TIME SERIES BEHAVIOR OF MERGERS & ACQUISITIONS: A “MARKOV MEAN-FILTERING” APPROACH

Abstract

A novel framework for modelling the time series behavior of US aggregate merger levels is developed using a Markov regime-based filter (“Markov mean-filter”) that identifies and eliminates the effects of aperiodic mean shifts in the series. The filter proves advantageous in both its ease of implementation and its ability to capture Markov regime properties into an autoregressive scheme without explicit incorporation, allowing operational flexibility while maintaining replicability and accuracy. The performance of the filter is measured against a traditional ARIMA approach, and marked improvements in both characterization and forecasting are demonstrated. Forecasts using rolling windows both within the observation period and beyond the period were tested, the latter of which prompted the characterization of the probability of a merger “wave” occurring. The probabilities were measured using estimated Markov state transition probabilities and properties of the first-order Markov chain.