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Business cycles analysis is one of the most important tasks for economists and statisticians. Various methods such as HP filter, BP filter, CF filter spectral analysis and Fourier transformation are used in time series analysis. All of these methods are sensitive to stationarity of time series. Also the traditional methods don't offer information in scale analysis. In this paper we introduce the Wavelet theory and its applications especially to economics .Also decomposition of seasonal GDP of Iran and analysis of business cycles are the other main propose. Results of GDP decomposition show 7 cycles with length of 16-32 quarters and 13 cycles with 8-16 quarters. Volatility analysis implies no change in variance of Wavelet coefficients in prewar and war periods .However volatility of GDP increased in the post war period.
JEL Clarification: C14, C22, C19, E32