arXiv subjects

Emil S. Jørgensen

Publications and source records attributed to Emil S. Jørgensen.

3 recordsLinked to original sources

arXiv2026

Prediction-based inference for integrated diffusions with high-frequency data

We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if positions are recorded and speed is modelled by a diffusion. In finance, realized volatility or variations thereof can be used to construct observations of the latent integrated volatility process. Specifically, we assume that the integrated process is observed at equidistant, deterministic time points and consider the high-frequency/infinite horizon asymptotic scenario, where the number of observations, the sampling frequency and the time of the last observation all go to infinity. Subject to mild standard regularity conditions on the diffusion model, we prove the asymptotic existence and uniqueness of a consistent estimator for useful and tractable classes of prediction-based estimating functions. Asymptotic normality of the estimator is obtained under an additional assumption on the rates. The proofs are based on the useful Euler-Ito expansions of transformations of diffusions and integrated diffusions, which we study in some detail.

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arXiv2021

Data Optimisation for a Deep Learning Recommender System

This paper advocates privacy preserving requirements on collection of user data for recommender systems. The purpose of our study is twofold. First, we ask if restrictions on data collection will hurt test quality of RNN-based recommendations. We study how validation performance depends on the available amount of training data. We use a combination of top-K accuracy, catalog coverage and novelty for this purpose, since good recommendations for the user is not necessarily captured by a traditional accuracy metric. Second, we ask if we can improve the quality under minimal data by using secondary data sources. We propose knowledge transfer for this purpose and construct a representation to measure similarities between purchase behaviour in data. This to make qualified judgements of which source domain will contribute the most. Our results show that (i) there is a saturation in test performance when training size is increased above a critical point. We also discuss the interplay between different performance metrics, and properties of data. Moreover, we demonstrate that (ii) our representation is meaningful for measuring purchase behaviour. In particular, results show that we can leverage secondary data to improve validation performance if we select a relevant source domain according to our similarly measure.

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arXiv2020

Prediction-based estimation for diffusion models with high-frequency data

This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are observations of a diffusion process at $n$ equidistant time points $Δ_n i$, and the asymptotic scenario is $Δ_n \to 0$ and $nΔ_n \to \infty$. For a useful and tractable classes of prediction-based estimating functions, existence of a consistent estimator is proved under standard weak regularity conditions on the diffusion process and the estimating function. Asymptotic normality of the estimator is established under the additional rate condition $nΔ_n^3 \to 0$. The prediction-based estimating functions are approximate martingale estimating functions to a smaller order than what has previously been studied, and new non-standard asymptotic theory is needed. A Monte Carlo method for calculating the asymptotic variance of the estimators is proposed.

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