Recent studies show that the zero-process of observed intraday financial returns is frequently characterized by non-stationary periodicity. As liquidity varies across the trading day, not only does unconditional volatility change, but also the unconditional zero-probability. While scaling returns by the time-varying intraday volatility may stabilize volatility, it does not make the zero-process of scaled returns stationary. This invalidates standard methods of risk estimation, and recent studies document that the use of such invalid methods can have major effects on risk estimates. Formal tests for nonstationary periodicity in the zero-process can therefore be of great value in guiding the choice of a suitable risk estimation procedure. Despite this, little attention has been devoted to the derivation of such tests. Here, we help filling this gap by developing user-friendly yet flexible and powerful tests that hold under mild assumptions. Next, our empirical study reveals that intraday financial returns are widely characterized by non-stationary periodicity in the zero-process. This has important and potentially wide-ranging implications for future research
Stauskas, Ovidijus & De Vos, Ignace (2024)
Handling Distinct Correlated Effects with CCE
Oxford Bulletin of Economics and Statistics, s. 1- 28. Doi: 10.1111/obes.12650
The common correlated effects (CCE) approach by Pesaran is a popular method for estimating panel data models with interactive effects. Due to its simplicity, i.e., unobserved common factors are approximated with cross-section averages of the observables, the estimator is highly flexible and lends itself to a wide range of applications. Despite such flexibility, however, the properties of CCE estimators are typically only examined under the restrictive assumption that all the observed variables load on the same set of factors, which ensures joint identification of the factor space. In this article, we take a different perspective, and explore the empirically relevant case where the dependent and explanatory variables are driven by distinct but correlated factors. Hence, we consider the case of Distinct Correlated Effects. Such settings can be argued to be relevant for practice, for instance in studies linking economic growth to climatic variables. In so doing, we consider panel dimensions such that as , which is known to induce an asymptotic bias for the pooled CCE estimator even under the usual common factor assumption. We subsequently develop a robust bootstrap-based toolbox that enables asymptotically valid inference in both homogeneous and heterogeneous panels, without requiring knowledge about whether factors are distinct or common.
The Common Correlated Effects (CCE) methodology is now well established for the analysis of factor-augmented panel data models. Yet, it is often neglected that the pooled variant is biased unless the cross-section dimension ( ) of the dataset dominates the time series length ( ). This is problematic for inference with typical macroeconomic datasets, where is often equal or larger than . In response, we establish in this paper the theoretical foundation of the cross-section (CS) bootstrap for inference with CCE estimators in large and panels with . This resampling scheme is often used to estimate standard errors, yet without theoretical justification, and with unused potential, as we show it also provides a solution to the bias problem. We derive conditions under which the scheme replicates the distribution of the CCE estimators, such that bias can be eliminated and asymptotically valid inference can ensue. In so doing, we also spend attention to the case where factors need not be common across the dependent and explanatory variables, or when slopes are heterogeneous. Since we find that the CS-bootstrap applies in each case, researchers can stay agnostic on these issues. Simulation experiments show that the asymptotic properties also translate well to finite samples.
Stauskas, Ovidijus (2022)
Complete Theory for CCE Under Heterogeneous Slopes and General Unknown Factors
A recent study of Westerlund (CCE in Panels with General Unknown Factors, The Econometrics Journal, 21, 264-276, 2018) showed that a very popular common correlated effects (CCE) estimator is significantly more applicable than it was thought before. Specifically, the common factors can have much more general time series properties than stationarity. This helps to alleviate the uncertainty over deterministic model components (e.g. trends) since they can be treated as unknown, similarly to unobserved stochastic (possibly non-stationary) factors. While very promising, these theoretical results concern only the baseline scenario of the pooled (CCEP) estimator in the restrictive case of homogeneous model parameters, which is asymptotically biased and requires bias correction. Economic theory often hints at individuals exhibiting slope heterogeneity, which is a more realistic case when CCE is unbiased. Therefore, it is natural to extend the findings on general unknown factors to the case of unit-specific slopes and understand if unbiasedness still holds, which would be an empirically handy feature. It is especially interesting, because many previous studies on heterogeneous slopes did not rigorously account for the usual situation when the factors are proxied by more explanatory variables than needed. Hence, the current study introduces more completeness in the CCE theory. We demonstrate that save for some regularity conditions, CCEP and the mean group (CCEMG) estimators are asymptotically normal and unbiased under heterogeneous slopes and general unknown factors.
