Presence Of Smooth Research Articles

NHITS: Neural Hierarchical Interpolation for Time Series Forecasting

Recent progress in neural forecasting accelerated improvements in the performance of large-scale forecasting systems. Yet, long-horizon forecasting remains a very difficult task. Two common challenges afflicting the task are the volatility of the predictions and their computational complexity. We introduce NHITS, a model which addresses both challenges by incorporating novel hierarchical interpolation and multi-rate data sampling techniques. These techniques enable the proposed method to assemble its predictions sequentially, emphasizing components with different frequencies and scales while decomposing the input signal and synthesizing the forecast. We prove that the hierarchical interpolation technique can efficiently approximate arbitrarily long horizons in the presence of smoothness. Additionally, we conduct extensive large-scale dataset experiments from the long-horizon forecasting literature, demonstrating the advantages of our method over the state-of-the-art methods, where NHITS provides an average accuracy improvement of almost 20% over the latest Transformer architectures while reducing the computation time by an order of magnitude (50 times). Our code is available at https://github.com/Nixtla/neuralforecast.

Sparsely observed functional time series: estimation and prediction

Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, as is often the case with independent functional data, it may well happen that the data available to the analyst are not the actual sequence of curves, but relatively few and noisy measurements per curve, potentially at different locations in each curve's domain. Under this sparse sampling regime, neither the established estimators of the time series' dynamics, nor their corresponding theoretical analysis will apply. The subject of this paper is to tackle the problem of estimating the dynamics and of recovering the latent process of smooth curves in the sparse regime. Assuming smoothness of the latent curves, we construct a consistent nonparametric estimator of the series' spectral density operator and use it develop a frequency-domain recovery approach, that predicts the latent curve at a given time by borrowing strength from the (estimated) dynamic correlations in the series across time. Further to predicting the latent curves from their noisy point samples, the method fills in gaps in the sequence (curves nowhere sampled), denoises the data, and serves as a basis for forecasting. Means of providing corresponding confidence bands are also investigated. A simulation study interestingly suggests that sparse observation for a longer time period, may be provide better performance than dense observation for a shorter period, in the presence of smoothness. The methodology is further illustrated by application to an environmental data set on fair-weather atmospheric electricity, which naturally leads to a sparse functional time-series.

Approximations by multivariate sublinear and Max-product operators under convexity

Abstract Here we search quantitatively under convexity the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate Max-product operators. These are of Bernstein type, of Favard-Szász-Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite-Fejér interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated which fulfills a convexity assumption.

Approximation by multivariate sublinear and max-product operators

Here we study quantitatively the approximation of multivariate function by general multivariate positive sublinear operators with applications to multivariate max-product operators. These are of Bernstein type, of Favard–Szasz–Mirakjan type, of Baskakov type, of sampling type, of Lagrange interpolation type and of Hermite–Fejer interpolation type. Our results are both: under the presence of smoothness and without any smoothness assumption on the function to be approximated.

A second-order globally convergent direct-search method and its worst-case complexity

Direct-search algorithms form one of the main classes of algorithms for smooth unconstrained derivative-free optimization, due to their simplicity and their well-established convergence results. They proceed by iteratively looking for improvement along some vectors or directions. In the presence of smoothness, first-order global convergence comes from the ability of the vectors to approximate the steepest descent direction, which can be quantified by a first-order criticality (cosine) measure. The use of a set of vectors with a positive cosine measure together with the imposition of a sufficient decrease condition to accept new iterates leads to a convergence result as well as a worst-case complexity bound. In this paper, we present a second-order study of a general class of direct-search methods. We start by proving a weak second-order convergence result related to a criticality measure defined along the directions used throughout the iterations. Extensions of this result to obtain a true second-order optimality one are discussed, one possibility being a method using approximate Hessian eigenvectors as directions (which is proved to be truly second-order globally convergent). Numerically guaranteeing such a convergence can be rather expensive to ensure, as it is indicated by the worst-case complexity analysis provided in this paper, but turns out to be appropriate for some pathological examples.

Nonlinearity and smoothing in venture capital performance data

Abstract Performance indices for illiquid investments are known to suffer from returns smoothing, and the purpose of this paper is to investigate the presence and nature of such smoothing in the context of venture capital. We find that while the standard techniques may or may not indicate the presence of smoothing, significant evidence of smoothing exists when a nonlinear regime-dependent model is specified. Further, the model suggests the presence of regime-specific responsiveness of venture capital returns whereby different weights are placed on newly arrived information in different regimes.

