Quantile-Frequency Analysis detects nonlinear dynamics in financial time series.
problem Detecting nonlinear dynamics in financial time series models.
method Quantile periodogram and trigonometric quantile regression.
result QFA provides additional insights into financial time series models.
Using methods introduced by Scargle in 1978 we derive a cumulative version of the Lomb periodogram that exhibits frequency independent statistics when applied to cumulative noise. We show how this cumulative Lomb periodogram allows us to estimate the significance of log-periodic signatures in the S&P 500 anti-bubble th…
ARISE models efficient markets without periodogram or Gaussianity assumptions.
problem Mimicking and learning long-term memory in efficient markets.
method ARISE process using aperiodic spectrum estimation and infinite-sum function of known processes.
result ARISE process has mean-square convergence, consistency, and asymptotic normality without periodogram and Gaussianity assumptions.
Paper proposes a robust framework for detecting multiple periodic components in time series.
problem Detecting multiple periodic components in time series with interlaced patterns and external noise.
method Applying maximal overlap discrete wavelet transform to isolate periodic components, ranking them by wavelet variance, and detecting single periodicity robustly.
result The proposed algorithm outperforms other methods for both single and multiple periodicity detection.
We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local X-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
The price of electricity is far more volatile than that of other commodities normally noted for extreme volatility. The possibility of extreme price movements increases the risk of trading in electricity markets. However, underlying the process of price returns is a strong mean-reverting mechanism. We study this featur…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among brain regions. In this paper, we develop a non-asymptotic theory for regularize…
Period estimation is one of the central topics in astronomical time series analysis, where data is often unevenly sampled. Especially challenging are studies of stellar magnetic cycles, as there the periods looked for are of the order of the same length than the datasets themselves. The datasets often contain trends, t…
In this letter, we propose a method for period estimation in light curves from periodic variable stars using correntropy. Light curves are astronomical time series of stellar brightness over time, and are characterized as being noisy and unevenly sampled. We propose to use slotted time lags in order to estimate corrent…
Investigates methods to regularize quantile regression for accurate predictions.
problem Improving accuracy and fairness in quantile regression predictions.
method Various regularization techniques including expected pinball loss, monotonicity constraints, and rate constraints.
result Deep lattice networks can maintain non-crossing quantiles and improve calibration and fairness.
A new method avoids quantile crossing in time series forecasting.
problem Quantile crossing in joint quantile regressions.
method Incremental (Spline) Quantile Functions (I(S)QF) with neural network.
result Improves consistency and accuracy in time series forecasting.
New risk measures for quantiles under ambiguity improve risk sharing.
problem Risk optimization under ambiguity using quantiles.
method Introducing Choquet quantiles and Choquet Expected Shortfall.
result Optimal allocations for quantile agents under ambiguity.
Paper finds robust Λ-quantiles equal to extremal distributions.
problem Investigating robust models for Λ-quantiles with partial loss information. method Extending classical quantiles using Λ-quantiles and applying results from robust quantiles. result Robust Λ-quantiles equal to Λ-quantiles of extremal distributions. SCQRNN prevents quantile crossing and improves computational efficiency.
problem Quantile crossing issue in regression models.
method Integrates ad hoc sorting in training to prevent quantile crossing and enhance computational efficiency.
result SCQRNN achieves faster convergence and non-intersecting quantiles.
Axiomatizes Λ-quantiles, a generalization of quantiles.
problem Found an axiomatization for Λ-quantiles. method Characterized Λ-quantiles using the locality property. result Local changes in distribution do not affect Λ-quantiles. Develops a method to ensure accurate quantile forecasts across multiple levels.
problem Ensuring accurate quantile forecasts at multiple levels, even under distribution shifts.
method Multi-level quantile tracker (MultiQT) wraps around any forecaster to produce calibrated forecasts.
result Guaranteed calibration of quantile forecasts at multiple levels, even against adversarial shifts.
Develops quantile diffusions for risk analysis in continuous time.
problem Stochastic dynamics of quantiles in continuous time.
method Construction of quantile processes through composite maps of distribution and quantile functions.
result Powerful method for interpreting quantile process characteristics in terms of model parameters.
Proposes a method to estimate conditional quantiles using both high-fidelity and low-fidelity data.
problem Difficulty in estimating conditional quantiles with scarce high-fidelity data.
method Two-stage, model-agnostic method using local quantile link and level function estimation.
result The method yields more accurate quantile estimates and tighter prediction intervals.
Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis …
The paper proposes a method for predicting equity premium using penalized quantile regression.
problem Heteroscedasticity and heavy-tails in equity premium prediction.
method Penalized quantile regression with consistent variable selection across multiple quantiles.
result The proposed method outperforms benchmark methods and reveals interesting predictor relationships.
We argue that the word ``critical'' in the title is not purely literary. Based on our and other previous work on nonlinear complex dynamical systems, we summarize present evidence, on the Oct. 1929, Oct. 1987, Oct. 1987 Hong-Kong, Aug. 1998 global market events and on the 1985 Forex event, for the hypothesis advanced f…
Supervised learning is an active research area, with numerous applications in diverse fields such as data analytics, computer vision, speech and audio processing, and image understanding. In most cases, the loss functions used in machine learning assume symmetric noise models, and seek to estimate the unknown function …
Improved conformalized quantile regression for adaptive prediction intervals.
problem Lack of adaptiveness in the conformal step of conformalized quantile regression.
method Cluster explanatory variables by permutation importance and apply k conformal steps.
result Improved prediction intervals are more adaptive to heteroscedasticity.
