DeepAI AI Chat
Log In Sign Up

Some recent trends in embeddings of time series and dynamic networks

by   Dag Tjøstheim, et al.

We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal components for time series, the literature on time-varying nonlinear embedding is rather sparse. The most promising approaches in the literature is neural network based, and has recently performed well in forecasting competitions. We also touch upon different forms of dynamics in topological data analysis. The last part of the paper deals with embedding of dynamic networks where we believe there is a gap between available theory and the behavior of most real world networks. We illustrate our review with two simulated examples. Throughout the review, we highlight differences between the static and dynamic case, and point to several open problems in the dynamic case.


Topological Data Analysis (TDA) for Time Series

The study of topology is strictly speaking, a topic in pure mathematics....

Topological Time Series Analysis

Time series are ubiquitous in our data rich world. In what follows I wil...

Testing for explosive bubbles: a review

This review discusses methods of testing for explosive bubbles in time s...

Dynamic and interpretable hazard-based models of traffic incident durations

Understanding and predicting the duration or "return-to-normal" time of ...

Nonlinear Time Series Classification Using Bispectrum-based Deep Convolutional Neural Networks

Time series classification using novel techniques has experienced a rece...

Consistency of Generalized Dynamic Principal Components in Dynamic Factor Models

We study the theoretical properties of the generalized dynamic principal...

Mixed Membership Models for Time Series

In this article we discuss some of the consequences of the mixed members...