Real Time Analysis Based on Reproducing Kernel Henderson Filters

2021 ◽  
Vol 28 (3) ◽  
pp. 553-574
Author(s):  
Silvia Bianconcini ◽  
Benoit Quenneville
Keyword(s):  
Reproducing Kernel ◽  
Time Series Data ◽  
Reproducing Kernels ◽  
Series Data ◽  
Linear Filter ◽  
Nonparametric Estimators ◽  
Real Time Analysis ◽  
Bandwidth Parameter ◽  
Starting Point ◽  
Kernel Hilbert Spaces

Recently, reproducing kernel Hilbert spaces have been introduced to provide a common approach for studying several nonparametric estimators used for smoothing functional time series data (Dagum and Bianconcini, 2006 and 2008). The reproducing kernel representation is based on the derivation of the density function (i.e. a second order kernel) embedded on the linear filter. This is the starting point for deriving higher order kernels, which are obtained from the product of the density and its orthonormal polynomials. This paper focuses on the Henderson filter, for which two density functions and corresponding hierarchies have been derived. The properties of the Henderson reproducing kernels are analyzed when the filters are adapted at the end of the sample period. The optimality criterion satisfied as well as the influence of the kernel order and bandwidth parameter are studied.

scholarly journals On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces

2017 ◽  
Vol 69 (1) ◽  
pp. 54-106 ◽  
Author(s):  
Michael Hartz
Keyword(s):  
Hilbert Spaces ◽  
Special Class ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Isomorphism Problem ◽  
Reproducing Kernel Hilbert Spaces ◽  
Universal Space ◽  
Kernel Hilbert Spaces ◽  
Arveson Space ◽  
Multiplier Algebras

AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.

scholarly journals ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350014 ◽  
Author(s):  
HAIZHANG ZHANG ◽  
LIANG ZHAO
Keyword(s):  
Applied Sciences ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Reproducing Kernel Hilbert Spaces ◽  
Inclusion Relation ◽  
Feature Maps ◽  
Translation Invariant ◽  
Inclusion Relations ◽  
Kernel Hilbert Spaces

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert–Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.

scholarly journals Blazhko effect in Cepheids and RR Lyrae stars

2013 ◽  
Vol 9 (S301) ◽  
pp. 241-248
Author(s):  
Róbert Szabó
Keyword(s):  
Time Series Data ◽  
Period Doubling ◽  
High Order ◽  
Series Data ◽  
Theoretical Point ◽  
Rr Lyrae Stars ◽  
Rr Lyrae ◽  
Starting Point ◽  
Blazhko Effect ◽  
Lyrae Stars

AbstractThe Blazhko effect is the conspicuous amplitude and phase modulation of the pulsation of RR Lyrae stars that was discovered in the early 20th century. The field of study of this mysterious modulation has recently been invigorated thanks to the space photometric missions providing long, uninterrupted, ultra-precise time-series data. In this paper I give a brief overview of the new observational findings related to the Blazhko effect, such as extreme modulations, irregular modulation cycles and additional periodicities. I argue that these findings together with dedicated ground-based efforts provide us now with a fairly complete picture and a good starting point to theoretical investigations. Indeed, new, unpredicted dynamical phenomena have been discovered in Blazhko RR Lyrae stars, such as period doubling, high-order resonances, three-mode pulsation and low-dimensional chaos. These led to the proposal of a new explanation to this century-old enigma, namely a high-order resonance between radial modes. Along these lines I present the latest efforts and advances from the theoretical point of view. Lastly, amplitude variations in Cepheids are discussed.

scholarly journals General construction of reproducing kernels on a quaternionic Hilbert space

2017 ◽  
Vol 29 (05) ◽  
pp. 1750017
Author(s):  
K. Thirulogasanthar ◽  
S. Twareque Ali
Keyword(s):  
Hilbert Space ◽  
Positive Operator ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Extension Theorem ◽  
Reproducing Kernels ◽  
Reproducing Kernel Hilbert Spaces ◽  
Positive Operator Valued Measures ◽  
Kernel Hilbert Spaces ◽  
Quaternionic Hilbert Space

