DecoKAN: Interpretable Decomposition for Forecasting Cryptocurrency Market Dynamics

Accurate and interpretable forecasting of multivariate time series is crucial for understanding the complex dynamics of cryptocurrency markets in digital asset systems. Advanced deep learning methodologies, particularly Transformer-based and MLP-based architectures, have achieved competitive predictive performance in cryptocurrency forecasting tasks. However, cryptocurrency data is inherently composed of long-term socio-economic trends and local high-frequency speculative oscillations. Existing deep learning-based 'black-box' models fail to effectively decouple these composite dynamics or provide the interpretability needed for trustworthy financial decision-making. To overcome these limitations, we propose DecoKAN, an interpretable forecasting framework that integrates multi-level Discrete Wavelet Transform (DWT) for decoupling and hierarchical signal decomposition with Kolmogorov-Arnold Network (KAN) mixers for transparent and interpretable nonlinear modeling. The DWT component decomposes complex cryptocurrency time series into distinct frequency components, enabling frequency-specific analysis, while KAN mixers provide intrinsically interpretable spline-based mappings within each decomposed subseries. Furthermore, interpretability is enhanced through a symbolic analysis pipeline involving sparsification, pruning, and symbolization, which produces concise analytical expressions offering symbolic representations of the learned patterns. Extensive experiments demonstrate that DecoKAN achieves the lowest average Mean Squared Error on all tested real-world cryptocurrency datasets (BTC, ETH, XMR), consistently outperforming a comprehensive suite of competitive state-of-the-art baselines. These results validate DecoKAN's potential to bridge the gap between predictive accuracy and model transparency, advancing trustworthy decision support within complex cryptocurrency markets.

The Procrustean Bed of Time Series: The Optimization Bias of Point-wise Loss

Optimizing time series models via point-wise loss functions (e.g., MSE) relying on a flawed point-wise independent and identically distributed (i.i.d.) assumption that disregards the causal temporal structure, an issue with growing awareness yet lacking formal theoretical grounding. Focusing on the core independence issue under covariance stationarity, this paper aims to provide a first-principles analysis of the Expectation of Optimization Bias (EOB), formalizing it information-theoretically as the discrepancy between the true joint distribution and its flawed i.i.d. counterpart. Our analysis reveals a fundamental paradigm paradox: the more deterministic and structured the time series, the more severe the bias by point-wise loss function. We derive the first closed-form quantification for the non-deterministic EOB across linear and non-linear systems, and prove EOB is an intrinsic data property, governed exclusively by sequence length and our proposed Structural Signal-to-Noise Ratio (SSNR). This theoretical diagnosis motivates our principled debiasing program that eliminates the bias through sequence length reduction and structural orthogonalization. We present a concrete solution that simultaneously achieves both principles via DFT or DWT. Furthermore, a novel harmonized $\ell_p$ norm framework is proposed to rectify gradient pathologies of high-variance series. Extensive experiments validate EOB Theory's generality and the superior performance of debiasing program.

On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies

Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.

Efficient Deep Learning for Short-Term Solar Irradiance Time Series Forecasting: A Benchmark Study in Ho Chi Minh City

Reliable forecasting of Global Horizontal Irradiance (GHI) is essential for mitigating the variability of solar energy in power grids. This study presents a comprehensive benchmark of ten deep learning architectures for short-term (1-hour ahead) GHI time series forecasting in Ho Chi Minh City, leveraging high-resolution NSRDB satellite data (2011-2020) to compare established baselines (e.g. LSTM, TCN) against emerging state-of-the-art architectures, including Transformer, Informer, iTransformer, TSMixer, and Mamba. Experimental results identify the Transformer as the superior architecture, achieving the highest predictive accuracy with an R^2 of 0.9696. The study further utilizes SHAP analysis to contrast the temporal reasoning of these architectures, revealing that Transformers exhibit a strong "recency bias" focused on immediate atmospheric conditions, whereas Mamba explicitly leverages 24-hour periodic dependencies to inform predictions. Furthermore, we demonstrate that Knowledge Distillation can compress the high-performance Transformer by 23.5% while surprisingly reducing error (MAE: 23.78 W/m^2), offering a proven pathway for deploying sophisticated, low-latency forecasting on resource-constrained edge devices.

Empirical Mode Decomposition and Graph Transformation of the MSCI World Index: A Multiscale Topological Analysis for Graph Neural Network Modeling

This study applies Empirical Mode Decomposition (EMD) to the MSCI World index and converts the resulting intrinsic mode functions (IMFs) into graph representations to enable modeling with graph neural networks (GNNs). Using CEEMDAN, we extract nine IMFs spanning high-frequency fluctuations to long-term trends. Each IMF is transformed into a graph using four time-series-to-graph methods: natural visibility, horizontal visibility, recurrence, and transition graphs. Topological analysis shows clear scale-dependent structure: high-frequency IMFs yield dense, highly connected small-world graphs, whereas low-frequency IMFs produce sparser networks with longer characteristic path lengths. Visibility-based methods are more sensitive to amplitude variability and typically generate higher clustering, while recurrence graphs better preserve temporal dependencies. These results provide guidance for designing GNN architectures tailored to the structural properties of decomposed components, supporting more effective predictive modeling of financial time series.

On Conditional Independence Graph Learning From Multi-Attribute Gaussian Dependent Time Series

Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models where one associates a scalar time series with each node. In multi-attribute graphical models, each node represents a random vector or vector time series. In this paper we provide a unified theoretical analysis of multi-attribute graph learning for dependent time series using a penalized log-likelihood objective function formulated in the frequency domain using the discrete Fourier transform of the time-domain data. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We do not impose any incoherence or irrepresentability condition for our convergence results. We also empirically investigate selection of the tuning parameters based on the Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.

