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In financial time series forecasting, the naive forecast is a notoriously difficult benchmark to surpass because of the stochastic nature of the data. Motivated by this challenge, this study introduces the movement prediction-adjusted naive…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
This paper introduces a new algorithm to improve the accuracy of numerical phase-averaging in oscillatory, multiscale, differential equations. Phase-averaging is a timestepping method which averages a mapped variable to remove highly…
The paper develops a Transformer architecture for estimating dynamic factors from multivariate time series data under flexible identification assumptions. Performance on small datasets is improved substantially by using a conventional…
Instance normalization (IN) is widely used in non-stationary multivariate time series forecasting to reduce distribution shifts and highlight common patterns across samples. However, IN can over-smooth instance-specific structural…
Climate change stands as one of the most pressing global challenges of the twenty-first century, with far-reaching consequences such as rising sea levels, melting glaciers, and increasingly extreme weather patterns. Accurate forecasting is…
Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier…
Neural network (NN) ensembles can reduce large prediction variance of NN and improve prediction accuracy. For highly nonlinear problems with insufficient data set, the prediction accuracy of NN models becomes unstable, resulting in a…
We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies…
Time-frequency (TF) representations of time series are intrinsically subject to the boundary effects. As a result, the structures of signals that are highlighted by the representations are garbled when approaching the boundaries of the TF…
Time series forecasting is essential for many practical applications, with the adoption of transformer-based models on the rise due to their impressive performance in NLP and CV. Transformers' key feature, the attention mechanism,…
Forecasting multivariate time series data, such as prediction of electricity consumption, solar power production, and polyphonic piano pieces, has numerous valuable applications. However, complex and non-linear interdependencies between…
Stationarity transformations are standard preprocessing in time series forecasting, yet their actual impact on accuracy across different non-stationarity types and model families has received little controlled evaluation. We construct…
Detrend fluctuation analysis (DFA) has become a choice method for effective analysis of a broad variety of nonstationary signals. We show in the present article that, provided the nonstationary fluctuations occur at a large enough time…
This paper presents \textbf{FreEformer}, a simple yet effective model that leverages a \textbf{Fre}quency \textbf{E}nhanced Trans\textbf{former} for multivariate time series forecasting. Our work is based on the assumption that the…
Forecasting anomalies (anomaly prediction) in multivariate time series from different real-world, dynamic, and complex systems is vital for preempting critical failures, leading to a substantial minimization in operational costs and human…
Accurate volatility forecasts are vital in modern finance for risk management, portfolio allocation, and strategic decision-making. However, existing methods face key limitations. Fully multivariate models, while comprehensive, are…
Multivariate long-term time series forecasting has been suffering from the challenge of capturing both temporal dependencies within variables and spatial correlations across variables simultaneously. Current approaches predominantly…
Time series foundation models (FMs) have emerged as a popular paradigm for zero-shot multi-domain forecasting. These models are trained on numerous diverse datasets and claim to be effective forecasters across multiple different time series…