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This study decomposes the trend-cycle components of the stock market indices of the United States and China in a time series framework over the period of 1980–2021, and 1992–2021 years, respectively. Using the extended Kalman filter (EKF) method, the changing dynamics of stock market prices can be analysed more effectively since stock market prices can have a nonlinear pattern, and the EKF allows estimated system parameters to change over time under the nonlinear state-space model. As the impacts of shocks to trend and cycle on the stock market can be observed more efficiently due to flexible time-varying parameter estimation, the EKF offers more reasonable results than other decomposition tools. The empirical findings of this study prove that the EKF extracts the trend and cycle components by giving quite consistent forecasts for stock market prices in both advanced and emerging market countries.

An analysis of stock market prices by using extended Kalman filter: The US and China cases