Abstract
This article deals with problems of detecting abrupt changes in time series ba Change Point Model (CPM) framework. We propose a fuzzification in a Fuzzy Time Series (FTS) model to eliminate a trend in a contaminated dependent series. The independent residuals are then inputed on the CPM method. In simulating an abrupt change, an ARIMA(1,1,1) and variance of the model are considered. The abrupt change is modelled as an AO (Additive Outlier) type of outliers. The minimum weight or breaksize of the abrupt change is defined based on the ARIMA variance formulated in this article. The percentage of uncorrelated residuals obtained by the FTS model and the percentage of correct detection of the proposed procedure are shown by simulation. The proposed detecting algorithm is implemented to detect abrupt changes in monthly tourism series in literature, i.e., in Taiwan and in Bali. The first series shows a slowly increasing trend with one abrupt change while the second series exhibits not only a slowly increasing trend but also a strong seasonal pattern with two abrupt changes. For comparison, we detect the changes in the empirical examples on an existing automatic detection procedure using tso package in R. For the first example, the results show that both detecting procedures give exactly a similar location of one change point where the package recognises it as an AO type of outliers. The abrupt change is related to the period of SARS outbreak in Taiwan. On the second example, the proposed procedure locates 4 change points which form two locations of changes, i.e., the first two change points are within 2 time points so do the last two change points. The locations are closed to times of Bali Bombing events. Meanwhile, the automatic procedure recognizes only one AO outlier on the series.
Highlights
Structural breaks in a time series statistically mean that there is at least a shift in their distributional parameters, e.g., in mean and/or in variance
As the variance of ARIMA model depends on the time observation, we report the variance of ARIMA models at particof the observation at the targeted change point T
We briefly review some definitions in fuzzy sets, fuzzy time series, and fuzzy logical relationship in [24], [12] and [13], respectively
Summary
Structural breaks in a time series statistically mean that there is at least a shift in their distributional parameters, e.g., in mean and/or in variance. A decline trend of tourist arrivals following 2002 Bali Bombing had a short run-effect on Bali and other famous tourist destinations in Indonesia [2]. A good news, the effects of terrorist attacks in 2002 and 2005 on the number of tourist arrivals in Bali is transitory [3]. The authors imply that these considered changes occur at any instant times during the observations, treating, in some sense, that characteristics of the series are constants before and after the changes. Structural breaks in a time series are shown by changes only on some parts in the time series plot
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