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The purpose of this paper is to investigate the sources of the apparent episodic stationarity of the P/E ratio.

The Stock–Watson procedure is used to decompose a VAR/VMA model into changes in structure and changes volatility. In theory, if the P/E ratio is properly anticipated and shocks are random, according to Samuelson's proof, it should exhibit the characteristics of a pure martingale and therefore it should not be possible to statistically reject trend nonstationary.

Using a rolling window, the P/E ratio is shown to have episodic periods when trend nonstationarity could be rejected and that the P/E ratio was not properly anticipated. However, if there were changes in the structure of the underlying P/E ratio model or changes in the volatility of the underlying model, it suggests that the shocks impacting the P/E ratio would not be random and it might be possible to reject nonstationarity. This is investigated further with the objective of determining whether there was underlying structural change or volatility changes that are associated with these periods when trend nonstationarity in the P/E ratio could be rejected. The results are tested and found to be robust to a number of different specifications examined, including different data periods and frequencies.

Results findings should be tested in other countries and in other periods.

The paper developed a methodology whereby it is possible to detect periods there the P/E ratio is not properly anticipated.