The recent economy internationalization, the market integration process and the perspective of obtaining differentiated conditions through scale led to production restructuring and fomented a higher economic concentration by means of continuous mergers and acquisitions of companies. This scenario inserts the study of the variability and persistence of growth rates of accounting indicators of companies among the most relevant subjects of corporate finance. The accounting variables selected in this work were the annual growth rates of the gross revenue, of the EBITDA and of the operating profit of companies listed at São Paulo Stock Exchange (BOVESPA) during the period 1994-2002. The observed variability and the non persistence of the growth rates represents a relevant obstacle to forecasting exercises in the Brazilian market. Additional simulations were performed, in order to test the effect of the firms` size and of the transaction multiples of their respective stocks ont growth rates. Looking for a deeper understanding of the strong resistance to the persistence of consecutive annual rates above market median values along the eight years period of analysis, econometric tests essential to ARIMA model (Box and Jenkins) were applied, and the resuts portrayed the non correlation and non-partial correlation between the annual growth rates for all variables, characterizing a classical white noise process, signaling a typical random walk or a random walk with drift behavior.