Semiparametric Time Series Modelling
A natural question that arises in time series is: can we reconstruct the input signal in a non-parametric way? Identifying the input or innovation process in a non-parametric way, while modeling the dynamics in a parametric way leads to a semi-parametric time series model.
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Non-parametric methods in time series are well known. Schuster's periodogram was applied in 1898 to disprove Knott's hypothesis that earthquakes are a periodic phenomenon, while later it was used to analyse the periodicity of Sunspots. Nonetheless, such non-parametric periodogram based methods are typically considered an exploratory tool to understand the dynamics present in time series data. In that paradigm, such a non-parametric analysis can be used as a preparatory step towards a parametric model building within the Autoregressive(-Integrated) Moving Average (ARIMA) framework.
Time series analysis is somewhat complementary to system identification where the most important difference is the experimental design and the proceeding data analysis. In system identification, one has access to the input and output time series whereas in time series analysis only the output time series is measurable such that the input time series is typically denoted as the innovation process. A natural question that arises in time series is: can we reconstruct the input signal in a non-parametric way? Identifying the input or innovation process in a non-parametric way, while modeling the dynamics in a parametric way leads to a semi-parametric time series model.
In this lecture, we will explore this question. A reconstruction in the strict sense is not possible however we will see that by virtue of Wold's decomposition theorem a proxy of the innovations driving the time series can be built. Furthermore, we check the scenarios where one should prefer such a semi-parametric time series model. It is particularly advantageous when the innovation process exhibits non-stationarities while the dynamics remain time-invariant. This aspect will be illustrated by the COVID-19 pandemic.
Kurt Barbé
Kurt Barbé received the master’s degree in mathematics (specialising in applied mathematics and statistics) and the Ph.D. degree in engineering from Vrije Universiteit Brussel (VUB), Brussels, Belgium, in 2005 and 2009, respectively. He is currently a Professor with the Department of Biostatistics and Medical Informatics, VUB. Furthermore, he is the founder of VUB's core-facility on statistics supporting researchers in their quantitative data-analysis. His current research interests include numerical methods for time series analysis, in particular long-memory time series arising from fractional Ornstein–Uhlenbeck processes for applications in bioimpedance and biomedical dielectric spectroscopy. Recently, his team customized random forest and random subspace methods for dealing with time series data for applications in dosimetry for cancer as well as muscle fatigability measurements in elderly patients.
Dr. Barbé was a postdoctoral Research Fellow with the Flemish Research Foundation and the VUB-Coordinator of FLAMES—the Flemish interuniversity training network on research methodology and statistics. He was a member of the Editorial Board of the Journal of Stochastics and The Scientific World: Probability and Statistics from 2013 to 2016. He was a recipient of the Outstanding Young Engineer Award from the IEEE Instrumentation and Measurement Society in 2011 and the Andy Chi Best Paper Award of the IEEE Transactions on Instrumentation and Measurement in 2013. Currently, he is the senior area editor of the IEEE Transactions on Instrumentation and Measurement in the area of medical, biomedical and healthcare instrumentation and measurement and serves in the steering committee (AdCom) of the IEEE Instrumentation and Measurement Society and the royal Statistical Society of Belgium.
Teacher/speaker
Kurt Barbé
Kurt Barbé received a master’s degree in mathematics (specialising in applied mathematics and statistics) and a PhD degree in engineering from Vrije Universiteit Brussel (VUB), Brussels, Belgium, in 2005 and 2009, respectively. He is currently a Professor at the Department of Biostatistics and Medical Informatics, VUB. Furthermore, he is the founder of VUB's core-facility on statistics supporting researchers in their quantitative data-analysis. His current research interests include numerical methods for time series analysis, in particular long-memory time series arising from fractional Ornstein–Uhlenbeck processes for applications in bioimpedance and biomedical dielectric spectroscopy. Recently, his team customized random forest and random subspace methods for dealing with time series data for applications in dosimetry for cancer as well as muscle fatigability measurements in elderly patients.
Dr Barbé was a postdoctoral Research Fellow with the Flemish Research Foundation and the VUB-Coordinator of FLAMES—the Flemish interuniversity training network on research methodology and statistics. He was a member of the Editorial Board of the Journal of Stochastics and The Scientific World: Probability and Statistics from 2013 to 2016. He was a recipient of the Outstanding Young Engineer Award from the IEEE Instrumentation and Measurement Society in 2011 and the Andy Chi Best Paper Award of the IEEE Transactions on Instrumentation and Measurement in 2013. Currently, he is the senior area editor of the IEEE Transactions on Instrumentation and Measurement in the area of medical, biomedical and healthcare instrumentation and measurement and serves in the steering committee (AdCom) of the IEEE Instrumentation and Measurement Society and the royal Statistical Society of Belgium.
AI for Time Series
Several research groups in the Flanders AI Research Program conduct world-class research on time series, both in the development of algorithms and tools, as in a wide area of application fields. In a recent poll in the Flanders AI community, ‘time series’ came up as the most wanted topic for future workshops or courses. With this seminar series, we bring together researchers that are interested in, or are conducting research related to, time series. We offer a varied program of national and international speakers.
Klik on the separate webinars below to (re)watch the recordings.
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