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Peaks, gaps, and time‐reversibility of economic time series

By locating the running maxima and minima of a time series, and measuring the current deviation from them, it is possible to generate processes that are relevant for the analysis of the business cycle and for characterizing bull and bear phases in financial markets. First, the measurement of the time distance from the running peak originates a first‐order Markov chain, whose characteristics can be used for testing time‐reversibility of economic dynamics and specific types of asymmetries in financial markets. Second, the gap processes can be combined to provide a non‐parametric measure of the growth cycle. The article derives the time series properties of the gap process and other related processes that arise from the same measurement context, and proposes new non‐parametric tests of time‐reversibility and new measures of the output gap.