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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
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An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
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An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this...
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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
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A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show comparisons among categories. The bars can be rectangles, or they can be rectangular boxes (used in three-dimensional plots). One axis of the graph represents the specific categories being compared, and the other axis shows a discrete value. In this graph, the length of the bar for each category is proportional to the number or percent of individuals...
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Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Visibility Graph Based Time Series Analysis.

Mutua Stephen1,2, Changgui Gu1, Huijie Yang1

  • 1Business School, University of Shanghai for Science and Technology, Shanghai 200093, China.

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Summary
This summary is machine-generated.

This study introduces visibility graph time series analysis, a novel network method. It transforms time series into networks of networks, offering rich data for stock market and fractional Gaussian motion predictions.

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Area of Science:

  • Complex Systems
  • Network Science
  • Time Series Analysis

Background:

  • Network-based time series analysis offers insights into microscopic and macroscopic behaviors.
  • Existing static network approaches limit the understanding of evolutionary dynamics in time series data.

Purpose of the Study:

  • To introduce a novel method for time series analysis using visibility graphs.
  • To convert time series into a temporal network and a network of networks for enhanced analysis.
  • To leverage network of networks perspective for time series investigation.

Main Methods:

  • Mapping time series segments to visibility graphs to represent states.
  • Linking successively occurring states to form a temporal network.
  • Constructing a network of networks from the temporal network.

Main Results:

  • Empirical analysis on US stock markets (S&P500, Nasdaq) and fractional Gaussian motions.
  • Demonstrated ability to provide rich information for both short-term and long-term predictions.
  • Validation of the network of networks approach for time series analysis.

Conclusions:

  • Visibility graph time series analysis provides a powerful framework for understanding time series dynamics.
  • The network of networks perspective offers novel insights into temporal data.
  • The method shows promise for predictive modeling in financial markets and complex systems.