Timely identification of turning points in economic time series is important for planning control actions and achieving profitability. This paper compares sequential methods for detecting peaks and troughs in stock values and deciding the time to trade. Three semi-parametric methods are considered: double exponential smoothing, time-varying parameters and prediction error statistics. These methods are widely used in monitoring, forecasting and control, and their common features are recursive computation and exponential weighting of observations. The novelty of this paper is the selection of smoothing and alarm coefficients for maximisation of the gain (the difference in level between subsequent peaks and troughs) of sample data. The methods are compared on applications to leading financial series and with simulation experiments.