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Given a time series in $R^n$ with a piecewise constant mean and independentnoises, we propose an exact dynamic programming algorithm to minimize a leastsquare criterion with a multiscale penalty promoting well-spread changepoints.Such a penalty has been proposed in Verzelen et al. (2020), and it achievesoptimal rates for changepoint detection and changepoint localization. Ourproposed algorithm, named Ms.FPOP, extends functional pruning ideas of Rigaill(2015) and Maidstone et al. (2017) to multiscale penalties. For large signals,$n \geq 10^5$, with relatively few real changepoints, Ms.FPOP is typicallyquasi-linear and an order of magnitude faster than PELT. We propose anefficient C++ implementation interfaced with R of Ms.FPOP allowing to segment aprofile of up to $n = 10^6$ in a matter of seconds. Finally, we illustrate onsimple simulations that for large enough profiles ($n \geq 10^4$) Ms.FPOP usingthe multiscale penalty of Verzelen et al. (2020) is typically more powerfullthan FPOP using the classical BIC penalty of Yao (1989).

Ms.FPOP: An Exact and Fast Segmentation Algorithm With a Multiscale Penalty