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Related Concept Videos

Types of Skewness01:09

Types of Skewness

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If the frequency distribution of a data set is more inclined towards smaller or larger values, the distribution is said to be skewed. If data values are skewed to the right, then the distribution is called positively skewed. Conversely, if the plot is skewed to the left, the distribution is called negatively skewed.
For instance, in the middle of a pandemic, the geographical distribution of vaccine coverage may be positively skewed towards populations in the global north countries. However,...
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Skewness01:06

Skewness

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The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency...
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Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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Modified Boxplots00:57

Modified Boxplots

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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
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Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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On improved volatility modelling by fitting skewness in ARCH models.

P Mantalos1, A Karagrigoriou2, L Střelec3

  • 1Department of Economics and Statistics, Linnaeus University, Vaxjo, Sweden.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

This study introduces robust tests for skewness in financial volatility models like GARCH-GJR, addressing deviations from normal distributions. The proposed methods enhance the analysis of financial data by accurately detecting skewness.

Keywords:
ARCH/GARCH modelNoVaSRobust test for normalitykurtosisskewness

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Area of Science:

  • Econometrics
  • Financial Modeling
  • Statistical Inference

Background:

  • Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized ARCH (GARCH) models are widely used in finance.
  • Deviations from normality, particularly skewness, are common in financial data and can impact model performance.
  • Existing normality tests may not be robust to these deviations.

Purpose of the Study:

  • To develop and evaluate robust statistical tests for detecting skewness in financial time series data.
  • To specifically address normality assumptions in ARCH/GARCH models, including GARCH-GJR but excluding EGARCH.
  • To propose a novel testing procedure for skewness within autoregressive conditional volatility models.

Main Methods:

  • Development of robust normality tests applicable to original and transformed data (NoVaS and modified NoVaS).
  • Application of these tests to GARCH-GJR models, acknowledging limitations for EGARCH.
  • Investigation of test power through simulations using various underlying data-generating processes.

Main Results:

  • The proposed robust tests demonstrate effectiveness in detecting skewness in financial data.
  • The novel test procedure for skewness in conditional volatility models is shown to be applicable.
  • Simulation results confirm the power of the developed tests across different model specifications.

Conclusions:

  • The developed robust tests provide a valuable tool for assessing normality assumptions in financial volatility modeling.
  • The proposed skewness testing procedure enhances the reliability of analyses involving ARCH/GARCH-type models.
  • Empirical applications highlight the practical utility and capability of the new testing framework for financial data analysis.