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When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
The proliferation of mobile devices has led to the collection of large amounts of population data. This situation has prompted the need to utilize this rich, multidimensional data in practical applications. In response to this trend, we…
Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic, operator-valued filters,…
Time series analysis finds wide applications in fields such as weather forecasting, anomaly detection, and behavior recognition. Previous methods attempted to model temporal variations directly using 1D time series. However, this has been…
We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while…
Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…
Time series classification is a task that aims at classifying chronological data. It is used in a diverse range of domains such as meteorology, medicine and physics. In the last decade, many algorithms have been built to perform this task…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
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…
Time series forecasting has always been a thought-provoking topic in the field of machine learning. Machine learning scientists define a time series as a set of observations recorded over consistent time steps. And, time series forecasting…
Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for…
We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Forecast combinations have been widely applied in the last few decades to improve forecasting. Estimating optimal weights that can outperform simple averages is not always an easy task. In recent years, the idea of using time series…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
Systems are commonly monitored for health and security through collection and streaming of multivariate time series. Advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible…
Forecasting is an indispensable element of operational research (OR) and an important aid to planning. The accurate estimation of the forecast uncertainty facilitates several operations management activities, predominantly in supporting…
Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of…
A key challenge when designing particle filters in high-dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution. Recent advances in particle flow filters provide a promising avenue…