In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique ( Shao, 2010 ) to testing and estimation of a single change-point in the linear trend of a nonstationary time series. We further combine the SN-based change-point test with the NOT algorithm ( Baranowski et al., 2019 ) to achieve multiple change-point estimation. Using the proposed method, we analyze the trajectory of the cumulative COVID-19 cases and deaths for 30 major countries and discover interesting patterns with potentially relevant implications for effectiveness of the pandemic responses by different countries. Furthermore, based on the change-point detection algorithm and a flexible extrapolation function, we design a simple two-stage forecasting scheme for COVID-19 and demonstrate its promising performance in predicting cumulative deaths in the U.S.

This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the statistical inference methods based on the Gaussian quasi-maximum likelihood estimation (GQMLE) become non-standard, and their asymptotics require the data to have a finite sixth moment, which narrows applicable scope in studying heavy-tailed data. To overcome this deficiency, this paper develops a systematic statistical inference procedure based on the self-weighted GQMLE for the augmented DAR model. Except for the Lagrange multiplier test statistic, the Wald, quasi-likelihood ratio and portmanteau test statistics are all shown to have non-standard asymptotics. The entire procedure is valid as long as the data is stationary, and its usefulness is illustrated by simulation studies and one real example.where u, φ i ∈ R, ω > 0, α i > 0, {η t } is a sequence of independent and identically distributed (i.i.d.) random variables with zero mean and unit variance, and η t is independent of {y s ; s < t}. Model (1.1) was first termed by Ling (2004), and it is a subclass of ARMA-ARCH models in Weiss (1984) and of nonlinear AR models in Cline and Pu (2004), but it is different from Engle's ARCH model if some φ i = 0.

We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based

We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing heavy-tailed RCOV, which is an important stylized fact but could not be handled adequately by the Wishart-based models. To further mimic the long memory feature of the RCOV, a special CBF model with the conditional heterogeneous autoregressive (HAR) structure is introduced. Moreover, we give a systematical study on the probabilistic properties and statistical inferences of the CBF model, including exploring its stationarity, establishing the asymptotics of its maximum likelihood estimator, and giving some new inner-product-based tests for its model checking. In order to handle a large dimensional RCOV matrix, we construct two reduced CBF models-the variance-target CBF model (for moderate but fixed dimensional RCOV matrix) and the factor CBF model (for high dimensional RCOV matrix). For both reduced models, the asymptotic theory of the estimated parameters is derived. The importance of our entire methodology is illustrated by simulation results and two real examples.

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We propose a novel and unified framework for change‐point estimation in multivariate time series. The proposed method is fully non‐parametric, robust to temporal dependence and avoids the demanding consistent estimation of long‐run variance. One salient and distinct feature of the proposed method is its versatility, where it allows change‐point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the core of our method, we couple the self‐normalisation‐ (SN) based tests with a novel nested local‐window segmentation algorithm, which seems new in the growing literature of change‐point analysis. Due to the presence of an inconsistent long‐run variance estimator in the SN test, non‐standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN‐based change‐point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state‐of‐the‐art approaches in the literature.

Clinical and animal studies have reported that low-dose doxepin may have positive effects on generalized anxiety disorder (GAD); however, its effectiveness and clinical safety are less well understood. This study is a before-after study and aims to investigate the effectiveness and side effects of low-dose doxepin by evaluating Hamilton Anxiety Scale (HAMA) scores, hormones, blood glucose, serum lipids, body weight, and body mass index (BMI) in patients with GAD. Forty-nine patients (20 males and 29 females) with GAD were randomly assigned to receive low-dose doxepin (6.25 mg–12.5 mg per day) for 12 weeks between February 2015 and March 2016. HAMA scores, fasting blood glucose (FBG) body weight, BMI, and some serum biochemical indexes, such as adrenocorticotropic hormone (ACTH), free triiodothyronine (FT3), total cholesterol (TC), triglyceride (TG), and low-density lipoprotein cholesterol (LDLC), and FBG, were assessed during pretreatment and post-treatment. Mean scores of HAMA decreased from 19.50 ± 1.22 to 8.50 ± 3.61 after low-dose doxepin treatment ( P < .01). The serum levels of ACTH (4.33 ± 2.14 vs 6.12 ± 3.02 pmol/L), FT3 (4.78 ± 0.51 vs 5.15 ± 0.52 pg/mL), TC (4.55 ± 1.01 vs 5.93 ± 1.66 mmol/L), TG (1.69 ± 1.51 vs 3.39 ± 2.86 mmol/L), and LDLC (2.43 ± 0.88 vs 3.76 ± 1.25 mmol/L), and FBG (5.06 ± 0.43 vs 5.78 ± 0.81 mmol/L) were higher than that pretreatment with a significant difference ( P < .01). Bodyweight (62.00 ± 7.45 vs 64.00 ± 6.44 kg, P = .23) and BMI (23.70 ± 2.35 vs 24.48 ± 2.11 kg/m 2 , P = .14) had no difference after treatment. These results suggest that low-dose doxepin has beneficial clinical efficacy and safety. Low-dose doxepin can ameliorate anxiety in GAD patients and has some effects on neuroendocrine systems and the metabolic activity of serum glucose and lipid.

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