Dynamic panel fuzzy time series model and its application to econometric time series
Introduction
Fuzzy time series (FTS) models are widely used in time series forecasting due to the ability of modeling the time series that are incomplete, vagueness and linguistic. FTS model firstly proposed by Song and Chissom [1] consists of three main steps as fuzzification, determining fuzzy relations and forecasting and defuzzification. In the fuzzification step, crisp time series is converted into fuzzy time series. For this objective, fuzzy sets, correspond to classical time series should be determined for the time series under consideration via partitioning universe of discourse or via fuzzy clustering. The second step includes determining fuzzy relations between successive fuzzy sets. In the last step, firstly, fuzzy forecasts are obtained based on fuzzy relations and then fuzzy forecasts are converted to classical ones. So far, many FTS models have been developed to improve the prediction and forecasting performance. While some of these studies have focused on improving of the fuzzification step [2], [3], [4], [5], [6], [7], [8], some studies have focused on step of determining of fuzzy relations [8], [9], [10], [11], [12]. The developed FTS models have been applied to the time series in many fields, including finance [13], [14], atmospheric [15], [16], environment [7], [17], [18] etc.
But, in these studies, each time series is evaluated individually and thus, local FTS model is constructed for each time series even if large number of time series relating to same variable exist. In this study, Dynamic Panel Data Fuzzy Time Series (DPDFTS) approach is proposed to handle a large number of time series simultaneously. The first advantage of proposed approach is to find global fuzzy sets and fuzzy relations in the fuzzification step. Thanks to this property, once FTS models are constructed with proposed approach, they can be used for modeling a new time series relating to same variable as well. The second advantage is to able to deal with the time series with small sample size since it is based on combining a large number of time series. As can be understood, DPFTS can only use in case that there exist more than two time series relating to same variable, and it is proposed for only this kind of problems.
The remainder of the study is organized as follows. Section 2 presents the fundamental concepts relating to FTS. Section 3 introduces the DPFTS. Section 4 gives the experimental results and then the study is concluded in the last section.
Section snippets
Fuzzy time series
Basic concepts of fuzzy time series are given as below.
Let be universe of discourse, a fuzzy set defined in U can be described as follows: Where is membership function of and .
Definition 1 () is a subset of . Let be the universe of discourse U defined by fuzzy sets . is called as fuzzy time series if it consists of .
Definition 2 If there is a relationship between and denoted as ,
Dynamic panel fuzzy time series model
Panel data analysis is widely used statistical technique to analyze the cross-sectional data, which have time dimension. It is understood, panel data () contains the time series data (, ), which consist of observations collected at a regular time interval, and cross-sectional data (, ), which consist of the observations collected for a unit at a constant time. Panel data analysis utilizes the more information since the number of observations increases. Thus, it yields
Experimental results
In order to evaluate the efficiency of DPFTS and compare it with TFTS, two case studies are performed. In the first case, three versions of both DPFTS and TFTS are applied to the time series artificially generated according to ten different scenarios. The second case includes the real time examples conducted on six econometric variables, each of which consisting of a large number of time series. In both of two case studies, FTS models based on FCM are called as DPFTS1 and TFTS1, FTS models
Conclusion
This study proposes a new FTS approach, based on dynamic panel data analysis and TFTS model. The fundamental objective of proposed approach is to globally estimating FTS models so that a large number of time series represent simultaneously. Three versions of proposed approach, based on FCM (DPFTS1) and GK(DPFTS2) and FKM (DPFTS3) clustering are developed. The performances of these three approaches are compared with their traditional equivalents (TFTS1, TFTS2, TFTS3 respectively). In order to
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (23)
- et al.
Forecasting enrollments with fuzzy time series – Part 1
Fuzzy Sets Syst.
(1993) Heuristic models of fuzzy time series for forecasting
Fuzzy Sets Syst.
(2001)Effective lengths of interval to improve forecasting in fuzzy time series
Fuzzy Sets Syst.
(2001)- et al.
Multi-attribute fuzzy time series method based on fuzzy clustering
Expert Syst. Appl.
(2008) - et al.
A FCM-based deterministic forecasting model for fuzzy time series
Comput. Math. Appl.
(2008) - et al.
Fuzzy time series forecasting method based on Gustafson-Kessel fuzzy clustering
Expert Syst. Appl.
(2011) - et al.
A new fuzzy clustering based on robust clustering for forecasting of air pollution
Ecol. Inform.
(2018) - et al.
A comparison of fuzzy forecasting and Markov modeling
Fuzzy Sets Syst.
(1994) Forecasting enrollments based on fuzzy time series
Fuzzy Sets Syst.
(1996)- et al.
The application of neural networks to forecast fuzzy time series
Physica A
(2006)