The availability of high-frequency intraday data allows us to accurately estimate stock volatility. This paper employs a bivariate diffusion to model the price and volatility of an asset and investigates kernel type estimators of spot volatility based on highfrequency return data. We establish both pointwise and global asymptotic distributions for the estimators. Jianqing Fan is Frederick Moore...

Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high density grid, which can then be used to generate meteorological maps at a broad range of spatial and temporal scales. In addition to point predictions, quantific...

The daily volatility is typically unobserved but can be estimated using high frequent tick-by-tick data. In this paper, we study the problem of forecasting the unobserved volatility using past values of measured volatility. Specifically, we use daily estimates of volatility based on high frequency data, called realized variance, and construct the optimal linear forecast of future volatility. Ut...

This paper proposes a novel multiscale estimator for the integrated volatility of an Itô process with harmonizable increments, in the presence of market microstructure noise. The multiscale structure is modelled frequency-by-frequency and the concept of the multiscale ratio is introduced to quantify the bias in the quadratic variation due to the microstructure noise process. The multiscale rati...

We propose a technique to avoid spurious detection of jumps in high frequency data via an explicit thresholding on available test statistics. We prove that it eliminates asymptotically all spurious jumps. Monte Carlo results show that it performs also well in finite samples. Our empirical investigation of Dow Jones stocks reveals that the spurious detections represent up to 50% of the jumps det...

To treat with social phenomena, statistical and mathematical physics provides a powerful and rigorous method [1], and several papers have studied the models of social phenomena based on stochastic processes. Many researchers in econometrics or biometrics have proposed that the discrete choice including binary analysis may be formulated as the AR (autoregressive), logit, and probit models [2]. I...

In this paper we describe ways to transform a curve constituted by a series of data points delivered by monitoring devices into a series of bends and lines between them. The resulting qualitative representation of the curve can easily be utilized in a Knowledge Based System. Since the representation obtained resembles the way humans describe curves, e.g. "this bend is not sharp enough to be nor...

There has in recent years been a vast increase in the amount of high frequency data available. There has also been an explosion in the literature on the subject. In this course, we start from scratch, introducing the probabilistic model for such data, and then turn to the estimation question in this model. We shall be focused on the (for this area) emblematic problem of estimating volatility. S...

Price discrimination offers sellers the possibility of increasing revenue by capturing a market’s consumer surplus: arising from the low price elasticity segment of customers that would have been prepared to pay more than the current market price. First degree price discrimination requires a seller to know the maximum (reserve) price that each consumer is willing to pay. Discouragingly, this in...