Suppression of High Frequencies in Time Series Using Fuzzy Transform of Higher Degree

Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets

“…However, by the fact that the lower the degree of m is the better the reduction of irregular fluctuation is (i.e. the smaller the values of , —see Nguyen and co‐workers (Holčapek & Nguyen, 2016; 2018; Nguyen & Holčapek, 2018)), we have to choose m as small as possible. A rule of thumb says that if the observed trend‐cycle is a nearly linear function then we should choose m =0 or m =1; otherwise, choose m =2 or m =3. Choosing the bandwidth h Let be the residuum of the time series after subtracting the inverse F‐transform.…”

“…Recently, a novel approach to this issue has been introduced using monomial bases that make it possible to compute the components in a way that is simpler than the original one (see Nguyen et al 2017; Holčapek & Nguyen, 2018; Holčapek et al 2018). This simplifies applications of the F‐transform; for applications in time‐series analysis and elsewhere, see, for example, Holčapek and Nguyen (Holčapek & Nguyen, 2016; 2018; Nguyen & Holčapek, 2018) and Novák et al (2016).…”

F-Transform Inspired Weak Solution to a Boundary Value Problem

“…Let us remind readers that sufficient conditions on the triplet (K, α, N) for constructing a generalized uniform fuzzy partitions of [a, b] are given in [12,17]. Moreover, from Definition 3, one can see that there are at most 2(τ + 1) basic functions that cover an arbitrary point in [a, b]…”

“…Below, we consider the European put option problem [23] as a particular case of Black-Scholes equation (17) with the following boundary and initial conditions:…”