Sara Mazzonetto

Bio: Sara Mazzonetto is an academic researcher from University of Lorraine. The author has contributed to research in topics: Brownian motion & Statistical physics. The author has an hindex of 2, co-authored 2 publications receiving 8 citations.

Rates of convergence to the local time of Oscillating and Skew Brownian Motions

Abstract: In this paper a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motions is considered. Their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.

Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations

Abstract: We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift parameters, both assuming continuous and discrete time observations. In the ergodic case, we derive consistency and speed of convergence of these estimators in long time and high frequency. Based on these results, we develop a test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to short-term US interest rates modeling.

Testing Continuous-Time Models of the Spot Interest Rate

Abstract: Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean.

Filling the gaps

Abstract: 80 IE E E S P E C T R U M • Ju n e 20 02 T echnology is a language-generating machine. With letters, phonemes, prefixes, suffixes, and words as its raw materials, technology constantly manufactures shiny new acronyms, words, and phrases to describe its onrush of new ideas, processes, and products. While technology has always stamped out new words at an impressive clip, most of these terms remain warehoused within the narrow tech communities that defined them. Some of them, however, are shipped out on the linguistic equivalents of planes, trains, and automobiles and get distributed far and wide. A few even morph into general-purpose words and phrases. For example, nuclear technology provided us with such terms as ground zero, fallout, and meltdown; radio spun off flip side, fine-tune, and stereo; aviation contributed push the envelope, automatic pilot, bail out, and gremlin; the car industry donated spark plug, bypass, blow a gasket, and rev up; and even earlier, the railroads gave us derail, sidetrack, streamline, and pick up steam. But though technology has always been a kind of new-word assembly line, what’s different these days is that technology is cranking out fresh terms at a rate that is downright exponential. That’s not because people are making up new words in their spare time, but because we now have more technology than ever. We don’t just have telephones, we have mobile phones, pagers, satellite phones, and wireless devices. We don’t just have computers, we have desktops, servers, notebooks, palmtops, PDAs, and Internet appliances. New gadgets, new technologies, new services, and new ideas stride purposefully down Technology Road, each one pulling a bright red wagon full of newly minted words and phrases. These now have a super-efficient method of propagation: the electronic byways of e-mail, chat rooms, instant messaging, and the Web. In the pre-Internet world, new words would tend to stay within the cultural tributary that coined them; only a few would get swept into the mainstream. Today there is a subculture—the Internet and its adjunct technologies—of hundreds of millions of people, that by definition is part of the mainstream. This means it doesn’t take much for new words and phrases to catch on. Keeping up with this deluge of newfangled technical terms will be the future focus of the Technically Speaking column. I’ll examine new words and phrases that have jumped down from their technological niches and are poised to set up shop in the broader piazza of general language use. This column introduces Paul McFedries as the new author of Technically Speaking, which appears every other month. Readers are invited to correspond with him at techspkg@ieee.org. P E T E R H O R V A T H TECHNICALLY SPEAKING

Rates of convergence to the local time of Oscillating and Skew Brownian Motions

Abstract: In this paper a class of statistics based on high frequency observations of oscillating Brownian motions and skew Brownian motions is considered. Their convergence rate towards the local time of the underling process is obtained in form of a Central Limit Theorem.

Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations

Abstract: We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift parameters, both assuming continuous and discrete time observations. In the ergodic case, we derive consistency and speed of convergence of these estimators in long time and high frequency. Based on these results, we develop a test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to short-term US interest rates modeling.