We investigate the behavior of the Shanghai Stock Exchange Composite (SSEC) index for the period from 1990:12 to 2007:06 using an unconstrained two-regime threshold autoregressive (TAR) model with an unit root developed by Caner and Hansen. The method allows us to simultaneously consider non-stationarity and nonlineari…
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48 results for “unit root processes”
Polynomials' roots count tied to surface umbilics.
problem Relating roots of polynomials to umbilics on surfaces.
method Constructing a convex surface from a polynomial, determining umbilic index, and applying Hamburger's bound.
result Bounding the number of roots inside the unit circle for polynomials with self-inversive second derivatives.
New proof for symmetric spaces with rectangular lattices.
problem Characterizing symmetric spaces with rectangular unit lattices.
method Explicit construction of isometric embeddings and analysis of root systems.
result Symmetric spaces with rectangular unit lattices are symmetric R-spaces.
Study on Jones polynomials and their roots in the unit circle and complex plane.
problem Understanding the roots of Jones polynomials for knots and links.
method Analyzing solutions of the equation for double-twist knots and links.
result The set of solutions to is dense in the unit circle and complex plane.
Study tail risk in high-frequency finance using -regularized regression.
problem Measuring tail risk dynamics in high-frequency financial markets.
method Dynamic extreme value regression model with -regularized maximum likelihood estimator.
result Severity of extreme losses well predicted by low price impact in high volatility periods.
This study applies old and new generations of panel unit root tests to test the validity of long-run real interest rate parity (RIP) hypothesis for ten Central and Eastern European Countries (CEECs) with respect to the Euro area and an average of the CEECs' real interest rates, respectively. When the panel unit root te…
Novel approach integrates Multivariate Square-root Lasso into Synthetic Control for high-dimensional data.
problem Challenges in practical implementation and computational efficiency of Synthetic Control method for high-dimensional disaggregated data.
method Integrates Multivariate Square-root Lasso into Synthetic Control framework.
result Demonstrates superior computational efficiency without compromising estimation accuracy.
To each unit complex number with positive imaginary part there is defined a Tristram-Levine knot signature function. The set of all such signature functions is linearly independent as a set of functions defined on the set of all knots. The set of averaged signature functions forms a linearly independent set of homomoro…
A new method simulates square-root processes efficiently.
problem Simulating square-root processes accurately and efficiently.
method Simulate the integrated square-root process instead of the square-root process itself.
result High precision with low number of time steps, and exact limiting Inverse Gaussian distributions.
The signature function of a knot is a locally constant integer valued function with domain the unit circle. The jumps (i.e., the discontinuities) of the signature function can occur only at the roots of the Alexander polynomial on the unit circle. The latter are important in deforming U(1) representations of knot group…
Hikami observed a discontinuity in a WRT invariant at roots of unity.
problem Discontinuity of a WRT invariant at roots of unity.
method Using Bailey's lemma and false theta functions.
result Generalized Hikami's observation about the discontinuity.
We study a natural Lie algebra structure on the free vector space generated by all rooted planar trees as the associated Lie algebra of the nonsymmetric operad (non- operad, preoperad) of rooted planar trees. We determine whether the Lie algebra and some related Lie algebras are finitely generated or not, and prove …
The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.
problem Investigating the roots of Alexander polynomials of random positive 3-strand braids.
method Experimental data analysis, conjectures refinement, and proof of results using tools like the signature function of links and Lyapunov exponent of the Burau representation.
result Generically, at least 69% of the roots of Alexander polynomials are on the unit circle, with a large root-free region near the origin.
We present a self-consistent model for explosive financial bubbles, which combines a mean-reverting volatility process and a stochastic conditional return which reflects nonlinear positive feedbacks and continuous updates of the investors' beliefs and sentiments. The conditional expected returns exhibit faster-than-exp…
The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.
problem Non-uniqueness of limiting distributions in the Volterra square-root process.
method Establishing existence of limiting distributions using integrability of the Volterra convolution kernel and exponential-affine transformation.
result The limiting distributions of the Volterra square-root process depend on the initial state and belong to weighted Besov spaces.
