Estimation of integrated multivariate volatilities of an Ito process is an interesting and important issue in finance, for example, in order to evaluate portfolios. New non-parametric estimators have been recently proposed by Malliavin and Mancino (2002) and Hayashi and Yoshida (2005a) as alternative methods to classical realized quadratic covariation. The purpose of this article is to compare these alternative estimators both theoretically and empirically, when high frequency data is available. We found that the Hayashi-Yoshida estimator performs the best among the alternatives in view of the bias and the MSE. The other estimators are shown to have possibly heavy bias mostly toward the origin. We also applied these estimators to Japanese Government Bond futures to obtain the results consistent with our simulation.High frequency data, Integrated volatility, Nonparametric estimators, Weighted realized volatility,

We examined the phenomenon of fewer new confirmed cases on Monday in Japan, which we refer to as the Monday effect. In Japan, prefectures aggregate and announce the number of daily confirmed cases. We analyzed the impact of this effect in each prefecture. The effect is mainly found in prefectures with populations of 2 million or more. This effect is also constantly observed in the three major metropolitan areas in Japan. However, the magnitude of the observed effect is uncorrelated with both the number of positives per 1,000 people and the population size. Our results suggest that the reporting delay occurs in prefectures above a specific size, but the magnitude of the delay differs among prefectures. We consider two possible explanations for this effect: 1) delays caused by the administrative system. 2) fewer tests are conducted on the previous day. Our results indicate that delays are caused by the administrative system in some prefectures and that some prefectures with larger populations are less likely to conduct screenings on holidays.

The daily announcement of positive COVID-19 cases had a major socioeconomic impact. In Japan, it is well known that the characteristic of this number as time series data is the weekly periodicity. We assume that this periodicity is generated by changes in the timing of reporting on the weekend. We analyze a lag structure that shows how congestion that occurs over the weekend affects the number of new confirmed cases at the beginning of the following week. We refer to this reporting delay as the weekend effect. Our study aims to describe the geographical heterogeneity found in the time series of reported positive cases. We use data on the number of new positives reported by the prefectures. Our results suggest that delays generally occur in prefectures with a population of more than 2 million, including Japan’s three largest metropolitan areas, Tokyo, Osaka, and Nagoya. The number of new positives was higher in the more populated prefectures. This will explain the weekend effect.

This note proposes an iterative method for exponentially weighted rolling regression (EWRR), which was proved to be an optimal estimator of volatility by Foster and Nelson [Econometrica 64 (1996)]. The method accelerates the numerical evaluation of EWRR under certain circumstances. An alternative to usual realized volatility is proposed for its application.  2004 Elsevier Inc. All rights reserved.