Summary. Leading economic indicators are often used to anticipate changes in key economic variables. Understanding the dynamics of these indicators is of primary interest for policy-making objectives and for sustainable economic welfare. We are concerned with the problem of setting a dynamic threshold above which the value of leading indicators would be considered as extreme. We propose a dynamic threshold modelling approach based on fractionally integrated processes where a semiparametric method is used to determine the amount of differencing that is required to obtain a weakly stationary process—to which standard methods of statistics of extremes apply. Given that our approach is linked to the Box–Jenkins method, we refer to the procedure proposed and applied herein as the Box–Jenkins–Pareto procedure. We use our approach to analyse the weekly number of unemployment insurance claims in the USA and explore the connection between its threshold exceedances and the US business cycle.