时变空间权重矩阵面板数据模型稳健LM检验有效性研究

空间权重矩阵是描述个体间空间关系的重要工具,通常基于个体间的地理距离构造不随时间而改变的空间权重矩阵。然而,当个体间的空间关系源自经济/社会/贸易距离或人口流动性/气候等特征时,空间权重矩阵本质上可能将随时间而改变。由此,本研究提出时变空间权重矩阵面板数据模型的稳健LM检验。大量Monte Carlo模拟结果显示：从检验水平和功效角度来看,基于误设的非时变空间权重矩阵的稳健LM检验存在较大偏差,但是基于时变空间权重矩阵的稳健LM检验能够有效地识别面板数据中的空间关系类型。尤其是,在时间较长和个体较多等情况下,时变空间权重矩阵的稳健LM检验功效更高。     

The Estimation and Inference of a Panel Cointegration Model with a Time Trend

This article investigates the asymptotic properties of coefficient estimators in the panel cointegration model with a time trend. We find that the bias of OLS estimator for the slope coefficient in the panel cointegration model with a time trend is distinct from that in the panel cointegration model without a time trend. Meanwhile, the variance of the limiting distribution for the slope coefficient is larger in the panel cointegration model with a time trend than without a time trend.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

Smoothing Time Series with Local Polynomial Regression on Time

Time series smoothers estimate the level of a time series at time t as its conditional expectation given present, past and future observations, with the smoothed value depending on the estimated time series model. Alternatively, local polynomial regressions on time can be used to estimate the level, with the implied smoothed value depending on the weight function and the bandwidth in the local linear least squares fit. In this article we compare the two smoothing approaches and describe their similarities. Through simulations, we assess the increase in the mean square error that results when approximating the estimated optimal time series smoother with the local regression estimate of the level.     

Modelling the travel time of transit vehicles in real‐time through a GTFS‐based road network using GPS vehicle locations

Predicting the arrival time of a transit vehicle involves not only knowledge of its current position and schedule adherence, but also traffic conditions along the remainder of the route. Road networks are dynamic and can quickly change from free‐flowing to highly congested, which impacts the arrival time of transit vehicles, particularly buses which often share the road with other vehicles, so reliable predictions need to account for real‐time and future traffic conditions. The first step in this process is to construct a framework with which road state (traffic conditions) can be estimated using real‐time transit vehicle position data. Our proposed framework implements a vehicle model using a particle filter to estimate road travel times, which are used in a second model to estimate real‐time traffic conditions. Although development and testing took place in Auckland, New Zealand, we generalised each component to make the framework compatible with other public transport systems around the world. We demonstrate the real‐time feasibility and performance of our approach in real‐time, where a combination of R and C++ was used to obtain the necessary performance results. Future work will use these estimated traffic conditions in combination with historical data to obtain reliable arrival time predictions of transit vehicles.     

Forecasting functional time series using weighted likelihood methodology

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).     

Posterior consistency for the spectral density of non-Gaussian stationary time series

Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation involving a nonparametric correction of a parametric likelihood has been proposed in the literature with a proof of posterior consistency for spectral density estimation in combination with the Bernstein–Dirichlet process prior for Gaussian time series. In this article, we will extend the posterior consistency result to non-Gaussian time series by employing a general consistency theorem for dependent data and misspecified models. As a special case, posterior consistency for the spectral density under the Whittle likelihood is also extended to non-Gaussian time series. Small sample properties of this approach are illustrated with several examples of non-Gaussian time series.     

Forward and Backward Recurrence Times and Length Biased Sampling: Age Specific Models

Consider a chronic disease process which is beginning to be observed at a point in chronological time. The backward recurrence and forward recurrence times are defined for prevalent cases as the time with disease and the time to leave the disease state, respectively, where the reference point is the point in time at which the disease process is being observed. In this setting the incidence of disease affects the recurrence time distributions. In addition, the survival of prevalent cases will tend to be greater than the population with disease due to length biased sampling. A similar problem arises in models for the early detection of disease. In this case the backward recurrence time is how long an individual has had disease before detection and the forward recurrence time is the time gained by early diagnosis, i.e., until the disease becomes clinical by exhibiting signs or symptoms. In these examples the incidence of disease may be age related resulting in a non-stationary process. The resulting recurrence time distributions are derived as well as some generalization of length-biased sampling.     

Modeling Interval Time Series with Space–Time Processes

We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space–time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals’ center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.     

The “Caterpillar”-SSA method for analysis of time series with missing values

The paper concerns the problem of applying singular spectrum analysis to time series with missing data. A method of filling in the missing data is proposed and is applied to time series of finite rank. Conditions of exact reconstruction of missing data are developed and versions of the algorithm applicable to real-life time series are presented. The proposed algorithms result in the extraction of additive components of time series such as trends and periodic components, with simultaneous filling in of the missing data. An example is presented.     

Fitting Cox Models with Doubly Censored Data Using Spline‐Based Sieve Marginal Likelihood

In some applications, the failure time of interest is the time from an originating event to a failure event while both event times are interval censored. We propose fitting Cox proportional hazards models to this type of data using a spline‐based sieve maximum marginal likelihood, where the time to the originating event is integrated out in the empirical likelihood function of the failure time of interest. This greatly reduces the complexity of the objective function compared with the fully semiparametric likelihood. The dependence of the time of interest on time to the originating event is induced by including the latter as a covariate in the proportional hazards model for the failure time of interest. The use of splines results in a higher rate of convergence of the estimator of the baseline hazard function compared with the usual non‐parametric estimator. The computation of the estimator is facilitated by a multiple imputation approach. Asymptotic theory is established and a simulation study is conducted to assess its finite sample performance. It is also applied to analyzing a real data set on AIDS incubation time.     

