Testing predictability is known to be an important issue for the balanced predictive regression model. Some unified testing statistics of desirable properties have been proposed, though their validity depends on a predefined assumption regarding whether or not an intercept term nevertheless exists. In fact, most financial data have endogenous or heteroscedasticity structure, and the existing intercept term test does not perform well in these cases. In this paper, we consider the testing for the intercept of the balanced predictive regression model. An empirical likelihood based testing statistic is developed, and its limit distribution is also derived under some mild conditions. We also provide some simulations and a real application to illustrate its merits in terms of both size and power properties.

A direct application of autoregressive (AR) models with independent and identically distributed (iid) errors is sometimes inadequate to fit the time series data well. A natural alternative is further to assume the model errors following an AR process, whose structure however has essential impacts on the statistical inferences related to the autoregressive models. In this paper, we construct a new unified test for checking the AR error structure based on the empirical likelihood method. The proposed test is desirable because its limit distribution is always chi-squared regardless of whether the autoregressive model is stationary or non-stationary, with or without an intercept term. Some simulations are also provided to illustrate the finite sample performance of this test. Finally, we apply the proposed test to a financial real data set.

In this paper, we consider semiparametric efficient inferences in the generalised partially linear models. A novel bias-corrected estimating procedure and a bias-corrected empirical log-likelihood ratio are developed, respectively, for point estimation and confidence regions for parameters of interest. Under mild conditions, the resulting likelihood ratio is shown to be standard chi-squared distributed asymptotically. Moreover, it is noteworthy that the range of bandwidth in this paper covers the optimal bandwidth due to the implementation of a new bias-corrected technique. Therefore, no undersmoothing is needed here for guaranteeing the asymptotically standard chi-squared distribution of the proposed statistic. Simulation study and real application are also provided in order to illustrate the performance of resulting procedure.

Autoregressive exogenous, hereafter ARX, models are widely adopted in time series-related domains as they can be regarded as the combination of an autoregressive process and a predictive regression. Within a more complex structure, extant diagnostic checking methods face difficulties in remaining validity in many conditions existing in real applications, such as heteroscedasticity and error correlations exhibited between the ARX model itself and its exogenous processes. For these reasons, we propose a new serial correlation test method based on the profile empirical likelihood. Simulation results, as well as two real data examples, show that our method has a good performance in all mentioned conditions.

Background: The novel coronavirus SARS-CoV-2 (coronavirus disease 2019, COVID-19) has caused serious consequences on many aspects of social life throughout the world since the first case of pneumonia with unknown etiology was identified in Wuhan, Hubei province in China in December 2019. Note that the incubation period distribution is key to the prevention and control efforts of COVID-19. This study aimed to investigate the conditional distribution of the incubation period of COVID-19 given the age of infected cases and estimate its corresponding quantiles from the information of 2172 confirmed cases from 29 provinces outside Hubei in China. Methods: We collected data on the infection dates, onset dates, and ages of the confirmed cases through February 16th, 2020. All the data were downloaded from the official websites of the health commission. As the epidemic was still ongoing at the time we collected data, the observations subject to biased sampling. To address this issue, we developed a new maximum likelihood method, which enables us to comprehensively study the effect of age on the incubation period. Results: Based on the collected data, we found that the conditional quantiles of the incubation period distribution of COVID-19 vary by age. In detail, the high conditional quantiles of people in the middle age group are shorter than those of others while the low quantiles did not show the same differences. We estimated that the 0.95-th quantile related to people in the age group 23 ∼55 is less than 15 days. Conclusions: Observing that the conditional quantiles vary across age, we may take more precise measures for people of different ages. For example, we may consider carrying out an age-dependent quarantine duration in practice, rather than a uniform 14-days quarantine period. Remarkably, we may need to extend the current quarantine duration for people aged 0 ∼22 and over 55 because the related 0.95-th quantiles are much greater than 14 days.