arXiv subjects

Jordan Trinka

Publications and source records attributed to Jordan Trinka.

3 recordsLinked to original sources

arXiv2020

Functional Time Series Forecasting: Functional Singular Spectrum Analysis Approaches

In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of functional singular spectrum analysis and past observations in order to predict future data points where recurrent forecasting predicts one function at a time and the vector forecasting makes predictions using functional vectors. We compare our forecasting methods to a gold standard algorithm used in the prediction of functional, time-dependent data by way of simulation and real data and we find our techniques do better for periodic stochastic processes.

stat.ML↗

arXiv2020

Multivariate Functional Singular Spectrum Analysis Over Different Dimensional Domains

In this work, we develop multivariate functional singular spectrum analysis (MFSSA) over different dimensional domains which is the functional extension of multivariate singular spectrum analysis (MSSA). In the following, we provide all of the necessary theoretical details supporting the work as well as the implementation strategy that contains the recipes needed for the algorithm. We provide a simulation study showcasing the better performance in reconstruction accuracy of a multivariate functional time series (MFTS) signal found using MFSSA as compared to other approaches and we give a real data study showing how MFSSA enriches analysis using intraday temperature curves and remote sensing images of vegetation. MFSSA is available for use through the Rfssa R package.

stat.ME↗

arXiv2019

Functional Singular Spectrum Analysis

In this paper, we introduce a new extension of the Singular Spectrum Analysis (SSA) called functional SSA to analyze functional time series. The new methodology is developed by integrating ideas from functional data analysis and univariate SSA. We explore the advantages of the functional SSA in terms of simulation results and two real data applications. We compare the proposed approach with Multivariate SSA (MSSA) and dynamic Functional Principal Component Analysis (dFPCA). The results suggest that further improvement to MSSA is possible, and the new method provides an attractive alternative to the dFPCA approach that is used for analyzing correlated functions. We implement the proposed technique to an application of remote sensing data and a call center dataset. We have also developed an efficient and user-friendly R package and a shiny web application to allow interactive exploration of the results.

stat.ME↗