Subexponential asymptotics of the waiting time distribution in a single-server queue with multiple Markovian arrival streams

This paper considers subexponential asymptotics of the tail distributions of waiting times in stationary work-conserving single-server queues with multiple Markovian arrival streams, where all arrival streams are modulated by the underlying Markov chain with finite states and service time distributions may differ for different arrival streams. Under the assumption that the equilibrium distribution of the overall (i.e., customer-average) service time distribution is subexponential, a subexponential asymptotic formula is first shown for the virtual waiting time distribution, using a closed formula recently found by the author. Further when customers are served on a FIFO basis, the actual waiting time and sojourn time distributions of customers from respective arrival streams are shown to have the same asymptotics as the virtual waiting time distribution.     

Statistical methods for regular monitoring data

Summary.  Meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and spatial statistics, particularly when there are little or no missing data. This work investigates methods for modelling such data and ways of approximating the associated likelihood functions. Models for processes on the sphere crossed with time are emphasized, especially models that are not fully symmetric in space–time. Two approaches to obtaining such models are described. The first is to consider a rotated version of fully symmetric models for which we have explicit expressions for the covariance function. The second is based on a representation of space–time covariance functions that is spectral in just the time domain and is shown to lead to natural partially nonparametric asymmetric models on the sphere crossed with time. Various models are applied to a data set of daily winds at 11 sites in Ireland over 18 years. Spectral and space–time domain diagnostic procedures are used to assess the quality of the fits. The spectral-in-time modelling approach is shown to yield a good fit to many properties of the data and can be applied in a routine fashion relative to finding elaborate parametric models that describe the space–time dependences of the data about as well.     

Monitoring point patterns for the development of space–time clusters

Existing statistical methods for the detection of space–time clusters of point events are retrospective, in that they are used to ascertain whether space–time clustering exists among a fixed number of past events. In contrast, prospective methods treat a series of observations sequentially, with the aim of detecting quickly any changes that occur in the series. In this paper, cumulative sum methods of monitoring are adapted for use with Knox's space–time statistic. The result is a procedure for the rapid detection of any emergent space–time interactions for a set of sequentially monitored point events. The approach relies on a 'local' Knox statistic that is useful in retrospective analyses to detect when and where space–time interaction occurs. The distribution of the local Knox statistic under the null hypothesis of no space–time interaction is derived. The retrospective local statistic and the prospective cumulative sum monitoring method are illustrated by using previously published data on Burkitt's lymphoma in Uganda.     

Confidence intervals for the first crossing point of two hazard functions

The phenomenon of crossing hazard rates is common in clinical trials with time to event endpoints. Many methods have been proposed for testing equality of hazard functions against a crossing hazards alternative. However, there has been relatively few approaches available in the literature for point or interval estimation of the crossing time point. The problem of constructing confidence intervals for the first crossing time point of two hazard functions is considered in this paper. After reviewing a recent procedure based on Cox proportional hazard modeling with Box-Cox transformation of the time to event, a nonparametric procedure using the kernel smoothing estimate of the hazard ratio is proposed. The proposed procedure and the one based on Cox proportional hazard modeling with Box-Cox transformation of the time to event are both evaluated by Monte–Carlo simulations and applied to two clinical trial datasets.     

应用时间利用调查估算不计酬工作价值的方法简介——以澳大利亚为例

文章介绍了时间利用调查的概念及其分类的有关内容,并以澳大利亚的实践经验为例,阐述了如何应用时间利用调查估算不计酬工作价值,着重探讨了具体调查方法及计算方法,为充分发挥时间利用调查的作用提供了有价值的参考.     

Planning the duration of a survival group sequential trial with a fixed follow-up time for all subjects

To explore the operation characteristics of survival group sequential trials with a fixed follow-up period, the accrual time and total trial duration to ensure power and type I error rate requirements are explained and investigated for hazard ratios ranging from 1.3 to 3.0, with slow or high accrual rate, and in the presence or absence of censoring. Impacts of hazard rate, accrual rate, and competitive censoring on accrual time and subsequently on total trial duration are carefully illustrated. Real time for interim analyses, needed number of events, and recruited number of subjects at time of interim analyses are also tabulated.     

Multiple-index approach to multiple autoregressive time series model

Time series which have more than one time dependent variable require building an appropriate model in which the variables not only have relationships with each other, but also depend on previous values in time. Based on developments for a sufficient dimension reduction, we investigate a new class of multiple time series models without parametric assumptions. First, for the dependent and independent time series, we simply use a univariate time series central subspace to estimate the autoregressive lags of the series. Secondly, we extract the successive directions to estimate the time series central subspace for regressors which include past lags of dependent and independent series in a mutual information multiple-index time series. Lastly, we estimate a multiple time series model for the reduced directions. In this article, we propose a unified estimation method of minimal dimension using an Akaike information criterion, for situations in which the dimension for multiple regressors is unknown. We present an analysis using real data from the housing price index showing that our approach is an alternative for multiple time series modeling. In addition, we check the accuracy for the multiple time series central subspace method using three simulated data sets.     

Spectral Estimation of Covolatility from Noisy Observations Using Local Weights

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes, which are observed discretely with additive observation noise. The appropriate estimation for time‐varying volatilities is based on an asymptotic equivalence of the underlying statistical model to a white‐noise model with correlation and volatility processes being constant over small time intervals. The asymptotic equivalence of the continuous‐time and discrete‐time experiments is proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier non‐parametric methods in the literature for the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between various proposed methods.