This study improves estimation of locally stationary functional time series using NW method.
problem Accurately capturing time-dependence in locally stationary functional time series with time-varying covariates.
method Nadaraya-Watson (NW) estimation procedure for the conditional distribution of LSFTS.
result Established convergence rates of NW estimator for LSFTS with respect to Wasserstein distance.
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
Paper develops sparse learning for heavy-tailed time series with locally stationary dynamics.
problem Sparse learning for high-dimensional heavy-tailed locally stationary time series.
method Additive modeling with kernel smoothing, sparsity-inducing penalized estimation.
result Prediction-error bounds and convergence rates for different sparsity structures.
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzi…
NAST generalizes scattering transform for non-stationary time series analysis.
problem Analyzing non-stationary time series data.
method Neural activation of scattering transform with various activation functions and high pass filters.
result Central and non-central limit theorems for NAST of Gaussian processes.
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for long time horizons, however, averages over the time-dependent parameters. To model…
A new fuzzy time series method for non-stationary data.
problem Forecasting in non-stationary environments with concept drift.
method Non-Stationary Fuzzy Time Series (NSFTS) with time-varying parameters.
result The method can adapt to dynamic changes in the stochastic process.
We utilize a recently developed genetic algorithm, in conjunction with discrete wavelets, for carrying out successful forecasts of the trend in financial time series, that includes the NASDAQ composite index. Discrete wavelets isolate the local, small scale variations in these non-stationary time series, after which th…
New Hermite series estimator for Spearman rank correlation in non-stationary data.
problem Estimating time-varying Spearman rank correlation efficiently.
method Hermite series based sequential estimator for both stationary and non-stationary settings.
result Competitive performance compared to existing algorithms in simulations and real data.
Proposes a method to forecast non-stationary time series.
problem Challenges of non-stationary conditional distributions in deep learning.
method Bayesian dynamic model + deep conditional distribution model.
result Adapts to non-stationary time series better than state-of-the-art solutions.
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time series for clustering purposes. A robust algorithm for functional data is then app…
Framework for causal signals in non-stationary financial markets.
problem Constructing causal signals in non-stationary financial time series.
method Combines normalized indicators and causally computed derivatives, with hysteresis-based decision mapping.
result Demonstrates risk-reshaping effect with smoother trajectories and reduced drawdowns.
We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)-x(t)and the assumption is that the increment is distribute…
New algorithm uncovers causal relations in non-stationary time series.
problem Discovering causal relations from non-stationary time series data.
method Constraint-based, non-parametric algorithm for semi-stationary time series.
result Algorithm PCMCIΩ identifies causal graph with CI tests. Kernel-based tests detect dependencies in multivariate time series, including stationary and non-stationary data.
problem Detecting dependencies in multivariate time series data, especially non-stationary data.
method Kernel-based statistical tests of joint independence, extending dHSIC to handle both stationary and non-stationary processes.
result Robustly uncovers significant higher-order dependencies in synthetic and real-world data.
Paper introduces MN-DAG for modeling evolving causal relationships in multivariate time series.
problem Modeling causal relationships that evolve over time and occur at different scales.
method Probabilistic generative model based on spectral and causality theories, combined with Bayesian stochastic variational inference.
result MN-CASTLE outperforms baseline models in identifying causal relationships in multivariate time series data.
Study combines VICReg and TNC for better encoding of non-stationary seismic signals.
problem Ineffective self-supervised learning on non-stationary time series.
method Combines VICReg and Temporal Neighborhood Coding (TNC).
result Effective for self-supervised learning on non-stationary seismic signals.
TNC learns time series representations by leveraging temporal neighborhoods.
problem Complex, unlabeled time series data.
method Temporal Neighborhood Coding (TNC) with a debiased contrastive objective.
result TNC outperforms other unsupervised methods in time series clustering and classification.
Bayesian nonparametric method segments multi-sequence time series data.
problem Temporal segmentation of multi-sequence time series data into stationary segments.
method Gaussian process priors and nonparametric distribution for segment partitioning.
result Model effectively segments synthetic and real-time series data.
W-Transformers use wavelets to improve time series forecasting.
problem Forecasting non-stationary time series with long-range dependencies.
method Wavelet-based transformer architecture.
result W-Transformers outperform baseline models on various time series datasets.
A neural RNN model adapts time steps for non-stationary time series data.
problem Modeling and forecasting non-stationary time series with sharp changes.
method RNN-ODE-Adap model using neural ODE and adaptive time steps.
result Consistent estimation of intensity function for Hawkes-type data.
The study analyzes online predictions for non-stationary time series under model misspecification.
problem Analyzing predictive properties of statistical methods in non-stationary time series under model misspecification.
method Defining Kullback-Leibler risk, proving minimax predictive densities for dynamic models, extending results to multiple predictive densities.
result Dynamic random walk models produce exact minimax predictive densities under Gaussian assumptions and semi-martingale processes.
