Due to the complex nature of stock market, determining the stock market timing - when to buy or sell is a challenge for stock investors. There are two basic methodologies used in financial time series analysis - fundamental and technical. Fundamental analysis depends on external factors, such as economic environment, industry performance and company performance, but it is an arduous task to find out the external factors as many as possible and evaluate every factor’s weightiness. Technical analysis utilizes financial time series data, such as stock price and trading volume, to measure current movement or predict the future. Technical analysis is based on a theory that, at any given point in time, time series data already reflects all known factors affecting supply and demand for that particular market [7]. Trend following (TF) is an investment strategy based on the technical analysis of market prices. Trend followers do not aim to forecast or predict specific price levels. They simply jump on the uptrend and ride on it until the end of this uptrend. Most of trend followers determine the establishment and termination of uptrend based on their own peculiar reasons or rules. In this thesis, we propose a TF algorithm which employs three pairs of thresholds to determine the stock market timing. The optimal values of thresholds are obtained by Particle Swarm Optimization (PSO) and Simulated Annealing (SA). The experiment result demonstrates that our TF algorithm is effective.