Proposes a deep learning method to ensure non-crossing quantiles in conditional distributions.
problem Non-crossing quantiles issue in deep learning QR models.
method Generic deep learning algorithm enforcing quantile monotonicity.
result Ensures non-crossing quantiles up to machine precision.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
Private estimation of many quantiles using differential privacy.
problem Estimating quantiles of a distribution privately.
method Two approaches: 1) Private estimation of empirical quantiles, 2) Uniform density estimation.
result There is a tradeoff between estimating quantiles at specific points and uniformly estimating the quantile function.
Bayesian method improves quantile estimation and subset selection.
problem Estimating specific percentiles of the response distribution.
method Bayesian decision analysis perspective, optimal point estimates, interpretable uncertainty quantification, scalable subset selection.
result Substantial gains in quantile estimation accuracy, inference, and variable selection over competitors.
New quantile methods improve uncertainty quantification across various models.
problem Improper quantile loss limits model flexibility and accuracy.
method Developed new quantile methods that optimize for calibration, sharpness, and centered intervals.
result Improved conditional quantiles and better uncertainty quantification across diverse models.
This paper analyzes quantiles of heavy-tailed distributions, separating projection direction and quantile threshold effects.
problem Analyzing quantiles of heavy-tailed distributions with estimated parameters.
method Introduces a Q-Q orthogonality formulation to separate projection-direction and quantile-threshold effects.
result Decomposes the difference between empirical and population quantiles into three terms.
ConquerNet smooths quantile regression for deep learning with minimax guarantees.
problem Optimization challenges in quantile regression for deep models.
method ConquerNet uses convolution-smoothed quantile ReLU neural networks.
result ConquerNet provides minimax guarantees and outperforms standard quantile neural networks.
Improved quantile estimation model for VaR.
problem Improving quantile estimation under distribution estimation.
method Develops a compensatory model with a penalty term to control convergence error.
result Significant improvement in VaR performance.
We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk ma…
Paper proposes a method to estimate multiple dynamic quantiles jointly.
problem Limited joint estimation of multiple dynamic quantiles.
method Introduces a crossing penalty objective function for joint estimation.
result Validation through Monte Carlo experiments and empirical application on FTSE100 shows effectiveness.
A new method forecasts financial tail risks by combining and weighting quantiles.
problem Reducing uncertainty in financial tail risk forecasting.
method Two-step procedure: quantile combination followed by ES computation.
result The proposed framework outperforms individual models and simple approaches.
This paper examines quantile dependence between international stock markets and evaluates its use for improving volatility forecasting. First, we analyze quantile dependence and directional predictability between the US stock market and stock markets in the UK, Germany, France and Japan. We use the cross-quantilogram, …
New model predicts entire distribution of time series data.
problem Probabilistic forecasting of multivariate time series.
method Deep generative quantile-copula models with latent uniform distribution.
result Single neural network parameterizes joint predictive distribution.
IQ-BART models conditional quantiles using a non-parametric Bayesian approach.
problem Capturing multimodal predictive distributions in time series forecasting.
method Implicit Quantile BART (IQ-BART) augments data with quantile values for non-parametric quantile function estimation.
result IQ-BART provides flexible distribution-free regression with theoretical guarantees.
The paper introduces a new method for forecasting financial risk using quantile-based modeling.
problem Forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) for financial returns.
method Semiparametric approach using restricted quantile regression to model the conditional scale of financial returns.
result The method provides robust, distribution-free estimates of extreme losses and captures risk dynamics.
Paper introduces arctan pinball loss for XGBoost quantile regression.
problem Efficiently predicting multiple quantiles with XGBoost.
method Smooth approximation of pinball loss for XGBoost, using arctan pinball loss.
result Arctan pinball loss reduces quantile crossings and improves efficiency.
TQF models multivariate uncertainty by learning conditional quantiles.
problem Challenges in fully nonparametric estimation of multivariate conditional distributions.
method Tomographic Quantile Forests (TQF) learns conditional quantiles of directional projections.
result TQF reconstructs multivariate conditional distribution efficiently without convexity restrictions.
Quantile deep learning improves time series prediction accuracy and uncertainty quantification.
problem Uncertainty in multi-step time series prediction.
method Developed a novel quantile regression deep learning framework for multi-step time series prediction.
result Integrating quantile loss function with deep learning provides additional predictions for selected quantiles without loss in accuracy.
Improves random forest quantile estimation and prediction intervals.
problem Excessive bias in quantile estimates from random forests.
method Minimizes quantile coverage loss (QCL) by adjusting RF parameters.
result QCL-tuned RFs produce more accurate and narrower prediction intervals.
The paper derives formulas for moments of a Student t distribution and applies them to quantify Lp-quantiles.
problem Understanding the moments and quantiles of a Student t distribution.
method Developed formulas for partial and complete moments, and derived relationships between Lp-quantiles. result For a Student t distribution, the Ln−j+1-quantile and Lj-quantile coincide at any confidence level. MQF2 forecasts multivariate quantiles globally.
problem Forecasting multi-horizon dependencies with error accumulation.
method Multivariate quantile function using input-convex neural networks.
result MQF2 avoids quantile crossing and captures time dependency. Deep Huber QRNs predict Huber quantiles for house prices.
problem Predicting more functionals of predictive probability distributions.
method Training a DL algorithm with the Huber quantile scoring function.
result DHQRNs provide satisfactory absolute performance in house price prediction.
fastkqr speeds up kernel quantile regression by up to 10x.
problem Huge computational demands of kernel quantile regression.
method A novel finite smoothing algorithm and spectral technique.
result Significantly faster computation of quantile regression.
Bayesian method learns from aggregated quantile data.
problem Limited access to sensitive personal data.
method Bayesian quantile matching estimation based on order statistics.
result Correctly reflects uncertainty of empirical quantiles.