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

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.