Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
Time series models generalize ARMA and ARFIMA with non-Gaussian dependence.
problem Modeling non-Gaussian serial dependence in time series data.
method Infinite-order partial copula dependence in s-vine processes.
result Rich class of models that generalize linear processes.
Quantum model captures rare financial events not seen by Gaussian statistics.
problem Underestimation of rare financial events by Gaussian statistics.
method Quantum Bohmian Mechanics applied to multifractal random walk (MRW) models.
result Rare financial events generate a potential barrier in quantum potentials.
Unified framework for ensemble transport-based smoothing of non-Gaussian time series.
problem Bayesian time series re-analysis with non-Gaussian distributions.
method Measure transport approach to derive consistent prior-to-posterior transformations.
result General ensemble framework for transport-based smoothing of state-space models.
IAE extracts innovations sequences for non-Gaussian processes.
problem Extracting innovations sequences for non-Gaussian processes.
method Causal convolutional neural network.
result IAE effectively detects anomalies in non-Gaussian data.
The analysis of observed conditional distributions of both lagged and simultaneous intraday price increments of a basket of stocks reveals phenomena of dependence - induced volatility smile and kurtosis reduction. A model based on multivariate t-Student distribution shows that the observed effects are caused by colelct…
In this manuscript we present a comprehensive study on the multifractal properties of high-frequency price fluctuations and instantaneous volatility of the equities that compose Dow Jones Industrial Average. The analysis consists about quantification of dependence and non-Gaussianity on the multifractal character of fi…
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
The paper examines non-Gaussian models for financial data.
problem Modeling financial data with non-Gaussian distributions.
method Analysis of multivariate non-Gaussian models focusing on parsimony, dependence structure, and computational aspects.
result Characterization and calibration of models for financial log-returns.
In this work, we propose a model for estimating volatility from financial time series, extending the non-Gaussian family of space-state models with exact marginal likelihood proposed by Gamerman, Santos and Franco (2013). On the literature there are models focused on estimating financial assets risk, however, most of t…
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
A new HMM model captures kernel dependencies using context-specific Bayesian networks.
problem Traditional HMMs struggle with non-Gaussian data and independence assumptions.
method Kernel density estimation with context-specific Bayesian networks.
result The proposed model outperforms related HMMs in likelihood and classification accuracy.
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the returns distribution in terms of a Student-t distribution. Non-Gaussian closed-fo…
A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution based Legendre Polynomial (LP) like nonlinear transformations of the original time series Y(t) that enables us to adapt all the existing stationary linear Gaus…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock r…
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the returns distribution in terms of a Student-t (or Tsallis) distribution. Non-Gau…
A time series that represents daily values of the WIG index (the main index of Warsaw Stock Exchange) over last 5 years is examined. Non-Gaussian features of distributions of fluctuations, namely returns, over a time scale are considered. Some general properties like exponents of the long range correlation estimated by…
MD-CGAN models forecast time series with probabilistic posterior distributions.
problem Limited applications of GANs in time series forecasting, especially with probabilistic predictions.
method Mixture Density Conditional Generative Adversarial Model (MD-CGAN) using Gaussian mixture output.
result MD-CGAN outperforms benchmarks, especially in noisy time series.
TailedTS dataset benchmarks heavy-tailed time series forecasting and periodicity quantification.
problem Benchmarking robustness of time series models under heavy-tailed distributions.
method Derived from Wikipedia page views, introduces periodicity quantification and robust loss functions.
result Standard Gaussian models degrade on high-volume page categories, while robust alternatives perform consistently.
We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most (≃ 99.6%) of the wavelet coefficients can be neglected for th…
Granger causality reviewed and advanced for complex data.
problem Validity of inferring causal relationships from time series data.
method Recent advances in models for high-dimensional time series, accounting for nonlinear and non-Gaussian observations, and sub-sampled data.
result Improved computational tools for Granger causality.
ProbRes calibrates probabilistic forecasts by learning volatility dynamics.
problem Quantifying risk and uncertainty in time series forecasting.
method ProbRes learns conditional mean and volatility separately, generating well-calibrated prediction intervals.
result ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.