The Effects of Integration Intervals on Recursive RMS Value and Power Measurement in Nonsinusoidal Conditions

The effects of integration intervals on recursive rms value and power measurement in the presence of nonsinusoidal conditions are considered. The presence of time measurement intervals of both fixed and variable durations is assumed. Suitable formulas to evaluate the errors introduced by the desynchronization of measurement interval for active and apparent powers, power factor, and voltage and current rms values are developed; formulas accounting the contributions to the error of the cross products between couples of components at different frequencies are also developed. Then, the errors are evaluated in the presence of smoothing of the results over a variable number of consecutive measurements by means of proper formulas. Some numerical and experimental case studies conclude the analysis showing the effects of the different contributions to the error and the improvements of accuracy that can be obtained by smoothing the results.

How important is that footnote on page 3?

PurposeThe failure of the efficient market hypothesis has a direct bearing on the Geometric Brownian Motion model of asset returns. The current paper aims to investigate the effect that the autocorrelation in the time‐series of returns has on the calculation of expected shortfall (ES) for an asset‐liability investor.Design/methodology/approachThe regression model is selected according to the Akaike and the Schwarz information criterion. A series of tests are used to insure the stability of the autocorrelation parameters. Autocorrelation‐adjusted formulas for volatility and cross‐asset correlations are then employed for the computations.FindingsThe presence of autocorrelation changes the values of most of the correlation parameters used in the calculation of the ES of the risk bearing capital (RBC) – in some cases the cross‐asset correlation parameters double. Once the presence of smoothing is accounted for, the ES increases by 1 per cent in relative value.Research limitations/implicationsOther asset classes may also feature smoothed time‐series requiring thus an account of their autocorrelation structure and their interaction with the property asset. An analysis of the time stability of the cross‐asset correlations may also improve the estimation of the optimal RBC.Originality/valueThe proposed method focuses on the proper calculation of the RBC through the judicious estimation of the relevant risk measure for an investor who, while not having access to the underlying data pool from which the property index is computed, cannot adjust the index for the potential presence of temporal aggregation and market illiquidity.

Nonaxisymmetric cool spot distributions and dynamo action in close binaries

We investigate the nonaxisymmetric magnetic field distribution in the components of close binary systems, gen- erated by a stellar dynamo with a nonaxisymmetric distribution of the-coecient, proportional to the mean helicity of the convective motions in the stellar convective envelope. The nonaxisymmetry of is assumed to be connected with interaction with the binary companion, i.e. the reflection eect and tidal interaction. The degree of asymmetry is estimated from the known parameters of ER Vulpeculae, an active RS CVn-type star. We demonstrate that the synchronization of rotation and orbital motion of ER Vulpeculae due to tidal interaction is sucient to allow nonaxisymmetric magnetic structures to survive in the presence of smoothing by dierential rotation. The dynamo driven nonaxisymmetric magnetic structures are usually steady in the reference frame connected with the-spot. However, we found a resonant excitation of an oscillatory, strongly nonaxisym- metric, configuration, driven by the joint action of the-eect and dierential rotation. The magnetic structures obtained are predominantly manifested on the stellar surface in the form of spots of radial magnetic field. Their form and size are similar to the form and size of cool spots observed on the surfaces of both components of ER Vulpeculae, and their displacements from the-spots are comparable to that of the observed cool spots from the hot spots connected with the reflection eect. Possible relevant observations are discussed.

Measurements of the effect of laser beam smoothing on direct-drive inertial-confinement-fusion capsule implosions.

We present measurements of the effect of various levels of laser beam smoothing on both burnthrough time and the neutron yield in layered, deuterium-filled imploding microballoons. Burnthrough times are found to improve as smoothing is increased. This effect is believed to result from a reduction in the seeding of the Rayleigh-Taylor (RT) instability with increasing smoothing. The results are in agreement with simulations that model the development of the RT instability from initial perturbation spectra inconsistent with measured changes in uniformity. The neutron yields are also observed to increase in the presence of smoothing, but are much less sensitive to uniformity changes than the burnthrough rates.

Periodic solutions to Hamiltonian inclusions

We prove the existence of periodic trajectories of Hamiltonian inclusions, which reduce to the usual Hamiltonian equations in the presence of smoothness. This is accomplished via a direct variational principle involving a new action integral in an extended sense.