Trend Filtering Techniques for Time Series Analysis
Author
López Arias, DanielAdvisor
Dorronsoro Ibero, José RamónEntity
UAM. Departamento de Ingeniería InformáticaDate
2016-06Subjects
InformáticaNote
Master of Investigation and Innovation in Information and Communications TechnologyEsta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
Time series can be found almost everywhere in our lives and because of this being capable
of analysing them is an important task. Most of the time series we can think of are quite
noisy, being this one of the main problems to extract information from them. In this work
we use Trend Filtering techniques to try to remove this noise from a series and understand
the underlying trend of the series, that gives us information about the behaviour of the
series aside from the particularities that it can have when we look at it. We can also easily
learn by using Trend Filtering the points when the trend of the series changes.
We begin this work introducing the elements of the convex optimization theory, that
are key to solve the Trend Filtering problem. Then this problem is tackled as a convex
optimization one and we nd the solution to a number of di erent variations on this
problem. Some extensions to Trend Filtering are also explored, specially Polished Trend
Filtering, which uses the points that Trend Filtering nds to be those where the trend
changes to construct a more precise model.
Finally, we apply this technique to analyse and forecast the energy demand on Spain,
comparing our results with those of an autoregressive model, nding that, for short-term
predictions, Polished Trend Filtering can outperform it.
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