New method infers causal relationships from nonstationary time series data.
problem Challenges in inferring causal relationships from nonstationary time series data.
method Proposes a new class of restricted SCM with time-varying filters and stationary noise, leveraging asymmetry from nonstationarity.
result Demonstrates effectiveness of the proposed methodology on various synthetic and real datasets.
The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are non-Gaussian, therefore, the AR model with more general heavy-tailed innovations…
Stock networks, constructed from stock price time series, are a well-established tool for the characterization of complex behavior in stock markets. Following Mantegna's seminal paper, the linear Pearson's correlation coefficient between pairs of stocks has been the usual way to determine network edges. Recently, possi…
In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks log-returns than the simple correlation matrix. The two models considered are a multiv…
Many theoretical results on estimation of high dimensional time series require specifying an underlying data generating model (DGM). Instead, along the footsteps of~\cite{wong2017lasso}, this paper relies only on (strict) stationarity and β-mixing condition to establish consistency of lasso when data comes from a $β…
We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstra…
Neural networks model financial data with Lévy processes.
problem Forecasting chaotic financial time series with big jumps.
method Lévy-induced stochastic differential equation network approximated by neural networks.
result The method improves prediction accuracy using non-Gaussian Lévy processes.
Optimizes cryptocurrency portfolios using MNTS GARCH model.
problem Optimizing cryptocurrency portfolios with non-Gaussian return dynamics.
method Multivariate normal tempered stable (MNTS) GARCH model for non-Gaussian returns, Foster-Hart risk optimization.
result Foster-Hart optimization yields a more profitable portfolio with better risk-return balance.
Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired wit…
Predicting the dependencies between observations from multiple time series is critical for applications such as anomaly detection, financial risk management, causal analysis, or demand forecasting. However, the computational and numerical difficulties of estimating time-varying and high-dimensional covariance matrices …
The paper uses random matrix theory for multi-task regression, improving time series forecasting.
problem Improving time series forecasting using multi-task regression.
method Applying random matrix theory to multi-task regression problems, deriving closed-form solutions for optimization.
result Provides a robust foundation for hyperparameter optimization in multi-task regression scenarios.
Sparse Markovian Gaussian processes improve probabilistic model inference for large datasets.
problem Efficient inference for large-scale time series data.
method Combining inducing variables with Kalman filter-like recursions for linear scaling.
result General site-based approach for approximating non-Gaussian likelihoods.
The paper maps time-series onto networks to reveal hidden joint information.
problem Extract hidden joint information from uncorrelated time-series.
method Discretize time-series amplitudes, map onto networks, measure coupling deviations, and compare with Gaussian distributions.
result Markets may possess joint patterns even if initially uncorrelated.
We study a well-known estimator of the fractal index of a stochastic process. Our framework is very general and encompasses many models of interest; we show how to extend the theory of the estimator to a large class of non-Gaussian processes. Particular focus is on clarity and ease of implementation of the estimator an…
The aim here is to study the concept of pairing multifractality between time series possessing non-Gaussian distributions. The increasing number of rare events creates "criticality". We show how the pairing between two series is affected by rare events, which we call "coupled criticality". A method is proposed for stud…
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
A new machine learning method for spatial regression.
problem Spatial/temporal regression with scattered data and arbitrary dimensions.
method Modified Planar Rotator (MPRS) method, a non-parametric model with distance-dependent interactions.
result MPRS predictions are competitive with standard interpolation methods and superior in handling rough and non-Gaussian data.
We propose a family of models that enable predictive estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. The models are a white noise process with conditionally log-Laplace stochastic volatility. In contrast to other, similar stochastic volatility formalisms, th…
Time series forecasting is ubiquitous in the modern world. Applications range from health care to astronomy, and include climate modelling, financial trading and monitoring of critical engineering equipment. To offer value over this range of activities, models must not only provide accurate forecasts, but also quantify…
The paper analyzes the non-Gaussian behavior of inflation and unemployment over 70 years using multifractal methods.
problem Capturing unusual fluctuations in inflation and unemployment over long periods.
method Coupled multifractal approach to analyze non-Gaussian distributions of inflation and unemployment over 70 years.
result The non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year, while inflation's non-Gaussianity persists across all time scales.
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with t…
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires n≳d4 samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches n≳d2. We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scale…
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.