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There are many events that recur. These are evident either directly in time series or through their effects on economic outcomes. Examples include business and financial cycles, crises, high and low levels of volatility and sentiment, and floods and droughts. There are three key issues that need to be dealt with when discussing recurrent events. These are: (i) the description of the event via a set of statistics; (ii) the uses that can be made of these statistics; and (iii) the possibility of predicting these events, in particular by using information sets that contain more information than just calendar time. It pays to consider the basic issues involving recurrent events in the context of a simple example, and that is the modus operandi of this overview chapter.

The chapter discusses a particular way of producing rules to summarize the nature of the recurrent events. These rules come from the idea that the data incorporating the recurrent event can be captured by models that specify a number of regimes, and then using the information provided by the fitted model to date the recurrent event. The chapter discusses variants of Markov switching models in the context where there is only a single series in which the recurrent event is observed. It then deals with dating cycles with univariate series. Finally, it considers model-based rules for dating events with multivariate series.

This chapter presents methods for capturing the synchronization of recurrent events in bivariate and multiple series. The special features of the unconditional densities of binary series recommend the use of moment-based measures of synchronization. It looks at similarity across events in terms of a range of features, such as amplitudes. It then looks at the situation when model-based rules are used to define them, and further gives an application of the methods to studying the synchronization of cycles in industrial production across countries. The question often arises of whether there is synchronization of the events across a number of industries, countries, and so on. This involves multivariate synchronization and this is studied in the chapter. Finally, the chapter examines the relationship between the synchronization of cycles and the comovement in the continuous variables in which those cycles occur.

This chapter begins with a discussion of why we would expect to find that the time spent in expansions (bull markets, etc.) would be much greater than the time spent in contractions (bear markets, etc.). By focusing on the probabilities of getting particular outcomes for the binary variables summarizing the recurrent events, we can provide an explanation of this long-observed feature. The remainder of the chapter looks at many proposals for summarizing other features of the recurrent events. These involve well-known quantities such as durations and amplitudes, as well as lesser known ones, such as the sharpness of peaks and troughs.

This chapter looks at using the binary states describing the recurrent events to help in either constructing economic models of time series or evaluating the fit of such models. The chapter provides a general discussion of the issues that come up when using the binary states in regressions. It then turns to the analysis of complete economic models. In these it is very common to see variance decompositions computed and used to draw conclusions about which shocks are responsible for the recurrent events. It is shown that this methodology is flawed when it comes to shedding light on what causes the business cycle. What can be done is investigated in the chapter, which illustrates how to determine which shocks are important to a matching of the business cycle features discussed in Chapter 5. The discussion moves on to some economic models that have been constructed in the wake of the global financial crisis and which aim to highlight the role of financial shocks.

The chapter looks at how recurrent events might be dated by using a number of series rather than a single one. There is no one method to do this, but in many cases, the procedures come up with rather similar results. Much depends on how one wants to use the dating information. If it is for judging models or evaluating some macroeconomic propositions, then the ability to automate the selection process easily would be a paramount consideration. Alternatively, if it was desired to establish a definitive dating of cycles in activity or financial series, then it is probably the case that a variety of methods would be used with some judgment applied when determining the weight given to each. Further work is needed on how the methods perform when faced with simulations from estimated models rather than using actual data, as their effectiveness is unclear in such a changed environment.