Model based Level Shift Detection in Autocorrelated Data Streams using a moving window
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Standard Control Chart techniques to detect level shift in data streams assume independence between observations. As data today is collected with high frequency, this assumption is seldom valid. To overcome this, we propose to adapt the off-line test procedure for detection of outliers based on one-step prediction errors proposed by Tsay (1988) into an on-line framework by considering a moving window. Further, we present two algorithms, that in combination, estimate an appropriate test value for our control chart. We test our method on AR(1) processes exposed to level shifts of different sizes and compare it to CUSUM applied to one-step prediction errors. We find that, even though both methods perform comparable when tuned correctly, our method has higher probability of identifying the correct change point of the process. Furthermore, for more complicated processes our method is easier to tune, as the range of window size to be tested is independent of the process.
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