Detecting Structural Breaks with a Fusion Penalty
Type
working paper
Date Issued
2019-06
Author(s)
Abstract
In this paper, an L1-norm fusion penalty is added to detect structural breaks in a linear regression with time-varying parameters. The method is a more flexible extension of the method introduced in Qian and Su (2016). The idea of the fusion penalty is to start with the most general model and shrink the differences of parameters consecutive in time to zero. At points, at which the differences between the estimated parameters are non-zero, structural breaks are detected. The main advantage of the fusion penalty over the standard statistical tests is the flexibility of the model and allowing number of breaks to grow with the length of the time series. Regarding the estimation, an important issue is the optimal choice of shrinkage otherwise the number of breaks is over- or underestimated and/or the estimates are extremely biased. To select the optimal shrinkage, two criteria are taken from the literature and one new is introduced in the paper. If the method finds the correct number of breaks, it is proven that the time of the break is estimated consistently. In the simulation study, the criteria are compared to each other and to standard tests in terms of the correct number of detected breaks, the closeness to the true position of the break and the bias of the estimates. The results show that the relative position of the break can be consistently estimated. In small samples the criteria from the literature tend to underestimate the number of breaks and the parameters are strongly biased. The newly introduced criterion performs better regarding the bias and has better or comparable performance regarding the detection of the correct number of breaks in comparison to the other chosen criteria and the standard tests.
Keywords
structural breaks
fused lasso
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