We propose a statistical testing procedure to determine the number of stochastic trends of cointegrated functional time series taking values in the Hilbert space of square-integrable functions defined on a compact interval. Our test is based on a variance ratio statistic, adapted to a possibly infinite-dimensional setting. We derive the asymptotic null distribution and prove consistency of the test. Monte Carlo simulations show good performance of our test and provide some evidence that it outperforms the existing testing procedure. We apply our methodology to three empirical examples: age-specific US employment rates, Australian temperature curves, and Ontario electricity demand.
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