Paper: A Novel Time Series Forecasting Method Based on Fuzzy Visibility Graph

Problem

define a fuzzy visibility graph (undirected weighted graph), then give a new similarity measure of time series.

Problem: 1. some significant information of the time series, such as trend information is lost by using visibility graph. 2. the original method for constructing visibility graphs is very sensitive to noise.

Keywords

fuzzy visibility graph

What they did

they transform the time series into an undirected weighted graph, which include more edges than original VG method.

Related work

visibility graph

Methodology

1. convert time series into fuzzy visibility graphs.

the weight of the edge between each two nodes is the visibility.

2. the similarity of two time series

Time series forecasting method:

1. divide time window

X is divided into n - m + 1 subsequences with a window of length m and a step size of 1:

2. construct fuzzy visibility graphs

adjacency matrix A_i.

3. construct the difference subsequences;

difference sequence

the first-order difference sequence Dsi, which reflects the change trend of the subsequence C_i

4. calculate similarities between subsequences

calculate the similarities between C_n-m+1 and the front n-m subsequences.

5. calculate the predicted value at time t_n+1

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Results

the proposed method can obtain better prediction results on small-scale data sets.