Find jumps in the trend of a time series.

What is it about?

The Hodrick–Prescott filter is a popular tool in macroeconomics for decomposing a time series into a smooth trend and a business cycle component. The last few years have witnessed global events, such as the Global Financial Crisis, the COVID-19 pandemic, and the war in Ukraine, that have had abrupt structural impacts on many economic time series. Moreover, new regulations and policy changes generally lead to similar behaviours. Thus, those events should be absorbed by the trend component of the trend-cycle decomposition, but the Hodrick–Prescott filter does not allow for breaks. We propose a modification of the Hodrick–Prescott filter that contemplates breaks and automatically selects the time points at which the breaks occur. We provide efficient implementation of the new filter in an R package. We use our new filter to assess the impact of Italian labour market reforms on employment in different age groups.

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Why is it important?

The Hodrick-Prescott filter is widely used in economic time series analysis, but it can only produce a smooth trend. The trend of many economic time series has undergone abrupt changes, and our modification of the filter can identify these breaks and incorporate them into an otherwise smooth trend. The method is implemented in the R package "jumps" available on CRAN.