We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is distribute…
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48 results for “time averages”
Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Optionsq-fin.PR
The time average of geometric Brownian motion plays a crucial role in the pricing of Asian options in mathematical finance. In this paper we consider the asymptotics of the discrete-time average of a geometric Brownian motion sampled on uniformly spaced times in the limit of a very large number of averaging time steps.…
The paper investigates length averages in foliations, contrasting with time averages in dynamical systems.
problem Investigate the existence and non-existence of length averages in foliations.
method Generalize the existence problem of time averages in dynamical systems to foliations and introduce the concept of length averages.
result Length averages exist everywhere for codimension one orientable singular foliations without degenerate singularities on compact surfaces under a mild condition.
This paper improves forecasts for diverse time series by averaging similar ones.
problem Forecasting challenges in heterogeneous time series.
method Dynamic Time Warping to find similar time series, k-Nearest Neighbor averaging.
result Averaging improves forecasts of simple models.
Derives time-averaged active inference from control principles.
problem Finite-horizon or discounted-surprise problems in active inference.
method Derives infinite-horizon, average-surprise active inference from optimal control principles.
result Unified objective functional for sensorimotor control.
New moving average adapts weight dynamically based on polynomial and wavefunction.
problem Lagging traditional moving averages in adjusting to changes in data.
method Develops a moving average with weight as a polynomial of a wavefunction from an eigenproblem.
result Immediate 'switch' without lag, adapting to changes in data.
Study confirms the Epps effect using different volume time averaging methods for JSE stocks.
problem Demonstrating the Epps effect in stock market data using various aggregation methods.
method Used two non-parametric covariance estimators (Malliavin and Mancino, Hayashi and Yoshida) and two volume time averaging methods (asset intrinsic and synchronised volume time).
result MM estimator more representative of trade time reality, confirming market phenomenology.
The study revisits inaccuracies in time series averaging under dynamic time warping.
problem Inaccuracies in time series averaging under dynamic time warping.
method Analysis of existing correctness-criterion and introduction of drift-outs, showing their insufficiency and inconclusiveness.
result Sample means as global minimizers of a Fréchet function never drift out, and the adjusted drift-out is a test for coherence.
New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…
Geometric Brownian motion (GBM) is a model for systems as varied as financial instruments and populations. The statistical properties of GBM are complicated by non-ergodicity, which can lead to ensemble averages exhibiting exponential growth while any individual trajectory collapses according to its time-average. A com…
Improved TD learning with tail averaging and regularization achieves optimal convergence rates.
problem Convergence analysis of TD learning with linear function approximation.
method Tail-averaging and regularization applied to TD learning algorithm.
result Achieves optimal convergence rate in expectation and with high probability.
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers v…
Proposes two techniques for efficient tail averaging in streams.
problem Efficiently averaging the last examples in a stream with low memory and constant access.
method Two techniques with low constant memory cost and access to average at every time step. Improved accuracy at higher memory cost.
result Proposes techniques for efficient tail averaging with constant memory and access at every time step.
New TD method stabilizes average-reward learning.
problem Stability issues in average-reward TD learning.
method Implicit fixed point update for average-reward TD().
result Improved numerical stability and broader step-size range.
Averaging recent model checkpoints speeds up training time.
problem Training large vision or language models is time-consuming.
method Average the weights of the k latest checkpoints.
result Speeds up training by dozens of epochs, saving up to 68 GPU hours.
Logarithmic regret for continuous-time reinforcement learning.
problem Continuous-time Markov decision processes with unknown transition probabilities and holding times.
method Upper confidence reinforcement learning, mean holding time estimation, stochastic comparison of point processes.
result Logarithmic regret bound achieved in finite time.
Neural moving average model speeds up state space model inference for time series data.
problem Efficiently scaling approximate Bayesian inference for time series data.
method Proposes a novel generative model (neural moving average model) for latent temporal states in state space models.
result Achieves accurate parameter estimation in a short time for various models.
