1 1 Abstract WAVES AND PERSISTENCE IN MERGER AND ACQUISITION ACTIVITY Corresponding author. Tel. 1+617-552-3673, fax +1-617-552-2308, email baum@bc.edu. John T. Barkoulas Department of Economics and Finance Louisiana TechUniversity Ruston, LA 71272 USA Christopher F. Baum Department of Economics Boston College Chestnut Hill, MA 02467 USA Atreya Chakraborty Charles River Associates Boston, MA 02116 USA Markov regime-switching and sine-wave models have been used to cap￾ture the apparent wave-like behavior in aggregate U.S. merger and ac￾quisition (M&A) activity. In this paper we offer an alternative char￾acterization of the dynamic structure in M&A activity as a strongly dependent or long-memory process. Keywords: mergers, acquisitions, long memory, persistence JEL: G34, C12 1 1 Introduction Empirical evidence on the time series structure of aggregate merger and acquisition (M&A) activity in the U.S. economy has attracted considerable attention in the literature. The question that frequently arises is whether merger activity occurs in EwavesF, that is, whether there are oscillations between low and high levels of merger activity. The answer to this question is important both in forecasting M&A activity and in developing structural models of its stochastic behavior. Recent researchhas made signiGcant progress in deGning EwavesF and econometri￾cally estimating the wave-like behavior in merger activity. The Grst formal testing of the merger wave hypothesis models aggregate merger activity as a two-state Markov￾switching-regime model (Town, 1992). In this statistical framework, a merger wave is deGned as a large, discrete increase in the mean of the series. Wave-like M&A activity is consequently modeled as a combination of two AR processes withdiffering means with the transition from a high-wave (high-mean) state to a low-wave (low-mean) state based upon some probability law. Town Gnds that such a model Gts M&A time series behavior well, thus supporting the wave hypothesis. Golbe and White (1993) provide a second direct test of merger wave behavior based on sine-curve estimations for the M&A time series. They Gnd that the coefficient estimate for the amplitude of the sine wave, which is the critical parameter for the wave hypothesis, is statistically signiGcant, and thus conclude that the Gtted model adequately describes the temporal patterns of aggregate merger activity. They hypothesize a cycle length for merger activity of about forty years based upon the value of the coefficient estimate for the period of the wave. Contrary to Golbe and WhiteJs model, merger activity exhibits stretches of high and low values with no obvious hidden or strict periodicity. These temporal patterns of cyclic but nonperiodic behavior appear to be distinct phenomena that embody essential aspects of the data. We argue that this tendency to observe groups of high or low values in merger 2 2 2 This behavior has been called the EJoseph effectF by Mandelbrot and Wallis (1968) in reference to the Old Testament prophet who foretold of the seven years of plenty followed by the seven years of famine that Egypt was to experience. activity is consistent withan underlying data generating process exhibiting long memory or strong dependence. A long-memory process can give rise to suchstretches, or waves, which occur without any regularity in either time of occurrence or duration. If a time series exhibits the long-memory (long-term dependence) property, persistent temporal dependence exists even between distant observations. Suchseries exhibit hyperbolically declining autocorrelations and low-frequency peaks in their spectral distribution. If long memory is a feature of the temporal behavior of M&A activity, a shock to M&A activity persists for a long time, even though it eventually dissipates. To uncover persistent dependence in M&A activity, we estimate the long-memory or fractional-differencing parameter using the Gaussian semiparametric and exact maxi￾mum likeli