Time Series Seasonal Analysis Based on Fuzzy Transforms

Ferdinando Di Martino,Salvatore Sessa

doi:10.3390/sym9110281

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.

Highlights

Time series forecasting methods are quantitative techniques that analyse historical data of a variable for predicting its values
After de-trending the data by subtracting the trend from the time series dataset, we find a fuzzy partition of the dataset into seasonal subsets to which we apply the F-transforms by checking that the chosen partition is optimal for the density of the training data
In order to test the reliability of the forecasting results obtained by using the four forecasting methods, we have considered test datasets containing the measure of the analysed parameter in a time period and calculating the Root Mean Square Error (RMSE)

Summary

Introduction

Time series forecasting methods are quantitative techniques that analyse historical data of a variable for predicting its values. Traditional forecasting methods [1, 2, 3, 4, 14, 19, 20] use statistical techniques to estimate the future trend of a variable starting from numerical datasets. Different approaches have been developed to deal with trend and seasonal time series. Traditional approaches, such the moving average method, additive and multiplicative models, Holt-Winters exponential smoothing, etc. [3, 4, 14, 20], use statistical methods for removing the seasonal components: they decompose the series into trend, seasonal, cyclical and irregular components [32]. Other statistical approaches are based on the Box–Jenkins model, called

Objectives

Methods

Conclusion