A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator-valued measures and their connection to a class of generalized quaternionic coherent states are examined. A Naimark type extension theorem associated with the positive operator-valued measures is proved in a right quaternionic Hilbert space. As illustrative examples, real, complex and quaternionic reproducing kernels and reproducing kernel Hilbert spaces arising from Hermite and Laguerre polynomials are presented. In particular, in the Laguerre case, the Naimark type extension theorem on the associated quaternionic Hilbert space is indicated.

scholarly journals Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression

1985 ◽  
Vol 1 (1) ◽  
pp. 27-52 ◽  
Author(s):  
Radhey S. Singh ◽  
Aman Ullah
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Vector Autoregression ◽  
Series Data ◽  
Mixing Conditions ◽  
Conditional Mean ◽  
Nonparametric Estimators ◽  
Time Series Estimation ◽  
Series Estimation ◽  
Data Generating Process

In this paper we develop nonparametric estimators of the joint time series data generating process (DGP) of (xt,yt) at differentt-values, of conditional DGP, of the conditional mean ofxtgiven the past values ofxandy, and, more generally, the conditional mean of (xt,yt) given their past values (vector autoregression). We establish, among other results, the central limit theorems for these estimators under far weaker mixing conditions than those used in Robinson [23], where only thextseries is considered. Uniform consistency and rate results for the consistencies of various estimators are also obtained. The results of the paper are useful in light of the fact that often the functional form of the dynamic regression is not known and also the assumption of the Gaussian process is not true.

scholarly journals Reproducing Kernel Hilbert Space Associated with a Unitary Representation of a Groupoid

2021 ◽  
Vol 15 (5) ◽  
Author(s):  
Monika Drewnik ◽  
Tomasz Miller ◽  
Zbigniew Pasternak-Winiarski
Keyword(s):  
Unitary Representation ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Reproducing Kernels ◽  
Positive Definite ◽  
Reproducing Kernel Hilbert Spaces ◽  
Locally Compact Group ◽  
Positive Definite Kernel ◽  
Kernel Hilbert Spaces

AbstractThe aim of the paper is to create a link between the theory of reproducing kernel Hilbert spaces (RKHS) and the notion of a unitary representation of a group or of a groupoid. More specifically, it is demonstrated on one hand how to construct a positive definite kernel and an RKHS for a given unitary representation of a group(oid), and on the other hand how to retrieve the unitary representation of a group or a groupoid from a positive definite kernel defined on that group(oid) with the help of the Moore–Aronszajn theorem. The kernel constructed from the group(oid) representation is inspired by the kernel defined in terms of the convolution of functions on a locally compact group. Several illustrative examples of reproducing kernels related with unitary representations of groupoids are discussed in detail. The paper is concluded with the brief overview of the possible applications of the proposed constructions.

Real-time analysis and management of big time-series data

2013 ◽  
Vol 57 (3/4) ◽  
pp. 8:1-8:12 ◽  
Author(s):  
A. Biem ◽  
H. Feng ◽  
A. V. Riabov ◽  
D. S. Turaga
Keyword(s):  
Time Series ◽  
Real Time ◽  
Time Series Data ◽  
Series Data ◽  
Time Analysis ◽  
Real Time Analysis

scholarly journals Error in hydraulic head and gradient time-series measurements: a quantitative appraisal

2019 ◽  
Vol 23 (9) ◽  
pp. 3603-3629 ◽  
Author(s):  
Gabriel C. Rau ◽  
Vincent E. A. Post ◽  
Margaret Shanafield ◽  
Torsten Krekeler ◽  
Eddie W. Banks ◽  
...  
Keyword(s):  
Time Series ◽  
Water Level ◽  
Measurement Errors ◽  
Time Series Data ◽  
Measurement Techniques ◽  
Hydraulic Head ◽  
Series Data ◽  
Sufficient Information ◽  
Regional Flow ◽  
Starting Point

