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.     

Estimating Mean Survival Time: When is it Possible?

For right‐censored survival data, it is well‐known that the mean survival time can be consistently estimated when the support of the censoring time contains the support of the survival time. In practice, however, this condition can be easily violated because the follow‐up of a study is usually within a finite window. In this article, we show that the mean survival time is still estimable from a linear model when the support of some covariate(s) with non‐zero coefficient(s) is unbounded regardless of the length of follow‐up. This implies that the mean survival time can be well estimated when the support of linear predictor is wide in practice. The theoretical finding is further verified for finite samples by simulation studies. Simulations also show that, when both models are correctly specified, the linear model yields reasonable mean square prediction errors and outperforms the Cox model, particularly with heavy censoring and short follow‐up time.     

Statistical Engineering: An Idea Whose Time Has Come?

Several authors, including the American Statistical Association (ASA) guidelines for undergraduate statistics education (American Statistical Association Undergraduate Guidelines Workgroup) American Statistical Association Undergraduate Guidelines Workgroup (2014), “2014 Curriculum Guidelines for Undergraduate Programs in Statistical Science,” Alexandria, VA: American Statistical Asociation. Available at http://www.amstat.org/education/curriculumguidelines.cfm [Google Scholar], have noted the challenges facing statisticians when attacking large, complex, and unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of selecting the one “correct” statistical method for such problems is not sufficient; a new paradigm is needed. Statistical engineering has been proposed as a discipline that can provide a viable paradigm to attack such problems, used in conjunction with sound statistical science. Of course, to develop as a true discipline, statistical engineering must be clearly defined and articulated. Further, a well-developed underlying theory is needed, one that would prove helpful in addressing such large, complex, and unstructured problems. The purpose of this expository article is to more clearly articulate the current state of statistical engineering, and make a case for why it merits further study by the profession as a means of addressing such problems. We conclude with a “call to action.”     

Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—a Weight-adjusted Approach

In follow-up studies, survival data often include subjects who have had a certain event at recruitment and may potentially experience a series of subsequent events during the follow-up period. This kind of survival data collected under a cross-sectional sampling criterion is called truncated serial event data. The outcome variables of interest in this paper are serial sojourn times between successive events. To analyze the sojourn times in truncated serial event data, we need to confront two potential sampling biases arising simultaneously from a sampling criterion and induced informative censoring. In this study, nonparametric estimation of the joint probability function of serial sojourn times is developed by using inverse probabilities of the truncation and censoring times as weight functions to accommodate these two sampling biases under various situations of truncation and censoring. Relevant statistical properties of the proposed estimators are also discussed. Simulation studies and two real data are presented to illustrate the proposed methods.     

An Example Of The Use Of Andrews’ Plots To Detect Time Variations In Model Parameters And To Detect Outlying Observations

Andrews (1972) introduced a method of plotting highdimensional data in two dimensions. This method is exploited as a graphical tool for the examination of changes over time in the parameters of a time series model. An example using a Fourier series model is given to illustrate the method. It is also shown how outlying observations in the data can be found.

AMS (MOS) Subject Classifivations: 62M10, 62H30     

Comment on “Issues Involved With the Seasonal Adjustment of Economic Time Series” by William R. Bell and Steven C. Hiilmer

This article investigates the existence of multiple regimes in the U.S. economy during the 1923—1991 period. A technique known as regression tree analysis is applied to search for splits in the data, if any exist, rather than choosing a splitting point a priori as has been done in previous work. Using this technique, strong evidence for the existence of nonlinear behavior of U.S. output is found over this period. Monte Carlo results are presented to assess the significance of the regime changes that are found.     

A Note on Overdifferencing and the Equivalence of Seasonal Time Series Models With Monthly Means and Models With (0, 1, 1)12 Seasonal Parts When ⊖ = 1

Two general models for monthly seasonal time series are considered, one in which seasonality is modeled with monthly means and another in which seasonality is modeled with a (0, 1, 1)₁₂ ARIMA structure. The models are shown to be equivalent if the seasonal moving average parameter (?) is 1 and if the same assumptions about the 12 initial observations are made for both models. The role of the assumptions about the initial observations is analyzed, and it is argued that for practical purposes the two models can be regarded as equivalent when ? = 1. It is observed that the result extends easily to more general models involving overdifferencing.