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Testing stationarity of functional time series


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  • Horváth, Lajos
  • Kokoszka, Piotr
  • Rice, Gregory


Economic and financial data often take the form of a collection of curves observed consecutively over time. Examples include, intraday price curves, yield and term structure curves, and intraday volatility curves. Such curves can be viewed as a time series of functions. A fundamental issue that must be addressed, before an attempt is made to statistically model such data, is whether these curves, perhaps suitably transformed, form a stationary functional time series. This paper formalizes the assumption of stationarity in the context of functional time series and proposes several procedures to test the null hypothesis of stationarity. The tests are nontrivial extensions of the broadly used tests in the KPSS family. The properties of the tests under several alternatives, including change-point and I(1), are studied, and new insights, present only in the functional setting are uncovered. The theory is illustrated by a small simulation study and an application to intraday price curves.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 179 (2014)
Issue (Month): 1 ()
Pages: 66-82

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Handle: RePEc:eee:econom:v:179:y:2014:i:1:p:66-82

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Related research

Keywords: Change point; Functional data; Integrated time series; Intraday price curves; Test of stationarity;

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