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Relative Frequency Histogram01:14

Relative Frequency Histogram

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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...
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Relative Frequency Distribution00:55

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A relative frequency distribution is the proportion or fraction of times a value occurs in a data set. To find the relative frequencies, one can divide each frequency by the total number of data points in the sample. It is very similar to a regular frequency distribution, except that instead of reporting how many data values fall in a class, a relative frequency distribution reports the fraction of data values that fall in a class. These fractions or proportions are called relative frequencies...
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The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Dependency Structures in Cryptocurrency Market from High to Low Frequency.

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We analyzed cryptocurrency price correlations across various time scales, observing that finer time resolutions decrease inter-cryptocurrency correlation. Coarser resolutions reveal evolving hierarchical structures and shifting roles of major cryptocurrencies.

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Area of Science:

  • Quantitative Finance
  • Computational Economics
  • Network Science

Background:

  • Cryptocurrency markets exhibit complex interdependencies.
  • Understanding these relationships across different time scales is crucial for risk management and investment strategies.
  • Previous studies often focus on single time horizons, limiting insights into dynamic market structures.

Purpose of the Study:

  • To investigate the evolution of cross-correlations among 25 cryptocurrencies on the FTX exchange.
  • To analyze how network structures (MST and TMFG) change with varying time resolutions (15 seconds to 1 day).
  • To assess the stability, significance, and economic relevance of these evolving networks.

Main Methods:

  • Logarithmic price return cross-correlation analysis.
  • Construction and analysis of Minimum Spanning Trees (MST) and Triangulated Maximally Filtered Graphs (TMFG).
  • Examination of network properties across a spectrum of time resolutions.

Main Results:

  • Cryptocurrency correlations decrease at finer time resolutions (e.g., 15 seconds).
  • Network structures become more interconnected and hierarchical at coarser time resolutions (e.g., 1 day).
  • Mainstream cryptocurrencies show dynamic shifts in their hierarchical reference roles within the network.

Conclusions:

  • The hierarchical organization of cryptocurrency markets is time-dependent and evolves with sampling frequency.
  • Finer time scales reveal less correlated, more fragmented market behavior.
  • Coarser time scales highlight emergent structures and the changing influence of key digital assets.