Forecasting portfolio returns using weighted fuzzy time series methods

• Present a new weighted fuzzy time series (FTS) method to forecast portfolio returns.
• Generating trapezoidal numbers as fuzzy forecasts of the portfolio returns.
• Possibilistic moments approximate the uncertain parameters of the fuzzy portfolio.
• Compare performances of fuzzy and non-fuzzy methods using a Spanish IBEX35 data set.
• Assess the statistical significance of our FTS method for improving forecast accuracy.

We propose using weighted fuzzy time series (FTS) methods to forecast the future performance of returns on portfolios. We model the uncertain parameters of the fuzzy portfolio selection models using a possibilistic interval-valued mean approach, and approximate the uncertain future return on a given portfolio by means of a trapezoidal fuzzy number. Introducing some modifications into the classical models of fuzzy time series, based on weighted operators, enables us to generate trapezoidal numbers as forecasts of the future performance of the portfolio returns. This fuzzy forecast makes it possible to approximate both the expected return and the risk of the investment through the value and ambiguity of a fuzzy number.We incorporate our proposals into classical fuzzy time series methods and analyze their effectiveness compared with classical weighted fuzzy time series models, using historical returns on assets from the Spanish stock market. When our weighted FTS proposals are used to point-wise forecast portfolio returns the one-step ahead accuracy is improved, also with respect to non-fuzzy forecasting methods.