In time series problems often arise that involve large discrete solution spaces. It may happen that either searching such spaces cannot be accomplished by exhaustive enumeration or satisfactory methods do not exist which are able to yield the optimal solution for problems of moderate and large size. For instance, some nonlinear model parameter estimation, subset autoregression (possibly including moving average terms), outlier identification, clustering time series are all tasks that require the right combination of several parameters to be discovered. General local search methods, also called metaheuristics, or general heuristics, proved to be able to offer useful procedures that may solve such combinatorial-like problems in reasonable computing time. We consider the three most popular general local search methods, that is simulated annealing, tabu search and genetic algorithms. Their increasingly wide application in several fields, including many “classical” problem (graph coloring, vehicle routing and salesman traveling, for instance), prompted the use of such methods in statistics and, in particular, in time series analysis. Examples of procedures will be discussed, and some comparisons between metaheuristics and well established techniques will be presented. Then, suggestions for future developments will be briefly outlined which include, for instance, filter design and wavelet filtering, outlier detection in vector time series, and threshold autoregressive moving average models
