Time Series Seasonal Analysis Based on Fuzzy Transforms

Abstract

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of an assigned output. In the first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 to 2015 making predictions on mean temperature, max temperature and min temperature, all considered daily. In the second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, Auto Regressive Integrated Moving Average (ARIMA) and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples. In addition, the comparison results show that, for seasonal time series that have no consistent irregular variations, the performance obtained with our method is comparable with the ones obtained using Support Vector Machine- and Artificial Neural Networks-based models.

Keywords

• ARIMA
• forecasting
• fuzzy partition
• fuzzy transform
• time series