Inference of time-varying regression models

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1010 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

A fractional Dickey-Fuller test for unit roots

This paper presents a new test for fractionally integrated (FI) processes. In particular, it proposes a testing procedure in the time domain that extends the well-known Dickey-Fuller approach. Monte-Carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well, both in terms of power and size, when compared with others available in the literature. The paper ends with two empirical applications.Publicad

A Kernel Independence Test for Random Processes

A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for i.i.d pairs of variables. The asymptotic behaviour of HSIC is established when computed from samples drawn from random processes. It is shown that earlier bootstrap procedures which worked in the i.i.d. case will fail for random processes, and an alternative consistent estimate of the p-values is proposed. Tests on artificial data and real-world Forex data indicate that the new test procedure discovers dependence which is missed by linear approaches, while the earlier bootstrap procedure returns an elevated number of false positives. The code is available online: https://github.com/kacperChwialkowski/HSIC .Comment: In Proceedings of The 31st International Conference on Machine Learnin

(WP 2011-06) Do Stock Market Risk Premium Respond to Consumer Confidence?

During the 2007-9 Great Recession, the risk premium associated with U.S. stocks sharply increased and has since remained significantly higher compared to its range during the last 40 years. The increase in the equity risk premium has led many analysts to believe that risk aversion among stock investors has moved to a permanently higher range in recent years. Our empirical findings show that the recent increase in the equity risk premium primarily reflects a temporary collapse in consumer confidence. As long as the consumer confidence in the sustainability of economic recovery remains low, today\u27s elevated risk premium would persist. Once the confidence level starts to recover - as it has done after every recession since the 1960s - the required return among stock market investors should also diminish

The R-package phtt: Panel Data Analysis with Heterogeneous Time Trends

The R-package phtt provides estimation procedures for panel data with large dimensions n, T, and general forms of unobservable heterogeneous effects. Particularly, the estimation procedures are those of Bai (2009) and Kneip, Sickles, and Song (2012), which complement one another very well: both models assume the unobservable heterogeneous effects to have a factor structure. Kneip et al. (2012) considers the case in which the time varying common factors have relatively smooth patterns including strongly positive auto-correlated stationary as well as non-stationary factors, whereas the method of Bai (2009) focuses on stochastic bounded factors such as ARMA processes. Additionally, the phtt package provides a wide range of dimensionality criteria in order to estimate the number of the unobserved factors simultaneously with the remaining model parameters