perform seasonal adjustment

This paper addresses two key limitations of the standard Decomposition (Decomp) state-space model for seasonal adjustment: excessive smoothing of the trend component and misattribution of long-term variation to the autoregressive (AR) component when AR eigenvalues lie near the unit circle. To resolve these issues, we propose a novel constrained optimization framework that jointly penalizes the modulus and argument of AR eigenvalues, integrated with an L1/L2 hybrid regularization to enhance identifiability and interpretability between trend and AR components. By embedding these constraints within a state-space formulation, our method achieves precise control over trend smoothness and accurate attribution of persistent dynamics. Empirical evaluation across multiple real-world time series demonstrates substantial improvements in statistical robustness and decomposition reliability of seasonal adjustments compared to conventional approaches.

This work proposes an adaptive time series decomposition framework that eliminates the need to predefine or estimate seasonal periods, addressing the limitations of traditional methods in handling non-stationary, drifting, or multi-scale seasonal patterns. The approach decomposes a sequence into three components: a global trend, an adaptive local linear trend that implicitly captures seasonality, and a residual. An AutoTrend module dynamically partitions the local trend in an error-driven manner, while global smoothing ensures coherent long-term structure; seasonality emerges automatically as a recurring pattern in the local trends. Operating in linear time, the method demonstrates robust performance across synthetic datasets with fixed, transitioning, and varying seasonal periods, achieving high-quality, low-intervention decomposition even in scenarios where conventional techniques fail.

Existing time-series generation methods lack interpretable decomposition mechanisms, hindering faithful modeling of meaningful trend and seasonal patterns. To address this, we propose Seasonal-Trend Diffusion (STDiffusion), the first framework to deeply integrate learnable sequence decomposition with diffusion modeling. STDiffusion explicitly parameterizes the trend component via MLPs and captures multi-scale seasonality through adaptive wavelet distillation; it further introduces a component correction mechanism to enforce consistency and decoupling between trend and seasonal components. This design significantly enhances both interpretability across multiple resolutions and internal coherence of generated series. Evaluated on eight real-world datasets, STDiffusion achieves state-of-the-art performance across all generation benchmarks. Moreover, it demonstrates strong robustness and generalization in multi-window, long-horizon forecasting tasks.

To address insufficient modeling of seasonality and periodicity in Chennai’s climate time-series forecasting, this paper proposes a novel hybrid method integrating adaptive period estimation, unsupervised learning, and spline interpolation. The method first introduces an unsupervised clustering– and spectral analysis–based algorithm to estimate dominant periods directly from data, eliminating reliance on predefined periodic assumptions. Subsequently, it constructs a spline-enhanced ensemble time-series model that jointly captures trend, periodic, and residual components. Evaluated on a multi-source climate dataset from Chennai, the approach achieves an average 23.6% reduction in MAE over ARIMA, Prophet, and LSTM baselines. It notably improves long-horizon forecast accuracy and cross-seasonal robustness. By combining interpretability with minimal dependence on domain-specific prior knowledge, the framework establishes a new paradigm for regional climate forecasting.

Existing time-series forecasting models typically couple trend and seasonal components in a single modeling framework, limiting their ability to accurately capture dynamic temporal characteristics; moreover, conventional diffusion models apply noise indiscriminately, risking irreversible loss of critical sequential information. To address these limitations, we propose FDF—a decoupled forecasting framework featuring a novel Conditioned Denoising Seasonal Module (CDSM) and a Polynomial Trend Module (PTM). CDSM enables statistically informed seasonal denoising, while PTM provides smooth, interpretable trend estimation via polynomial regression. FDF synergistically integrates diffusion-based generation, conditional modeling, polynomial regression, and classical decomposition principles to achieve principled component-wise decoupling. Extensive experiments across multiple benchmark datasets demonstrate that FDF consistently outperforms state-of-the-art methods, achieving superior accuracy, strong generalization, and robust adaptability to diverse seasonal periods.

This study addresses the limitations of existing hierarchical time series forecasting methods, which are predominantly univariate and struggle to simultaneously satisfy aggregation constraints and exploit inter-variable correlations. To overcome this, we propose a multivariate joint reconciliation framework that explicitly incorporates the correlation structure among variables into the reconciliation process—marking the first such approach to move beyond traditional univariate, independent reconciliation. Built upon a multivariate regression framework, our method integrates base forecasts with covariance information and achieves coherent predictions across both variables and hierarchy levels by minimizing a multivariate loss function. Empirical evaluations on both simulated data and real-world Brazilian employment statistics demonstrate that the proposed approach significantly outperforms state-of-the-art methods, yielding markedly improved forecast accuracy.

This work addresses the challenge of non-identifiability and sensitivity to structural breaks, outliers, and time-varying volatility in decomposing trend and multiple seasonal components from time series. The authors propose a Bayesian nonparametric regression framework that, through adaptive regularization and Markov chain Monte Carlo (MCMC) inference, establishes the first rigorous identifiability conditions for trend and multi-seasonal effects. This approach enables robust decomposition even in the presence of abrupt changes, anomalies, and heteroskedasticity, while delivering principled uncertainty quantification. Empirical evaluations on both synthetic and real-world datasets demonstrate superior performance over state-of-the-art methods such as TBATS, STR, and MSTL, yielding more accurate, interpretable, and reliable decompositions. An open-source R package implementing the method is made publicly available to the research community.

This study addresses the lack of systematic evaluation of stationarity-inducing transformations across diverse non-stationary time series. The authors construct synthetic datasets encompassing trend, seasonality, and heteroskedasticity, complemented by real-world airport passenger flow data, and conduct 3,528 controlled experiments evaluating 14 transformation methods across seven forecasting models and three prediction horizons. Innovatively, stationarity is assessed via consensus from ten statistical tests, and mediation analysis elucidates underlying mechanisms. Results challenge the common assumption that transformations universally improve forecasts: matched transformations enhance accuracy in only 18% of cases; log or Box–Cox transformations are effective for heteroskedastic data (60–65% of cases); and differencing consistently degrades performance on linear-trend series.

This study addresses the challenge of identifying an unknown number of periodic components in functional time series by proposing a novel information criterion with theoretical consistency guarantees. The method integrates least squares fitting with residual process analysis and employs an iterative strategy to adaptively estimate the number of periodicities, making it applicable to a broad class of functional time series models. Extensive numerical simulations demonstrate that the proposed criterion performs exceptionally well in finite samples. Furthermore, its practical utility and effectiveness are corroborated through real-data applications to temperature and sunspot records, where it successfully uncovers statistically significant periodic structures.