Confidence sets for the date of a single break in linear time series regressions

This paper considers the problem of constructing confidence sets for the date of a single break in a linear time series regression. We establish analytically and by small sample simulation that the current standard method in econometrics for constructing such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that breaks of moderate magnitude are a theoretically and empirically relevant phenomenon, we proceed to develop an appropriate alternative. We suggest constructing confidence sets by inverting a sequence of tests. Each of the tests maintains a specific break date under the null hypothesis, and rejects when a break occurs elsewhere. By inverting a certain variant of a locally best invariant test, we ensure that the asymptotic critical value does not depend on the maintained break date. A valid confidence set can hence be obtained by assessing which of the sequence of test statistics exceeds a single number.     

The effect of data transformation on common cycle,cointegration, and unit root tests: Monte Carlo results and a simple test

Cointegration, common cycle, and related tests statistics are often constructed using logged data, even without clear reason why logs should be used rather than levels. Unfortunately, it is also the case that standard data transformation tests, such as those based on Box–Cox transformations, cannot be shown to be consistent unless assumptions concerning whether variables I(0)$I(0)$ or I(1)$I(1)$ are made. In this paper, we propose a simple randomized procedure for choosing between levels and log-levels specifications in the (possible) presence of deterministic and/or stochastic trends, and discuss the impact of incorrect data transformation on common cycle, cointegration and unit root tests.     

Specification tests of parametric dynamic conditional quantiles

This article proposes omnibus specification tests of parametric dynamic quantile models. In contrast to the existing procedures, we allow for a flexible specification, where a possible continuum of quantiles is simultaneously specified under fairly weak conditions on the serial dependence in the underlying data-generating process. Since the null limit distribution of tests is not pivotal, we propose a subsampling approximation of the asymptotic critical values. A Monte Carlo study shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application suggests that our methodology is a powerful alternative to standard backtesting procedures in evaluating market risk.     

A class of simple distribution-free rank-based unit root tests

We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference densityg, which need not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite-sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for which we provide a complete analysis of asymptotic relative efficiencies. Rather than stressing asymptotic optimality, however, we emphasize finite-sample performances, which also depend, quite heavily, on initial values. It appears that our rank-based tests significantly outperform the traditional Dickey-Fuller tests, as well as the more recent procedures proposed by Elliott et al. (1996), Ng and Perron (2001), and Elliott and Müller (2006), for a broad range of initial values and for heavy-tailed innovation densities. Thus, they provide a useful complement to existing techniques.     

Estimation of conditional moment restrictions without assuming parameter identifiability in the implied unconditional moments

A well-known difficulty in estimating conditional moment restrictions is that the parameters of interest need not be globally identified by the implied unconditional moments. In this paper, we propose an approach to constructing a continuum of unconditional moments that can ensure parameter identifiability. These unconditional moments depend on the “instruments” generated from a “generically comprehensively revealing” function, and they are further projected along the exponential Fourier series. The objective function is based on the resulting Fourier coefficients, from which an estimator can be easily computed. A novel feature of our method is that the full continuum of unconditional moments is incorporated into each Fourier coefficient. We show that, when the number of Fourier coefficients in the objective function grows at a proper rate, the proposed estimator is consistent and asymptotically normally distributed. An efficient estimator is also readily obtained via the conventional two-step GMM method. Our simulations confirm that the proposed estimator compares favorably with that of Domínguez and Lobato (2004, Econometrica) in terms of bias, standard error, and mean squared error.     

Powerful tests for structural changes in volatility

Detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence. We propose modified CUSUM and LM tests that are built on a robust estimator of the long-run variance of squared series. We establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative. The theory allows smooth and abrupt structural changes that can be small. The smoothing parameter is automatically selected such that the proposed test has good finite-sample size and meanwhile achieves decent power gain.