Nonparametric retrospection and monitoring of predictability of financial returns

We develop and evaluate sequential testing tools for a class of nonparametric tests for predictability of financial returns that includes, in particular, the directional accuracy and excess profitability tests. We consider both the retrospective context where a researcher wants to track predictability over time in a historical sample, and the monitoring context where a researcher conducts testing as new observations arrive. Throughout, we elaborate on both two-sided and one-sided testing, focusing on linear monitoring boundaries that are continuations of horizontal lines corresponding to retrospective critical values. We illustrate our methodology by testing for directional and mean predictability of returns in a dozen of young stock markets in Eastern Europe.Testing, monitoring, predictability, stock returns

Optimal Instruments in Time Series: A Survey

This article surveys estimation in stationary time series models using the approach of optimal instrumentation. We review tools that allow construction and implementation of optimal instrumental variables estimators in various circumstances { in single- and multiperiod models, in the absence and presence of conditional heteroskedasticity, by considering linear and nonlinear instruments. We also discuss issues adjacent to the theme of optimal instruments. The article is directed primarily towards practitioners, but also may be found useful by econometric theorists and teachers of graduate econometrics.Instrumental variables estimation; Moment restrictions; Optimal instrument; Effciency bounds; Stationary time series.

Inference in Regression Models with Many Regressors

We investigate the behavior of various standard and modified F, LR and LM tests in linear homoskedastic regressions, adapting an alternative asymptotic framework where the number of regressors and possibly restrictions grows proportionately to the sample size. When restrictions are not numerous, the rescaled classical test statistics are asymptotically chi-squared irrespective of whether there are many or few regressors. However, when restrictions are numerous, standard asymptotic versions of classical tests are invalid. We propose and analyze asymptotically valid versions of the classical tests, including those that are robust to the numerosity of regressors and restrictions. The local power of all asymptotically valid tests under consideration turns out to be equal. The "exact" F test that appeals to critical values of the F distribution is also asymptotically valid and robust to the numerosity of regressors and restrictions.Alternative asymptotic theory, linear regression, test size, test power, F test, Wald test, Likelihood Ratio test, Lagrange Multiplier test

Dynamic modeling under linear-exponential loss

We develop a methodology of parametric modeling of time series dynamics when the underlying loss function is linear-exponential (Linex). We propose to directly model the dynamics of the conditional expectation that determines the optimal predictor. The procedure hinges on the exponential quasi maximum likelihood interpretation of the Linex loss and nicely fits the multiple error modeling framework. Many conclusions relating to estimation, inference and forecasting follow from results already available in the econometric literature. The methodology is illustrated using data on United States GNP growth and Treasury bill returns.Linear-exponential loss, optimal predictor, quasi maximum likelihood, multiple error model, autoregressive conditional durations

Sequential Testing with Uniformly Distributed Size

Sequential procedures of testing for structural stability do not provide enough guidance on the shape of boundaries that are used to decide on acceptance or rejection, requiring only that the overall size of the test is asymptotically controlled. We introduce and motivate a reasonable criterion for a shape of boundaries which requires that the test size be uniformly distributed over the testing period. Under this criterion, we numerically construct boundaries for most popular sequential tests that are characterized by a test statistic behaving asymptotically either as a Wiener process or Brownian bridge. We handle this problem both in a context of retrospecting a historical sample and in a context of monitoring newly arriving data. We tabulate the boundaries by …tting them to certain exible but parsimonious functional forms. Interesting patterns emerge in an illustrative application of sequential tests to the Phillips curve model.Structural stability; sequential tests; CUSUM; retrospection; monitoring; boundaries; asymptotic size