In January 3, 2009, Satoshi Nakamoto gave rise to the "Bitcoin Block Chain" creating the first block of the chain hashing on his computers central processing unit (CPU). Since then, the hash calculations to mine Bitcoin have been getting more and more complex, and consequently the mining hardware evolved to adapt to th…
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective parameter. The residuals of the linear ARCH process are computed using historical data …
Boosted HP filter improves trend estimation in economic data.
problem Inadequate HP filter settings for trend estimation in economic data.
method Iterating the HP smoother to improve trend estimation and eliminate trends.
result Asymptotic recovery of trend mechanisms involving unit root processes and polynomial drifts.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
New deep architecture improves head motion prediction in 360° videos.
problem Predicting user head motion in 360-degree videos using past positions and video content.
method Re-examined existing deep-learning approaches, identified flaws, and designed a new TRACK architecture.
result TRACK achieves state-of-the-art performance, outperforming competitors by up to 20 percent.
Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.
problem High-dimensional predictive regression with many predictors and unit roots.
method LASSO with new probabilistic bounds for consistency.
result LASSO maintains its asymptotic guarantee with standardized predictors and improves forecasting of unemployment.
The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Usi…
Develops a new Gaussian process method for efficient Bayesian inference of plant root parameters in the Richards equation.
problem Estimating unknown parameters in nonlinear PDEs for agricultural studies.
method Gaussian process collocation with importance sampling and Bayesian optimization.
result Our method yields robust estimates with uncertainty quantification for plant root parameters.
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.
Root Cause Analysis in Lithium-Ion Battery Production with FMEA-Based Large-Scale Bayesian Networkstat.AP
New method combines FMEA and Bayesian Network for root cause analysis in lithium-ion battery production.
problem Complex cause-effect relationships in lithium-ion battery production.
method Combining FMEA with Bayesian Network to detect and resolve inconsistencies.
result Holistic method builds large-scale cross-process Bayesian Failure Network for root cause analysis.
Method identifies root causes of anomalies in causal processes.
problem Identifying root causes of anomalies in causal processes.
method Noisy functional causal model, Bayesian learning, gradient-based attribution.
result Proposes efficient method to compute anomaly attribution scores.
Volterra square-root process boundary behavior and martingale measures
problem Boundary behavior of the Volterra square-root process
method Comparison principles for Volterra integral equations and generalized Riemann-Liouville fractional equations
result Finiteness of negative -moments and atom at the boundary for rough kernels
In this paper we propose and investigate a novel nonlinear unit, called unit, for deep neural networks. The proposed unit receives signals from several projections of a subset of units in the layer below and computes a normalized norm. We notice two interesting interpretations of the unit. First…
Integration I(d) of Nonstationary Time Series: Stationary and nonstationary incrementsphysics.soc-ph
The method of cointegration in regression analysis is based on an assumption of stationary increments. Stationary increments with fixed time lag are called integration I(d). A class of regression models where cointegration works was identified by Granger and yields the ergodic behavior required for equilibrium expectat…
We prove that every homomorphism from the elementary Chevalley group over a finitely generated unital commutative ring associated with reduced irreducible classical root system of rank at least 2, and ME analogues of such groups, into acylindrically hyperbolic groups has an absolutely elliptic image. This result provid…
Efficiently computes matrix square roots and their inverses for large matrices.
problem Computing matrix square roots and inverses for large matrices efficiently.
method Combines Krylov subspace methods with rational approximation for quadratic-time computation.
result Achieves 4 decimal places of accuracy with fewer than 100 matrix-vector multiplications.
This paper presents a general framework for norm-based capacity control for weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an normalization where , and , we discuss properties of a width-independent ca…
The paper proposes a method to identify root causes of anomalies in time series data.
problem Challenges in identifying the root cause of anomalies in complex software systems.
method Analyzes time series fluctuations to track the propagation of effects through hidden states.
result Identifies causal patterns among observed fluctuations to isolate root causes.
Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Marketsq-fin.CP
Agent-based market shows herding cycles with square-root price impact.
problem Understanding herding cycles in agent-based markets.
method Agent-based model with 20,000 retail traders interacting with a single institutional agent.
result Agent discovers multi-cycle predatory strategy with 8-11 complete cycles over 2000 trading days.
Researchers create a teapot model for Mandelbrot set, proving connectedness.
problem Understanding the connectedness of the outside part of the Mandelbrot set.
method Defined a 'Master teapot' model and generalized kneading theory for principal veins.
result Outside part of the 'Thurston set' is path connected.
RAID algorithm detects anomalies in real-time IoT systems.
problem Anomaly detection limitations in multivariate dynamic processes.
method Adapts to non-stationary effects and handles data drift.
result Improved detection accuracy and root cause isolation.
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the independent components one after another. A novel method for deflationary ICA, referr…
TSFMs embed non-stationary time series data, revealing specific types of changes.
problem Understanding non-stationarity in TSFMs' embedding spaces.
method Examined mean shifts, variance changes, linear trends, and persistence in TSFMs.
result Different TSFMs exhibit distinct failure modes in detecting non-stationarity.
The study counts units and eigenvalue patterns in SL_n(Z) and Sp_{2n}(Z) in thin tubes.
problem Counting totally real units and eigenvalue patterns in SL_n(Z) and Sp_{2n}(Z) in thin tubes.
method Analyzes directional entropy of logarithmic embeddings and eigenvalue data in thin tubes around rays.
result The number of objects grows exponentially with the directional entropy, providing bounds for conjugacy classes.
The paper proposes a new probability distribution for rooted trees.
problem Overfitting in tree selection for statistical models.
method Bayesian approach with a generalized probability distribution for rooted trees.
result Recursive methods to evaluate the probability distribution without approximations.
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time…
Study examines dependence properties of Bayesian neural network units in finite-width networks.
problem Understanding dependence properties of hidden units in practical finite-width Bayesian neural networks.
method Theoretical analysis and empirical evaluation of depth and width impacts.
result Hidden units in finite-width Bayesian neural networks are dependent, contrary to the infinite-width limit assumption.
Given an element of the Bloch group of a number field~ and a natural number~, we construct an explicit unit in the field , well-defined up to $\nn$-th powers of nonzero elements of~. The construction uses the cyclic quantum dilogarithm, and under the identification of the Bloch group of~$F…
The set consisting of all rotations of the Euclidean plane is equipped with a quandle structure. We show that a knot is colorable by this quandle if and only if its Alexander polynomial has a root on the unit circle in . Further we enumerate all non-trivial colorings of a torus knot diagram by the quandle u…
A new probability distribution on full rooted trees helps in model selection.
problem Model selection for full rooted trees is problematic due to their hierarchical structure.
method Assume a prior distribution on full rooted trees, using Bayes decision theory.
result The proposed distribution enables optimal model selection and prevents overfitting.
Method estimates noise variance in Gaussian process regression.
problem Estimating noise variance in Gaussian process regression models.
method Reduces hyperparameter space, uses marginal likelihood function, derives bounds and asymptotes.
result Computational advantages and robustness compared to traditional methods.
This paper tackles federated learning for automatic latent variable selection in multi-output Gaussian processes.
problem Challenges in determining the adequate number of latent processes and relying on centralized learning for privacy and computational issues.
method Proposes a hierarchical model with spike-and-slab priors for automatic latent process selection and variational inference-based federated learning algorithm.
result Demonstrates the advantageous features of the proposed federated approach through simulations and real-world data.
Simulating integrated Volterra square-root processes and Volterra Heston models via Inverse Gaussianq-fin.MF
A new simulation method for Volterra processes improves convergence for rough kernels.
problem Simulating Volterra processes with singular kernels.
method iVi (integrated Volterra implicit) scheme based on Inverse Gaussian distribution.
result The iVi scheme achieves weak convergence with few time steps, especially for rough kernels.