Test for monotonic trend with seasonal effects in time series data
LE3 .A278 2016
Master of Science
Mathematics and Statistics
Mathematics & Statistics
Observational values may be recorded on a daily, weekly, monthly or quarterly basis over a certain time period. One way of detecting trend in seasonal time series data is to apply the seasonal Mann-Kendall test statistic on the data set. The current method of this test statistic assumes that the data over time are serially independent while taking into account the autocovariance between seasons. In this thesis, we instead assume that the underlying process of the data has some form of time dependence within seasons. We used the bootstrap method, both the block and the autoregressive sieve (AR-sieve), to capture these time dependence patterns. We relied on the theory of U-statistics when stationary time series data follow weakly dependent processes, so that an approximation to the limiting distribution of the seasonal Mann-Kendall test statistic could be obtained. Based on this approximation, the method developed was applied to real-world applications.
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