Time Series Decomposition

Empirical Mode Decomposition and Graph Transformation of the MSCI World Index: A Multiscale Topological Analysis for Graph Neural Network Modeling ArXiv ID: 2512.12526 “View on arXiv” Authors: Agustín M. de los Riscos, Julio E. Sandubete, Diego Carmona-Fernández, León Beleña Abstract 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. ...

Bitcoin Price Forecasting Based on Hybrid Variational Mode Decomposition and Long Short Term Memory Network ArXiv ID: 2510.15900 “View on arXiv” Authors: Emmanuel Boadi Abstract This study proposes a hybrid deep learning model for forecasting the price of Bitcoin, as the digital currency is known to exhibit frequent fluctuations. The models used are the Variational Mode Decomposition (VMD) and the Long Short-Term Memory (LSTM) network. First, VMD is used to decompose the original Bitcoin price series into Intrinsic Mode Functions (IMFs). Each IMF is then modeled using an LSTM network to capture temporal patterns more effectively. The individual forecasts from the IMFs are aggregated to produce the final prediction of the original Bitcoin Price Series. To determine the prediction power of the proposed hybrid model, a comparative analysis was conducted against the standard LSTM. The results confirmed that the hybrid VMD+LSTM model outperforms the standard LSTM across all the evaluation metrics, including RMSE, MAE and R2 and also provides a reliable 30-day forecast. ...

Extrapolating the long-term seasonal component of electricity prices for forecasting in the day-ahead market ArXiv ID: 2503.02518 “View on arXiv” Authors: Unknown Abstract Recent studies provide evidence that decomposing the electricity price into the long-term seasonal component (LTSC) and the remaining part, predicting both separately, and then combining their forecasts can bring significant accuracy gains in day-ahead electricity price forecasting. However, not much attention has been paid to predicting the LTSC, and the last 24 hourly values of the estimated pattern are typically copied for the target day. To address this gap, we introduce a novel approach which extracts the trend-seasonal pattern from a price series extrapolated using price forecasts for the next 24 hours. We assess it using two 5-year long test periods from the German and Spanish power markets, covering the Covid-19 pandemic, the 2021/2022 energy crisis, and the war in Ukraine. Considering parsimonious autoregressive and LASSO-estimated models, we find that improvements in predictive accuracy range from 3% to 15% in terms of the root mean squared error and exceed 1% in terms of profits from a realistic trading strategy involving day-ahead bidding and battery storage. ...

Successive one-sided Hodrick-Prescott filter with incremental filtering algorithm for nonlinear economic time series ArXiv ID: 2306.12439 “View on arXiv” Authors: Unknown Abstract We propose a successive one-sided Hodrick-Prescott (SOHP) filter from multiple time scale decomposition perspective to derive trend estimate for a time series. The idea is to apply the one-sided HP (OHP) filter recursively on the updated cyclical component to extract the trend residual on multiple time scales, thereby to improve the trend estimate. To address the issue of optimization with a moving horizon as that of the SOHP filter, we present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation and reduces the computational demand of the basic HP filtering. Actually, the new algorithm also applies effectively to other HP-type filters, especially for large-size or expanding data scenario. Numerical examples on real economic data show the better performance of the SOHP filter in comparison with other known HP-type filters. ...

The Chebyshev Polynomials Of The First Kind For Analysis Rates Shares Of Enterprises ArXiv ID: 2307.08465 “View on arXiv” Authors: Unknown Abstract Chebyshev polynomials of the first kind have long been used to approximate experimental data in solving various technical problems. Within the framework of this study, the dynamics of shares of eight Czech enterprises was analyzed by the Chebyshev polynomial decomposition: CEZ A.S. (CEZP), Colt CZ Group SE (CZG), Erste Bank (ERST), Komercni Banka (BKOM), Moneta Money Bank A.S. (MONET), Photon (PENP), Vienna insurance group (VIGR) in 2021. An investor, when making a decision to purchase a security , is guided largely by an heuristic approach . And variance and correlation are not observed by human senses. The vectors of decomposition of time series of exchange values of securities allow analyzing the dynamics of exchange values of securities more effectively if their dynamics does not correspond to the normal distribution law. The proposed model allows analyzing the dynamics of the exchange value of a securities portfolio without calculating variance and correlation. This model can be useful if the dynamics of the exchange values of securities does not obey, due to certain circumstances, the normal law of distribution. ...