FRWKV:Frequency-Domain Linear Attention for Long-Term Time Series Forecasting

Traditional Transformers face a major bottleneck in long-sequence time series forecasting due to their quadratic complexity $(\mathcal{O}(T^2))$ and their limited ability to effectively exploit frequency-domain information. Inspired by RWKV's $\mathcal{O}(T)$ linear attention and frequency-domain modeling, we propose FRWKV, a frequency-domain linear-attention framework that overcomes these limitations. Our model integrates linear attention mechanisms with frequency-domain analysis, achieving $\mathcal{O}(T)$ computational complexity in the attention path while exploiting spectral information to enhance temporal feature representations for scalable long-sequence modeling. Across eight real-world datasets, FRWKV achieves a first-place average rank. Our ablation studies confirm the critical roles of both the linear attention and frequency-encoder components. This work demonstrates the powerful synergy between linear attention and frequency analysis, establishing a new paradigm for scalable time series modeling. Code is available at this repository: https://github.com/yangqingyuan-byte/FRWKV.

Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform

Non-random missing data is a ubiquitous yet undertreated flaw in multidimensional time series, fundamentally threatening the reliability of data-driven analysis and decision-making. Pure low-rank tensor completion, as a classical data recovery method, falls short in handling non-random missingness, both methodologically and theoretically. Hankel-structured tensor completion models provide a feasible approach for recovering multidimensional time series with non-random missing patterns. However, most Hankel-based multidimensional data recovery methods both suffer from unclear sources of Hankel tensor low-rankness and lack an exact recovery theory for non-random missing data. To address these issues, we propose the temporal isometric delay-embedding transform, which constructs a Hankel tensor whose low-rankness is naturally induced by the smoothness and periodicity of the underlying time series. Leveraging this property, we develop the \textit{Low-Rank Tensor Completion with Temporal Isometric Delay-embedding Transform} (LRTC-TIDT) model, which characterizes the low-rank structure under the \textit{Tensor Singular Value Decomposition} (t-SVD) framework. Once the prescribed non-random sampling conditions and mild incoherence assumptions are satisfied, the proposed LRTC-TIDT model achieves exact recovery, as confirmed by simulation experiments under various non-random missing patterns. Furthermore, LRTC-TIDT consistently outperforms existing tensor-based methods across multiple real-world tasks, including network flow reconstruction, urban traffic estimation, and temperature field prediction. Our implementation is publicly available at https://github.com/HaoShu2000/LRTC-TIDT.

Deep Generative Models for Synthetic Financial Data: Applications to Portfolio and Risk Modeling

Synthetic financial data provides a practical solution to the privacy, accessibility, and reproducibility challenges that often constrain empirical research in quantitative finance. This paper investigates the use of deep generative models, specifically Time-series Generative Adversarial Networks (TimeGAN) and Variational Autoencoders (VAEs) to generate realistic synthetic financial return series for portfolio construction and risk modeling applications. Using historical daily returns from the S and P 500 as a benchmark, we generate synthetic datasets under comparable market conditions and evaluate them using statistical similarity metrics, temporal structure tests, and downstream financial tasks. The study shows that TimeGAN produces synthetic data with distributional shapes, volatility patterns, and autocorrelation behaviour that are close to those observed in real returns. When applied to mean--variance portfolio optimization, the resulting synthetic datasets lead to portfolio weights, Sharpe ratios, and risk levels that remain close to those obtained from real data. The VAE provides more stable training but tends to smooth extreme market movements, which affects risk estimation. Finally, the analysis supports the use of synthetic datasets as substitutes for real financial data in portfolio analysis and risk simulation, particularly when models are able to capture temporal dynamics. Synthetic data therefore provides a privacy-preserving, cost-effective, and reproducible tool for financial experimentation and model development.

Trend Extrapolation for Technology Forecasting: Leveraging LSTM Neural Networks for Trend Analysis of Space Exploration Vessels

Forecasting technological advancement in complex domains such as space exploration presents significant challenges due to the intricate interaction of technical, economic, and policy-related factors. The field of technology forecasting has long relied on quantitative trend extrapolation techniques, such as growth curves (e.g., Moore's law) and time series models, to project technological progress. To assess the current state of these methods, we conducted an updated systematic literature review (SLR) that incorporates recent advances. This review highlights a growing trend toward machine learning-based hybrid models. Motivated by this review, we developed a forecasting model that combines long short-term memory (LSTM) neural networks with an augmentation of Moore's law to predict spacecraft lifetimes. Operational lifetime is an important engineering characteristic of spacecraft and a potential proxy for technological progress in space exploration. Lifetimes were modeled as depending on launch date and additional predictors. Our modeling analysis introduces a novel advance in the recently introduced Start Time End Time Integration (STETI) approach. STETI addresses a critical right censoring problem known to bias lifetime analyses: the more recent the launch dates, the shorter the lifetimes of the spacecraft that have failed and can thus contribute lifetime data. Longer-lived spacecraft are still operating and therefore do not contribute data. This systematically distorts putative lifetime versus launch date curves by biasing lifetime estimates for recent launch dates downward. STETI mitigates this distortion by interconverting between expressing lifetimes as functions of launch time and modeling them as functions of failure time. The results provide insights relevant to space mission planning and policy decision-making.