The relationship between stock returns and inflation: new evidence from wavelet analysis

This paper presents a new perspective on the Fisher hypothesis, which states a positive relationship between nominal stock returns and inflation. The new approach is based on a wavelet multiscaling method that decomposes a given time series on a scale-by-scale basis. Empirical results show that there is a positive relationship between stock returns and inflation at the shortest scale (1-month period) and at the longest scale (128-month period), while a negative relationship is shown at the intermediate scales. This indicates that the nominal return results are supportive of the Fisher hypothesis for risky assets in d1 and s7 of the wavelet domain, while the stock returns do not play a role as an inflation hedge at the intermediate scales. The key empirical results show that time-scale decomposition provides a valuable means of testing the Fisher hypothesis, since a number of stock returns and inflation puzzles previously noted in the literature are resolved and explained by the wavelet analysis.