that uses entropy and finds itself restricted to pairwise tests of dependence. We show how serial dependence may be detected in S&P500 and PSI20 stock returns over different sample periods and frequencies. We apply the test to synthetic data to judge its ability to recover known temporal dependence structures.Comment: 22 pages, 7 figure

A Test for Serial Dependence Using Neural Networks

Testing serial dependence is central to much of time series econometrics. A number of tests that have been developed and used to explore the dependence properties of various processes. This paper builds on recent work on nonparametric tests of independence. We consider a fact that characterises serially dependent processes using a generalisation of the autocorrelation function. Using this fact we build dependence tests that make use of neural network based approximations. We derive the theoretical properties of our tests and show that they have superior power properties. Our Monte Carlo evaluation supports the theoretical findings. An application to a large dataset of stock returns illustrates the usefulness of the proposed tests.Independence, Neural networks, Strict stationarity, Bootstrap, S&P500

Hypotheses testing on infinite random graphs

Drawing on some recent results that provide the formalism necessary to definite stationarity for infinite random graphs, this paper initiates the study of statistical and learning questions pertaining to these objects. Specifically, a criterion for the existence of a consistent test for complex hypotheses is presented, generalizing the corresponding results on time series. As an application, it is shown how one can test that a tree has the Markov property, or, more generally, to estimate its memory

Identifying ENSO Phase Impacts on Area Yield Insurance Rates: An Application of Non-Parametric Analysis

The paper reports results of non-parametric analysis of peanut, corn, and cotton yield distributions by the ElNino Southern Oscillation (ENSO) phases in the Southeastern U.S. For validation purposes, the historical yield data is complemented by a set of simulated peanut yields generated using daily weather data. The hypothesis, justified by the observed South-Eastern climate differences and research on ENSO cycles and planting dates, is that different climate conditions during ENSO cycles translate into different yield distributions and, therefore, insurance premiums (loss to coverage ratios). Kernel density estimates of historical county yield data show consistent patterns in the actuarially fair rate schedules grouped by ENSO phases and geographical areas. In particular, corn and cotton yield insurance premiums appear to be the most dependent on the ENSO phases and are the highest, regardless of coverage, during ElNino and the lowest during LaNina. Peanut premiums are higher during Neutral years and lowest during LaNina. The results appear to be robust to the transformations used to make the yield series stationary. While these dependencies do not necessarily correspond to the precipitation and solar radiation characteristics of the corresponding ENSO cycles in the Southeastern US, drawing direct analogies with yield variability is premature as many less documented factors, like the spacing of sunny and rainy days, may be just as important. The comparisons of the empirical and simulated peanut yield distributions show that they are similar in many ways and that the dissimilarities can be explained by known factors. These findings should be more relevant for the area yield insurance as opposed to the APH arrangements as the yield data used in designing contracts for the former reflects the systemic risk more influenced by climate than by the farm-level, basis risk factors accommodated in the APH plans.Risk and Uncertainty, Q140, C220, G220,