Abstract. Hydraulic head and gradient measurements underpin practically all investigations in hydrogeology. There is sufficient information in the literature to suggest that head measurement errors can impede the reliable detection of flow directions and significantly increase the uncertainty of groundwater flow rate calculations. Yet educational textbooks contain limited content regarding measurement techniques, and studies rarely report on measurement errors. The objective of our study is to review currently accepted standard operating procedures in hydrological research and to determine the smallest head gradients that can be resolved. To this aim, we first systematically investigate the systematic and random measurement errors involved in collecting time-series information on hydraulic head at a given location: (1) geospatial position, (2) point of head, (3) depth to water, and (4) water level time series. Then, by propagating the random errors, we find that with current standard practice, horizontal head gradients <10-4 are resolvable at distances ⪆170 m. Further, it takes extraordinary effort to measure hydraulic head gradients <10-3 over distances <10 m. In reality, accuracy will be worse than our theoretical estimates because of the many possible systematic errors. Regional flow on a scale of kilometres or more can be inferred with current best-practice methods, but processes such as vertical flow within an aquifer cannot be determined until more accurate and precise measurement methods are developed. Finally, we offer a concise set of recommendations for water level, hydraulic head and gradient time-series measurements. We anticipate that our work contributes to progressing the quality of head time-series data in the hydrogeological sciences and provides a starting point for the development of universal measurement protocols for water level data collection.

scholarly journals Reproducing kernel Hilbert spaces on manifolds: Sobolev and diffusion spaces

2020 ◽  
pp. 1-34
Author(s):  
Ernesto De Vito ◽  
Nicole Mücke ◽  
Lorenzo Rosasco
Keyword(s):  
Sobolev Spaces ◽  
Riemannian Manifolds ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Differential Operators ◽  
Reproducing Kernels ◽  
Reproducing Kernel Hilbert Spaces ◽  
Kernel Hilbert Spaces ◽  
Euclidean Setting ◽  
And Diffusion

We study reproducing kernel Hilbert spaces (RKHS) on a Riemannian manifold. In particular, we discuss under which condition Sobolev spaces are RKHS and characterize their reproducing kernels. Further, we introduce and discuss a class of smoother RKHS that we call diffusion spaces. We illustrate the general results with a number of detailed examples. While connections between Sobolev spaces, differential operators and RKHS are well known in the Euclidean setting, here we present a self-contained study of analogous connections for Riemannian manifolds. By collecting a number of results in unified a way, we think our study can be useful for researchers interested in the topic.

scholarly journals Using person-specific networks in psychotherapy: challenges, limitations, and how we could use them anyway

BMC Medicine ◽  
2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Lino von Klipstein ◽  
Harriëtte Riese ◽  
Date C. van der Veen ◽  
Michelle N. Servaas ◽  
Robert A. Schoevers
Keyword(s):  
Time Series Data ◽  
Series Data ◽  
Case Conceptualization ◽  
Symptom Profiles ◽  
Starting Point ◽  
Context Variables ◽  
Consistent Manner ◽  
Collaborative Exploration ◽  
Insight Into

Abstract Background The complexity of psychopathology is evident from its multifactorial etiology and diversity of symptom profiles and hampers effective treatment. In psychotherapy, therapists approach this complexity by using case conceptualization. During this process, patients and therapists closely collaborate on a personalized working theory of the patient’s psychopathology. This is a challenging process and shows low reliability between therapists. With the experience sampling method (ESM), time-series data—valuable for case conceptualization—can be systematically gathered in a patient’s normal daily life. These data can be analyzed and visualized in person-specific networks (PSNs). PSNs may support case conceptualization by providing a schematic representation of association patterns between affective, cognitive, behavioral, and context variables. Main text We adopt a clinical perspective in considering how PSNs might be implemented to serve case conceptualization and what their role could be in psychotherapy. We suggest PSNs to be based on personalized ESM assessment to capture the unique constellation of variables in each patient. We reflect on the lack of a gold standard for creating PSNs, which may result in substantially different PSNs and thereby disparate information for case conceptualization. Moreover, even if PSNs are created in a consistent manner, results remain ambiguous as they are subject to multiple interpretations. Therefore, associations in PSNs do not allow for firm conclusions about a patient’s psychopathology, but they may nevertheless be valuable in the process of case conceptualization. PSNs are based on systematically gathered, ecologically valid ESM data and provide a unique personalized perspective. When used responsibly, PSNs may be able to support case conceptualization by generating questions that serve as a starting point for a dialog between therapists and patients. Well-targeted questions are an essential tool for therapists to gain insight into the patients’ psychopathology patterns and improve the quality of case conceptualization. Conclusions PSNs have limitations in terms of the reliability of the insights they provide directly. However, taking these challenges into account, we believe they have potential as a tool to help therapists and patients in their collaborative exploration of a patient’s psychopathology. Clearly, this would need to be validated in future clinical research.

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