Abstract
AbstractA common challenge in time series is to forecast data that suffer from structural breaks or changepoints which complicate modeling. If we naively forecast using one model for the whole data, the model will be incorrect, and thus, our forecast error will be large. There are two common practices to account for these changepoints when the goal is forecasting: (1) preprocess the data to identify the changepoints, incorporating them as dummy variables in modeling the whole data, and (2) include the changepoint estimation into the model and forecast using the model fit to the last segment. This article examines these two practices, using the computationally exact Pruned Exact Linear Time (PELT) algorithm for changepoint detection, comparing and contrasting them in the context of an important Software Engineering application.
Highlights
Structural breaks and changepoints occur in time series data arising from a variety of fields including; medicine1, environment2,3, psychology4 and finance5
This paper considers the different methods for accounting for changepoints when forecasting time series and compares and contrasts them
We have shown that these two approaches have different strengths depending on the dynamics of the data
Summary
Structural breaks and changepoints occur in time series data arising from a variety of fields including; medicine, environment, psychology and finance. The class of time series models we use for forecasting are seasonal Autoregressive Moving Average (ARMA). If the data are subject to changepoints, propose to only use post-break data to estimate the time series model used for forecasting. They estimate the location of the break to be the most recent changepoint which is obtained using a reversed CUSUM procedure. In each of the approaches, in order to detect changepoints, we use a penalized cost function approach which solves the constrained minimization problem exactly In such a setting, given a sequence of observations {yi}i=1,...,n, the aim is to find the number of changes, m, and the associated changepoints, {τj}j=1,...,m, which minimize: m+1.
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