Discrimination between non-stationarity and long-range dependency is a difficult and long-standing issue in modelling financial time series. This paper uses an adaptive spectral technique which jointly models the non-stationarity and dependency of financial time series in a non-parametric fashion assuming that the time…
All too often measuring statistical dependencies between financial time series is reduced to a linear correlation coefficient. However this may not capture all facets of reality. We study empirical dependencies of daily stock returns by their pairwise copulas. Here we investigate particularly to which extent the non-st…
OML-AD detects anomalies in non-stationary time series data.
problem Anomaly detection in non-stationary time series data.
method Online machine learning for anomaly detection.
result OML-AD outperforms state-of-the-art methods in accuracy and efficiency.
I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…
A TTA framework improves forecasting accuracy in non-stationary time series.
problem Improving forecasting accuracy in non-stationary time series.
method Normalization-based test-time adaptation for causal timeseries forecasting and direction classification.
result Normalization-based TTA improves forecasting error in synthetic gradual drift and can even hurt in aggressive norm-only adaptation in financial markets.
Stochastic optimization naturally arises in machine learning. Efficient algorithms with provable guarantees, however, are still largely missing, when the objective function is nonconvex and the data points are dependent. This paper studies this fundamental challenge through a streaming PCA problem for stationary time s…
The paper develops adaptive deep learning methods for nonlinear time series models.
problem Estimating mean functions of non-stationary and nonlinear time series models.
method Develops non-penalized and sparse-penalized DNN estimators for general non-stationary time series, derives minimax lower bounds, and shows the sparse-penalized DNN estimator is adaptive and optimal.
result Sparse-penalized DNN estimator achieves minimax optimal rates for many nonlinear AR models.
We introduce a new loss function for evaluating forecasts and estimate models using it.
problem Lack of a decision-theoretic foundation for evaluating forecasts using the Nash-Sutcliffe efficiency.
method We introduce and analyze the Nash-Sutcliffe loss function and its application in estimating models.
result Nash-Sutcliffe loss provides a decision-theoretic foundation for evaluating and estimating models.
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
problem Ambiguity in translation equivariant functional representations due to insufficient data points.
method Introduce Bayesian convolutional deep sets with task-dependent stationary prior.
result Improves representation quality compared to kernel smoother and non-parametric models.
Deep neural networks improve forecasting of non-stationary time-series data.
problem Forecasting non-stationary time-series data with structural breaks and high volatility.
method Evaluation of DNN models including MLP, CNN, LSTM-RNN, and GRU-RNN on 10 Indian financial stocks.
result DNN models show better performance for single-step forecasting but degrade for multi-step forecasting, especially for long forecast periods.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
We describe the impact of the intra-day activity pattern on the autocorrelation function estimator. We obtain an exact formula relating estimators of the autocorrelation functions of non-stationary process to its stationary counterpart. Hence, we proved that the day seasonality of inter-transaction times extends the me…
We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information ab…
Enhances time-series regression trees with latent factors for robust financial analysis.
problem Handling predictors with measurement error, trends, seasonality, and missing data.
method Integrates latent stationary factors extracted via state-space methods into time-series regression trees.
result Factor-augmented trees provide a reliable approach for macro-finance problems, exemplified by the lead-lag effect between equity volatility and the business cycle.
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …
PyChEst detects changes in non-stationary time series without distributional assumptions.
problem Detecting changes in non-stationary time series data.
method Nonparametric algorithms for consistent detection of multiple changepoints in piece-wise stationary processes.
result PyChEst consistently detects changes without distributional assumptions.
Stanza models complex time series with balance between traditional and deep learning approaches.
problem Capturing long-term structure in non-stationary time series.
method Nonlinear, non-stationary state space model.
result Achieves forecasting accuracy competitive with deep LSTMs, especially for multi-step ahead forecasting.
The paper uses neural networks to forecast time series data.
problem Forecasting high-dimensional stationary processes.
method Encoder-decoder neural network structure to model past observations.
result Upper bounds for forecast error under specific assumptions.
FreDN separates trends and periodicities in non-stationary time series forecasts.
problem Spectral entanglement and computational burden in frequency-domain methods for non-stationary time series.
method FreDN introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain, and uses a ReIm Block to reduce complexity.
result FreDN outperforms state-of-the-art methods by up to 10% on long-term forecasting benchmarks.
We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve the generalised Fourier transform with such a model, and present a family of non-…
Develops a new method to discover causal relationships from nonstationary time series data.
problem Challenges in inferring causal relationships from observational data, especially for nonstationary time series.
method State-Dependent Causal Inference (SDCI) for conditionally stationary time series.
result SDCI can recover underlying causal dependencies with provable identifiability for state-dependent causal structures.
Paper proposes a hybrid model for financial time series prediction using sentiment analysis.
problem Challenges in forecasting in non-stationary, complex environments with heterogeneous data.
method Hybrid model combining GANs with NLP-based sentiment analysis.
result Hybrid model enhances robustness in non-stationary environments.
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. …
New method clusters financial time series into volatility regimes.
problem Finding the number of volatility regimes in nonstationary financial time series.
method Change point detection and clustering of segment distributions.
result Optimized trading strategy based on learned volatility regimes.
Paper develops NW kernel estimator for LSPs with Wasserstein bounds.
problem Capturing nuanced dynamics in time series data with evolving statistical characteristics.
method Nadaraya-Watson kernel smoothing for conditional probability estimation, using Wasserstein and sliced Wasserstein distances.
result Established convergence rates and bounds for NW-based conditional probability estimator in LSPs.