Statistics and Its Interface

Volume 10 (2017)

Number 1

Testing trend stationarity of functional time series with application to yield and daily price curves

Pages: 81 – 92

DOI: http://dx.doi.org/10.4310/SII.2017.v10.n1.a8

Authors

Piotr Kokoszka (Department of Statistics, Colorado State University, Fort Collins, Co., U.S.A.)

Gabriel Young (Department of Statistics, Colorado State University, Fort Collins, Co., U.S.A.)

Abstract

Econometric and financial data often take the form of a collection of curves observed consecutively over time. Examples include intraday price curves, term structure curves, and intraday volatility curves. Such curves can be viewed as functional time series. A fundamental issue that must be addressed, before an attempt is made to statistically model or predict such series, is whether they can be assumed to be stationary with a possible deterministic trend. This paper extends the KPSS test to the setting of functional time series. We propose two testing procedures: Monte Carlo and asymptotic. The limit distributions of the test statistics are specified, the procedures are algorithmically described and illustrated by application to yield curves and daily price curves.

Keywords

functional data, daily price curves, integrated time series, random walk, trend stationarity

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