Quantile Estimation

Probabilistic Forecasting Cryptocurrencies Volatility: From Point to Quantile Forecasts ArXiv ID: 2508.15922 “View on arXiv” Authors: Grzegorz Dudek, Witold Orzeszko, Piotr Fiszeder Abstract Cryptocurrency markets are characterized by extreme volatility, making accurate forecasts essential for effective risk management and informed trading strategies. Traditional deterministic (point) forecasting methods are inadequate for capturing the full spectrum of potential volatility outcomes, underscoring the importance of probabilistic approaches. To address this limitation, this paper introduces probabilistic forecasting methods that leverage point forecasts from a wide range of base models, including statistical (HAR, GARCH, ARFIMA) and machine learning (e.g. LASSO, SVR, MLP, Random Forest, LSTM) algorithms, to estimate conditional quantiles of cryptocurrency realized variance. To the best of our knowledge, this is the first study in the literature to propose and systematically evaluate probabilistic forecasts of variance in cryptocurrency markets based on predictions derived from multiple base models. Our empirical results for Bitcoin demonstrate that the Quantile Estimation through Residual Simulation (QRS) method, particularly when applied to linear base models operating on log-transformed realized volatility data, consistently outperforms more sophisticated alternatives. Additionally, we highlight the robustness of the probabilistic stacking framework, providing comprehensive insights into uncertainty and risk inherent in cryptocurrency volatility forecasting. This research fills a significant gap in the literature, contributing practical probabilistic forecasting methodologies tailored specifically to cryptocurrency markets. ...

Using quantile time series and historical simulation to forecast financial risk multiple steps ahead ArXiv ID: 2502.20978 “View on arXiv” Authors: Unknown Abstract A method for quantile-based, semi-parametric historical simulation estimation of multiple step ahead Value-at-Risk (VaR) and Expected Shortfall (ES) models is developed. It uses the quantile loss function, analogous to how the quasi-likelihood is employed by standard historical simulation methods. The returns data are scaled by the estimated quantile series, then resampling is employed to estimate the forecast distribution one and multiple steps ahead, allowing tail risk forecasting. The proposed method is applicable to any data or model where the relationship between VaR and ES does not change over time and can be extended to allow a measurement equation incorporating realized measures, thus including Realized GARCH and Realized CAViaR type models. Its finite sample properties, and its comparison with existing historical simulation methods, are evaluated via a simulation study. A forecasting study assesses the relative accuracy of the 1% and 2.5% VaR and ES one-day-ahead and ten-day-ahead forecasting results for the proposed class of models compared to several competitors. ...

OrderFusion: Encoding Orderbook for End-to-End Probabilistic Intraday Electricity Price Forecasting ArXiv ID: 2502.06830 “View on arXiv” Authors: Unknown Abstract Probabilistic intraday electricity price forecasting is becoming increasingly important with the growth of renewable generation and the rise in demand-side engagement. Their uncertainties have increased the trading risks closer to delivery and the subsequent imbalance settlement costs. As a consequence, intraday trading has emerged to mitigate these risks. Unlike auction markets, intraday trading in many jurisdictions is characterized by the continuous posting of buy and sell orders on power exchange platforms. This dynamic orderbook microstructure of price formation presents special challenges for price forecasting. Conventional methods represent the orderbook via domain features aggregated from buy and sell trades, or by treating it as a multivariate time series, but such representations neglect the full buy-sell interaction structure of the orderbook. This research therefore develops a new order fusion methodology, which is an end-to-end and parameter-efficient probabilistic forecasting model that learns a full interaction-aware representation of the buy-sell dynamics. Furthermore, as quantile crossing is often a problem in probabilistic forecasting, this approach hierarchically estimates the quantiles with non-crossing constraints. Extensive experiments on the market price indices across high-liquidity (German) and low-liquidity (Austrian) markets demonstrate consistent improvements over conventional baselines, and ablation studies highlight the contributions of the main modeling components. The methodology is available at: https://runyao-yu.github.io/OrderFusion/. ...