Halting Time is Predictable for Large Models: A Universality Property and Average-case Analysismath.OC
New analysis shows halting time is predictable for large models, improving optimization efficiency.
problem Understanding the average-case complexity of optimization algorithms for large-scale models.
method Average-case analysis of first-order methods on random least squares and neural networks.
result Halting time is independent of input distribution, leading to tighter convergence rates.
The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetim…
Enhances Fourier estimator performance for asynchronous event-data.
problem Improving correlation and covariance estimation on event-data.
method Implement and test NUFFT methods with different averaging kernels.
result Demonstrates improved performance and relationship between averaging scales.
Enhances UPSA to reduce noise in financial data.
problem Noise in financial data affects UPSA's performance.
method Time-averaging optimal penalty weights and using Average Oracle correlation eigenvalues.
result Combining time-averaging and Average Oracle correlation eigenvalues improves UPSA's performance.
Paper proposes a mean-field gradient descent for zero-sum games, proving convergence to Nash equilibrium.
problem Finding mixed Nash equilibria in zero-sum games with multiple players.
method Mean-field gradient descent dynamics with time-averaging, incorporating exponentially discounted gradients.
result Exponential convergence rate to mixed Nash equilibrium with respect to total variation metric.
The paper develops time-uniform inference methods for stochastic approximation parameters.
problem Statistical inference for parameters in stochastic approximation problems.
method Analysis of averaged iterates convergence rates and construction of asymptotic confidence sequences.
result Valid asymptotic confidence sequences for parameters in stochastic approximation problems.
Estimates returns for dollar cost averaging using geometric Brownian motion.
problem Estimating returns for dollar cost averaging investing strategy.
method Uses geometric Brownian motion and log-Normal distribution to construct a lower bound for returns. Computes parameters recursively and in closed form for dollar cost averaging. Compares to lump sum investing for matching wealth distributions.
result Probability of negative returns is less than 2.5% for 40 years of annual dollar cost averaging.
SWAP uses large mini-batches to train DNNs faster with good generalization.
problem Training deep neural networks with small mini-batches is time-consuming.
method SWAP computes an approximate solution with large mini-batches and refines it by averaging weights of multiple parallel models.
result SWAP trains models as well as small-batch training but in significantly less time.
In this thesis, we consider the suitability of using the charged cold fluid model in the description of ultra-relativistic beams. The method that we have used is the following. Firstly, the necessary notions of kinetic theory and differential geometry of second order differential equations are explained. Then an averag…
Group averaging boosts model accuracy without training cost.
problem Challenging training of equivariant models in physics.
method Group averaging at test time, improving accuracy.
result Improves model accuracy by up to 37% in continuous dynamics.
New streaming methods improve convergence rates for optimization problems.
problem Optimizing large-scale, sequential data problems.
method Time-varying mini-batches and Polyak-Ruppert averaging for gradient-based algorithms.
result Time-varying mini-batches and averaging achieve optimal convergence and variance reduction.
This study uses moving average cluster entropy to analyze financial market dynamics.
problem Understanding long-range dependence in financial markets.
method Moving average cluster entropy approach applied to ARFIMA and FBM processes.
result Long-range positive correlation in financial markets is linked to the cluster entropy behavior.
New algorithm for average reward learning with bounded hitting time assumption.
problem Minimizing regret in average reward reinforcement learning with bounded hitting time.
method Optimistic Q-learning with a novel operator for bounded hitting time.
result Regret bound of for average reward learning.
New approach shapes error distribution in long-term forecasting.
problem Disparate error distributions in recent transformer models.
method Loss shaping constraints to respect upper bounds on loss at each time-step.
result Competitive average performance with shaped error distribution.
The paper offers precise bounds for averaged LSA iterates in linear systems.
problem Computing approximate solutions of linear systems with noisy observations.
method Finite-time analysis of LSA algorithms with Polyak-Ruppert averaging.
result Sharp high-probability bounds for averaged LSA iterates.
