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Orimar Sauri

Publications and source records attributed to Orimar Sauri.

13 recordsLinked to original sources

A Comparison of High-Dimensional Variable Selection Procedures for Electricity Spot Price Forecasting

The paper considers the problem of variable selection for forecasting electricity spot prices. High-dimensional methods such as LASSO and Elastic Net are widely used for this purpose, and while they exhibit strong predictive performance, their tendency to select over-parameterized models raises questions about interpretability. We evaluate the performance of six variable selection procedures, includingthe recently proposed Boosting Multiple Testing (BMT) method, using an extensive dataset from six regional electricity markets. We assess their performance in terms of both out-of-sample forecasting ac-curacy and model parsimony. We find that, although LASSO and Elastic Net achieve similar accuracy and outperform most screening alternatives, BMT matches their forecasting performance while using less than one-tenth as many variables. Our results reveal that BMT offers researchers and practitioners a substantially more interpretable and computationally efficient alternative to shrinkage methods, without any loss of forecasting accuracy. These findings suggest that the over-parameterization typically associated with regularization methods is not a necessary price for predictive accuracy in electricity price forecasting.

econ.EM

Estimating non-linear functionals of trawl processes

Trawl processes are a family of continuous-time, infinitely divisible, stationary processes whose correlation structure is entirely characterized by their so-called trawl function. This paper investigates the problem of estimating non-linear functionals of a trawl function under in-fill and long-span sampling schemes. Specifically, building on the work of \cite{SauriVeraart23}, we introduce non-parametric estimators for functionals of the type $Ψ_{t}(g)=\int_{0}^{t}g(a(s))\mathrm{d}s$ and $ Λ_t(g)=\int_{t}^{\infty}g(a(s))\mathrm{d}s$, where $a$ represents the trawl function of interest and $g$ a non-linear test function. We show that our estimator for $Ψ_{t}(g)$ is consistent and asymptotically Gaussian regardless of the memory of the process. We further demonstrate that the same phenomenon occurs for the estimation of $Λ_t(g)$ as long as $g(x)= \mathrm{O} (\lvert x\rvert^p)$, as $x\to0$, for some $p>3$. Additionally, we illustrate how our results can be used to construct a test statistic robust to memory effects for the presence of $T$-dependent.

math.PR

Nonparametric estimation of trawl processes: Theory and applications

Trawl processes belong to the class of continuous-time, strictly stationary, infinitely divisible processes; they are defined as Levy bases evaluated over deterministic trawl sets. This article presents the first nonparametric estimator of the trawl function characterising the trawl set and the serial correlation of the process. Moreover, it establishes a detailed asymptotic theory for the proposed estimator, including a law of large numbers and a central limit theorem for various asymptotic relations between an in-fill and a long-span asymptotic regime. In addition, it develops consistent estimators for both the asymptotic bias and variance, which are subsequently used for establishing feasible central limit theorems which can be applied to data. A simulation study shows the good finite sample performance of the proposed estimators. The new methodology is applied to model misspecification testing, forecasting high-frequency financial spread data from a limit order book and to estimating the busy-time distribution of a stochastic queue.

math.ST

Path properties of Lévy driven mixed moving average processes

We derive general sufficient conditions for the existence of càdlàg and continuous modifications of Lévy-driven mixed moving average processes. The conditions are explicit and easy to verify and applied to supOU, well-balanced supOU, trawl, and power-weighted supOU processes. In these examples, the conditions are shown to be close to optimal.

math.PR

The Euler Scheme for Fractional Stochastic Delay Differential Equations with Additive Noise

In this paper we consider the Euler-Maruyama scheme for a class ofstochastic delay differential equations driven by a fractional Brownian motion with index $H\in(0,1)$. We establish the consistency of the scheme and study the rate of convergence of the normalized error process. This is done by checking that the generic rate of convergence of the error process with stepsize $Δ_{n}$ is $Δ_{n}^{\min\{H+\frac{1}{2},3H,1\}}$. It turned out that such a rate is suboptimal when the delay is smooth and $H>1/2$. In this context, and in contrast to the non-delayed framework, we show that a convergence of order $H+1/2$ is achievable.

math.PR

Local Limit Theorems for Energy Fluxes of Infinite Divisible Random Fields

We study the local asymptotic behavior of divergence-like functionals of a family of $d$-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of fields when the region of integration shrinks to a single point. We show that in most cases, convergence stably in distribution holds after a proper normalization. Furthermore, the limit random fields can be described in terms of stochastic integrals with respect to a Lévy basis. We additionally discuss how our results can be used to measure the kinetic energy of a possibly turbulent flow.

math.PR

Limit Theorems for Trawl Processes

In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{iΔ_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as $n\uparrow\infty$, $Δ_{n}\downarrow0$ and $nΔ_{n}\rightarrowμ\in[0,+\infty]$. Second, we derive a functional limit theorem for trawl processes as the Lévy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.

math.PR

Invertibility of infinitely divisible continuous-time moving average processes

This paper studies the invertibility property of continuous time moving average processes driven by a Lévy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel involved and the characteristic triplet of the background driving Lévy process.

math.PR

On the Divergence and Vorticity of Vector Ambit Fields

This paper studies the asymptotic behavior of the flux and circulation of a subclass of random fields within the family of 2-dimensional vector ambit fields. We show that, under proper normalization, the flux and the circulation converge stably in distribution to certain stationary random fields that are defined as line integrals of a Lévy basis. A full description of the rates of convergence and the limiting fields is given in terms of the roughness of the background driving Lévy basis and the geometry of the ambit set involved. We further discuss the connection of our results with the classical Divergence and Vorticity Theorems. Finally, we introduce a class of models that are capable to reflect stationarity, isotropy and null divergence as key properties.

math.PR

Brownian semistationary processes and related processes

In this paper we find a pathwise decomposition of a certain class of Brownian semistationary processes ($\mathcal{BSS}$) in terms of fractional Brownian motions. To do this, we specialize in the case when the kernel of the $\mathcal{BSS}$ is given by $φ_α\left(x\right)=L\left(x\right)x^α$ with $α\in(-1/2,0)\cup(0,1/2)$ and $L$ a continuous function slowly varying at zero. We use this decomposition to study some path properties and derive Itô's formula for this subclass of $\mathcal{BSS}$ processes.

math.PR

On the class of distributions of subordinated Lévy processes

This article study the class of distributions obtained by subordinating Lévy processes and Lévy bases. To do this we derive properties of a suitable mapping obtained via Lévy mixing. We show that our results can be used to solve the so-called recovery problem for general Lévy bases as well as for moving average processes which are driven by subordinated Lévy processes.

math.PR

Selfdecomposable Fields

In the present paper we study selfdecomposability of random fields, as defined directly rather than in terms of finite-dimensional distributions. The main tools in our analysis are the master Lévy measure and the associated Lévy-Itô representation. We give the dilation criterion for selfdecomposability analogous to the classical one. Next, we give necessary and sufficient conditions (in terms of the kernel functions) for a Volterra field driven by a Lévy basis to be selfdecomposable. In this context we also study the so-called Urbanik classes of random fields. We follow this with the study of existence and selfdecomposability of integrated Volterra fields. Finally, we introduce infinitely divisible field-valued Lévy processes, give the Lévy-Itô representation associated with them and study stochastic integration with respect to such processes. We provide examples in the form of Lévy semistationary processes with a Gamma kernel and Ornstein-Uhlenbeck processes.

math.PR