Abstract: Multi-resolution wavelet analysis is an important method to decompose economic time series into periodic, trend, and noise components. Empirical analysis of China's real GDP data using multi-resolution wavelets shows that the use of biorthogonal 17/11 filtering can clearly reflect the "expansion" and "contraction" phases of China's economic cycle. In the "expansion" stage, the volatility of the economic cycle is relatively weak, while in the "contraction" stage, the volatility of the economic cycle is relatively intense. After 2010, the volatility of China's economic cycle gradually weakens, and the overall economic operation shows a stable trend.

Key words: economic cycle; double orthogonal 17/11 filtering; multi-resolution wavelet analysis