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Related Concept Videos

Time-Series Graph00:54

Time-Series Graph

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...
Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
First Derivative Test: Problem Solving01:25

First Derivative Test: Problem Solving

Imagine an asset price that crashes to a low point, rebounds sharply as bargain-hunters step in, and then gradually declines. Such behavior can be modeled with a smooth function whose turning points represent locally overvalued and undervalued regions. A convenient example that captures rebound followed by decay is:The high and low points of this curve are identified using the first derivative test, which determines where the function changes from increasing to decreasing or vice versa. To...
Relative Frequency Histogram01:14

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
Properties of Fourier series I01:20

Properties of Fourier series I

The Fourier series is a powerful tool in signal processing and communications, allowing periodic signals to be expressed as sums of sine and cosine functions. A foundational property of the Fourier series is linearity. If we consider two periodic signals, their linear combination results in a new signal whose Fourier coefficients are simply the corresponding linear combinations of the original signals' coefficients. This property is crucial in applications like frequency modulation (FM) radio,...
Properties of Fourier series II01:21

Properties of Fourier series II

Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...

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Related Experiment Videos

Forbidden patterns in financial time series.

Massimiliano Zanin1

  • 1Universidad Autónoma de Madrid, 28049 Madrid, Spain. massimiliano.zanin@hotmail.com

Chaos (Woodbury, N.Y.)
|April 2, 2008
PubMed
Summary
This summary is machine-generated.

Forbidden patterns analysis reveals deterministic behavior in financial time series like stock indices and bond rates. This method, related to permutation entropy, offers a robust way to study complex economic data dynamics.

Related Experiment Videos

Area of Science:

  • Time Series Analysis
  • Chaos Theory
  • Financial Econometrics

Background:

  • Forbidden patterns are a novel tool for time series analysis, offering insights into data dynamics.
  • Permutation entropy, related to forbidden patterns, shares properties with classic chaos indicators.
  • This method is effective for small datasets and requires fewer data points than traditional chaos indicators.

Purpose of the Study:

  • To investigate the presence of forbidden patterns in various financial time series.
  • To identify evidence of deterministic behavior in economic indicator evolutions.
  • To analyze the rate of forbidden pattern appearance and suggest underlying dynamics.

Main Methods:

  • Analysis of forbidden patterns in time series data.
  • Calculation of the rate of forbidden pattern appearance.
  • Application to financial indicators: Dow Jones Industrial Average, Nasdaq Composite, NYSE stocks (IBM, Boeing), and 10-year Bond interest rate.

Main Results:

  • Evidence of deterministic behavior was found in the studied financial time series.
  • The rate of forbidden pattern appearance was calculated for each indicator.
  • The study suggests underlying deterministic dynamics in economic indicator evolutions.

Conclusions:

  • Forbidden patterns analysis is a viable method for detecting deterministic behavior in financial markets.
  • The findings contribute to understanding the complex dynamics of economic indicators.
  • This approach provides a new perspective on time series analysis in econometrics.