Time Series Seasonal Analysis Based on Fuzzy Transforms

Abstract

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.

Quantile and expectile smoothing based on L1-norm and L2-norm fuzzy transforms

“…Definition 6. An L 1 -norm direct F -transform of a function f : [a, b] → R on the r-partition (P, A, r) is any (n + 2r − 2)-tuple of real numbers (G 2−r , ..., G n+r−1 ), where each G k minimizes the function k in (12).…”

“…The Fuzzy transform (F-transform) has been introduced by I. Perfilieva [32]; the books [31] and [35] contain recent and complete analysis of its possible implications for fuzzy modeling. The recent literature on F-transform is very rich, ranging from theoretical aspects [5,17,29,39,40,49,61] to applications in several fields of computational intelligence (see [10][11][12]30,33,34,[36][37][38]47,48]).…”

Seasonal Time Series Forecasting by F1-Fuzzy Transform

“…The ADANN method is applied by implementing the ADANN algorithm in References [17,28,29]; based on the experimental tests we have carried out, we apply a GA algorithm with a stopping criterion of 200 generations to search the optimal number of the input and hidden layer nodes. The TSSF method is applied implementing the TSSF algorithm in Reference [22].…”

“…In References [21,22], a novel forecasting algorithm is proposed by using the direct and inverse F-transform, called the Time Series Seasonal F-transform (TFSS). In the TFSS, a polynomial fitting is applied to evaluate the trend of the time series.…”

A classification algorithm based on multi-dimensional fuzzy transforms

“…The F-transform algorithm is a technique used to approximate an original function "f", of which a priori only a finite number values is known, but the expression of the function itself is unknown. The F-transform concept has been used in image processing (Di Martino and Sessa 2007, 2019a, b, 2020Di Martino et al 2008), data analysis (Di Martino et al 2010Martino et al , 2011Di Martino and Sessa 2017a, b, 2019a, b, 2020Novak et al 2014;Formato et al 2014;Perfilieva et al 2008)…”