Detecting deviations from second-order stationarity in locally stationary functional time series
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Date
2018
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Abstract
A time-domain test for the assumption of second order stationarity of a
functional time series is proposed. The test is based on combining individual cumulative
sum tests which are designed to be sensitive to changes in the mean, variance and
autocovariance operators, respectively. The combination of their dependent p-values
relies on a joint dependent block multiplier bootstrap of the individual test statistics.
Conditions under which the proposed combined testing procedure is asymptotically
valid under stationarity are provided. A procedure is proposed to automatically choose
the block length parameter needed for the construction of the bootstrap. The finitesample
behavior of the proposed test is investigated in Monte Carlo experiments and
an illustration on a real data set is provided.
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Keywords
alpha-mixing, change points, block multiplier bootstrap, auto-covariance operator, CUSUM-test