Extracting Conditionally Heteroskedastic Components using Independent Component Analysis

Jari Miettinen, Markus Matilainen, Klaus Nordhausen*, Sara Taskinen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
21 Downloads (Pure)

Abstract

In the independent component model, the multivariate data are assumed to be a mixture of mutually independent latent components. The independent component analysis (ICA) then aims at estimating these latent components. In this article, we study an ICA method which combines the use of linear and quadratic autocorrelations to enable efficient estimation of various kinds of stationary time series. Statistical properties of the estimator are studied by finding its limiting distribution under general conditions, and the asymptotic variances are derived in the case of ARMA-GARCH model. We use the asymptotic results and a finite sample simulation study to compare different choices of a weight coefficient. As it is often of interest to identify all those components which exhibit stochastic volatility features we suggest a test statistic for this problem. We also show that a slightly modified version of the principal volatility component analysis can be seen as an ICA method. Finally, we apply the estimators in analysing a data set which consists of time series of exchange rates of seven currencies to US dollar. Supporting information including proofs of the theorems is available online.

Original languageEnglish
Pages (from-to)293-311
JournalJournal of Time Series Analysis
Volume41
Issue number2
DOIs
Publication statusPublished - Mar 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • ARMA-GARCH process
  • asymptotic normality
  • autocorrelation
  • blind source separation
  • principal volatility component

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