The paper analyzes time-dependent streaming data with biased gradient estimates and proposes improved stochastic optimization methods.
problem Stochastic optimization in a streaming setting with time-dependent and biased gradient estimates.
method Analysis of several first-order methods including SGD, mini-batch SGD, and time-varying mini-batch SGD, along with their Polyak-Ruppert averages.
result Time-varying mini-batch SGD methods can break long- and short-range dependence structures, and biased SGD methods can achieve comparable performance to their unbiased counterparts.
New algorithms learn from expert demonstrations without needing a mixing time bound.
problem Existing algorithms for apprenticeship learning require an upper bound on mixing time.
method Builds on Markov chain theory to derive sampling algorithms without mixing time bounds.
result Provides theoretical bounds on sample-complexity and running time for new algorithms.
An average instantaneous cross-correlation function is introduced to quantify the interaction of the financial market of a specific time. Based on the daily data of the American and Chinese stock markets, memory effect of the average instantaneous cross-correlations is investigated over different price return time inte…
We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated group has the word problem solvable in subexponential time and has a subgroup of…
Automatically extracts features from time series data for improved forecasting.
problem Manual feature selection for time series forecasting is inefficient and prone to errors.
method Extracts features from time series using recurrence plots and computer vision algorithms.
result Automatically extracted features lead to highly comparable and sometimes superior forecasting performance.
Paper explores how combining tail-averaging and minibatching improves SGD convergence.
problem Understanding and optimizing learning properties of SGD variants.
method Least squares learning in a nonparametric setting, focusing on multiple passes, mini-batching, and averaging.
result Tail averaging allows faster convergence rates than uniform averaging in nonparametric settings.
A Lagrangian perspective on nonautonomous advection-diffusion processes in the low-diffusivity limitmath.AP
Study mass transport in low-diffusivity using Lagrangian coordinates.
problem Mass preserving transport of passive tracers in low-diffusivity limit.
method Lagrangian coordinates, time-averaged diffusion equation, weighted manifold structure.
result Leading order asymptotics extend to dominant nontrivial singular value in low-diffusivity limit.
Bayesian model averaging has become a widely used approach to accounting for uncertainty about the structural form of the model generating the data. When data arrive sequentially and the generating model can change over time, Dynamic Model Averaging (DMA) extends model averaging to deal with this situation. Often in ma…
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
This paper investigates the average-case time complexity of certifying RIP matrices.
problem Certifying the restricted isometry property (RIP) for large sparsity levels in random Gaussian matrices.
method Analysis of the low-degree likelihood ratio to determine the average-case time complexity.
result Subexponential runtime of is required for certifying RIP matrices.
The paper clarifies long-horizon investment and DCA, showing no risk reduction but different exposure profiles.
problem Misleading claims about reducing risk with longer investment horizons and DCA.
method Unified probabilistic framework, defining risk and uncertainty, and introducing effective investment exposure.
result Different investment timing strategies can lead to distinct exposure profiles over time, affecting risk and uncertainty.
Paper proposes an online adaptation algorithm for improving model performance.
problem Improving model fidelity in real-time for domain shift and time variance.
method Extended Kalman Filter with Exponential Moving Average and Dynamic Multi-Epoch strategy.
result Proposed algorithm outperforms existing methods in experiments.
A new framework for averaging spatio-temporal signals using optimal transport and soft alignments.
problem Averaging complex datasets with time and spatial components.
method Inspired by DTW, OT, and UOT, a new loss function is proposed to address shifts in time, space, and population size.
result The proposed loss function can be used to compute spatio-temporal barycenters efficiently.
There are non-vanishing price responses across different stocks in correlated financial markets. We further study this issue by performing different averages, which identify active and passive cross-responses. The two average cross-responses show different characteristic dependences on the time lag. The passive cross-r…
The average shape of a fluctuation: universality in excursions of stochastic processescond-mat.stat-mech
We study the average shape of a fluctuation of a time series x(t), that is the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law of the form <x(t) - x(0)>_T = T^αf(t/T) is obeyed. The scaling function f(s) is…