Empirical Economics (2002) 27:149–162 EMPIRICAL ECONOMICS ( Springer-Verlag 2002 New directions in business cycle research and financial analysis James D. Hamilton1, Baldev Raj2 1 Department of Economics, 0508, University of California, San Diego, La Jolla, CA 92093- 0508 (e-mail: jhamilton@ucsd.edu) 2 School of Business and Economics, Wilfrid Laurier University, 75 University Aveneu, Waterloo, Ontario, Canada N2L 3C5 (e-mail: braj@wlu.ca) First Version Received: August 2001/Final Version Received: October 2001 Abstract. This paper serves as a partial introduction to and survey of the literature on Markov-switching models. We review the history of this class of models, describe their mathematical structure, and exposit the basic ideas behind estimation and inference. The paper also describes how the approach can be extended in a variety of directions, such as non-Gaussian distributions, time-varyingtransitionprobabilities,vectorprocesses,state-spaceandGARCH models, and surveys recent methodological advances. The contributions of the other papers in this volume are reviewed. A final section o¤ers conclusions and implications for policy. Key words: Markov-switching, regime-switching, business cycles JEL classification: C32, E32 1. Introduction: The basic Markov-switching framework The normal behavior of economies is occasionally disrupted by dramatic events that seem to produce quite di¤erent dynamics for the variables that economists study. Chief among these is the business cycle, in which capitalist economies depart from their normal growth behavior and a variety of in- dicators go into decline. Other examples include currency crises, stock market bubbles, and sharp changes in the volatility of asset prices or exchange rates. One natural way to describe such features is with an autoregressive pro- cess. Suppose that y t represents the growth rate of real GDP in quarter t. In normal times, its dynamic behavior might be well characterized with a first- order autoregression, y t ¼ c 1 þ f 1 y t1 þ e t ;