arXiv research

In this note we discuss the mathematical tools to define trend indicators which are used to describe market trends. We explain the relation between averages and moving averages on the one hand and the so called exponential moving average (EMA) on the other hand. We present a lot of examples and give the definition of t…

New moving average adapts weight dynamically based on polynomial and wavefunction.

A new method for exponentially weighted moving models using approximations.

Improved averaging method for noisy observations converges strongly.

PACE optimizes training for averaged language models, improving performance.

Paper analyzes how EMA improves SGD in linear regression.

We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate…

We propose an explicit recursive method to approximate a power-law with a finite sum of weighted exponentials. Applications to moving averages with long memory are discussed in relationship with stochastic volatility models.

BEMA reduces bias in EMA, leading to faster convergence and better performance.

High fidelity behavior prediction of intelligent agents is critical in many applications. However, the prediction model trained on the training set may not generalize to the testing set due to domain shift and time variance. The challenge motivates the adoption of online adaptation algorithms to update prediction model…

Machine learning models outperform traditional technical analysis in Bitcoin trading.

While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $θ$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $θ_T$ for each time $T$ based on the earlier values $(x_t)_{t<T}$ using (…

Adaptive t-distribution estimates nonstationary time series using moving moments.

STORM-PG uses momentum for faster policy gradient updates.

We examine two different techniques for parameter averaging in GAN training. Moving Average (MA) computes the time-average of parameters, whereas Exponential Moving Average (EMA) computes an exponentially discounted sum. Whilst MA is known to lead to convergence in bilinear settings, we provide the -- to our knowledge …

GPA improves LLM training speed by 8.71% for Llama-160M models.

Classifying streaming data requires the development of methods which are computationally efficient and able to cope with changes in the underlying distribution of the stream, a phenomenon known in the literature as concept drift. We propose a new method for detecting concept drift which uses an Exponentially Weighted M…

Improving optimization for iterate-averaged language models

A new method normalizes flow mixtures for better inference across different data types.

The paper optimizes portfolios using MACD signals derived from price history.

Improved score-based models generate high-quality images up to 256x256.

New adaptive methods solve weakly convex stochastic optimization problems.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large …

We build a multiassets heterogeneous agents model with fundamentalists and chartists, who make investment decisions by maximizing the constant relative risk aversion utility function. We verify that the model can reproduce the main stylized facts in real markets, such as fat-tailed return distribution and long-term mem…

We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is lucidly expressed in terms of the past average of Reality's moves. From t…

We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood …

A new method Expectigrad improves on Adam and RMSProp by reducing divergence and improving performance.

This paper provides an insight to the time-varying dynamics of the shape of the distribution of financial return series by proposing an exponential weighted moving average model that jointly estimates volatility, skewness and kurtosis over time using a modified form of the Gram-Charlier density in which skewness and ku…

Behavior cloning training instabilities amplified by SGD noise over long horizons.

Time series analysis is a key component of machine learning, with applications in various fields.

Auto-regressive models improve smoothing efficiency with exponentially tapered windows.

This study uses moving average cluster entropy to analyze financial market dynamics.

Improved diffusion models for image synthesis with better training dynamics.

Study compares local and global models for hierarchical forecasting accuracy.

Adaptive estimation of alpha-Stable distribution and Hurst exponent for nonstationary time series.

This work provides a scaling rule for model EMA optimization across batch sizes.

Logarithmic regret for continuous-time reinforcement learning.

Optimal algorithms for Riemannian optimization with reduced complexity.

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient $ρ_{DMCA}(λ)$ with a moving average window length $λ$. We analytically show that the coefficient…

The Hurst exponent $H$ of long range correlated series can be estimated by means of the Detrending Moving Average (DMA) method. A computational tool defined within the algorithm is the generalized variance $σ_{DMA}^2={1}/{(N-n)}\sum_i [y(i)-\widetilde{y}_n(i)]^2\:$, with $\widetilde{y}_n(i)= {1}/{n}\sum_{k}y(i-k)$ the…

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For …

The possibility that price dynamics is affected by its distance from a moving average has been recently introduced as new statistical tool. The purpose is to identify the tendency of the price dynamics to be attractive or repulsive with respect to its own moving average. We consider a number of tests for various models…

InQMAD detects anomalies in streaming data using quantum measurements and density matrices.

In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modeled by either an Ornstein-Uhl…

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a fin…

The paper analyzes MACD using operator theory.

Paper predicts cryptocurrency bull and bear phases using Bitcoin's moving averages.

A new accelerated method with simpler momentum update rules.