The market price-earnings ratios differ from those of each share. Despite allowing for several pertinent analyses, authors have rarely addressed these valuation ratios in the Brazilian context. We can use it to evaluate whether the stock market is overvalued (undervalued). In this article, we analyze the mean reversion in a price-earnings ratio based on Ibovespa and identify periods of overvaluation (undervaluation) in the Brazilian stock market. We considered the period from December 2004 to

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... ne 2018. Until then, there are no studies that sought to identify periods of overvaluation (undervaluation) in this market. In the analyses, we used non-linear econometric methods. We analyzed the mean reversion in the price-earnings ratio using a unit root test that incorporates a Fourier function in the deterministic term. We identified the periods of market overvaluation (undervaluation) through the regime probabilities obtained from a Markov Switching model, estimated with the price-earnings ratio. The results evidenced that the price-earnings ratio based on the Ibovespa has a non-linear trend and exhibits mean reversion. Thus, this valuation ratio should provide information on the future stock market returns, mostly when it is very dispersed in relation to historical standards. We identified four periods of market overvaluation interposed with five periods of market undervaluation. Mean reversion in the price-earnings ratio contraposes the Efficient Markets Hypothesis. There are no other applications of unit root tests with a Fourier function in the Brazilian context. Furthermore, adopting a Markov Switching model to identify periods of market overvaluation (undervaluation) consists of a methodological contribution. Investors can take advantage of the identification of these periods to establish investment strategies.