Abstract
Detecting and interpreting influential turning points in time series data is a routine research question in many disciplines of applied social science research. Here we propose a method for identifying important turning points in a univariate time series. The most rudimentary methods are inadequate when the researcher lacks preexisting expectations or hypotheses concerning where such turning points ought to exist. Other alternatives are computationally intensive and dependent on strict model assumptions. Our method is fused LASSO regression, a variant of regularized least squares method, providing a convenient alternative for estimation and inference of multiple change points under mild assumptions. We provide two examples to illustrate the method in social science applications. First, we assessed the validity of our method by reanalyzing the Greenback prices data used in (Willard et al. in Am Econ Rev 86:1001–1017, 1996). We next used the method to identify major change points in President Clinton’s approval ratings.
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Notes
- 1.
As a side note, another issue with using \(\ell _1\)-norm penalty is that the estimation is biased. One way to account for this potential bias is to identify the change points by shrinkage and refit the model piecewise between change points under quadratic loss. In an engineering application, Chen et al. (2001) adopted a similar idea in developing their basis pursuit technique. In our simple problem of finding the jumps in a constant mean process, this amounts to computing numeric average of data points.
- 2.
According to the authors, although it did not go into effect until January 1, 1863, the actual structure of the proclamation was a realistic threat since there could no longer be any doubts about Lincoln’s willingness to tolerate slavery. This led people to raise the expected cost of the war.
- 3.
In some cases, our method identified clusters of dates as possible turning points. This is because, with daily data, it is difficult to pinpoint a single date as a turning point in the entire series that consists of over 1,200 days due to lack of information in a single data point. In such cases, therefore, we regard the cluster of dates as one turning point affected by the same series of events. Likewise, the bootstrapped probabilities associated with a single date are fused. Accordingly, for any given time point t, it would be more appropriate to simultaneously consider the probabilities associated with the surrounding dates.
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Hahn, K.S., Son, W., Choi, H., Lim, J. (2018). A Least Squares Method for Detecting Multiple Change Points in a Univariate Time Series. In: Choi, D., et al. Proceedings of the Pacific Rim Statistical Conference for Production Engineering. ICSA Book Series in Statistics. Springer, Singapore. https://doi.org/10.1007/978-981-10-8168-2_9
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