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Kurtosis

Definition

In probability theory and statistics, kurtosis is a measure of the "tailedness" of the probability distribution of a real-valued random variable. In a similar way to the concept of skewness, kurtosis is a descriptor of the shape of a probability distribution and, just as for skewness, there are different ways of quantifying it for a theoretical distribution and corresponding ways of estimating it from a sample from a population. Depending on the particular measure of kurtosis that is used, there are various interpretations of kurtosis, and of how particular measures should be interpreted.

Kurtosis

What is 'Kurtosis'

Kurtosis is a statistical measure that's used to describe the distribution, or skewness, of observed data around the mean, sometimes referred to as the volatility of volatility. Kurtosis is used generally in the statistical field to describes trends in charts. Kurtosis can be present in a chart with fat tails and a low, even distribution, as well as be present in a chart with skinny tails and a distribution concentrated toward the mean.

Explaining 'Kurtosis'

Put simply, kurtosis is a measure of the combined weight of a distribution's tails relative to the rest of the distribution. When a set of data is graphically depicted, it usually has a standard normal distribution, like a bell curve, with a central peak and thin tails. However, when kurtosis is present, the tails of the distribution are different than they would be under a normal bell-curved distribution.

Types of Kurtosis

There are three categories of kurtosis that can be displayed by a set of data. All measures of kurtosis are compared against a standard normal distribution, or bell curve.


Kurtosis FAQ

What kurtosis tells us?

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers.

How do you interpret kurtosis?

The general guideline for the interpretation of kurtosis is that if the number is greater than +1, then the distribution is too peaked. But if kurtosis' number is less than –1, it shows a flat distribution. Distributions exhibiting skewness and/or kurtosis that exceed these guidelines are considered non-normal." (Hair et al., 2017, p.

What does a kurtosis of 3 mean?

If the kurtosis is greater than 3, then the data set is said to have heavier tails than a normal distribution. When the kurtosis is less than 3, then the data set is interpreted to be more light-tailed than a normal distribution.

What is the normal range for kurtosis?

Both skew and kurtosis can be interpreted through descriptive statistics. Acceptable values of skewness fall between − 3 and + 3, and kurtosis is appropriate from a range of − 10 to + 10 when using SEM (Brown, 2006).

What is normal kurtosis?

The kurtosis of any univariate normal distribution is 3. It is therefore usual to contrast the kurtosis of a distribution to this value. Distributions whose kurtosis value is less than 3 are called platykurtic, although, this does not automatically mean that the distribution is "flat-topped" as is sometimes stated.

What is kurtosis in statistics with example?

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers. There are three types of kurtosis; mesokurtic, leptokurtic, and platykurtic.

What is a kurtosis in statistics?

Kurtosis is a statistical measure of data. It is done to determine whether it is heavy-tailed or light-tailed in comparison to a normal distribution. Data sets with high kurtosis are interpreted to be heavy-tailed/outliers, while data sets with low kurtosis are interpreted to be light-tailed/lack of outliers.

Further Reading

Autoregresive conditional volatility, skewness and kurtosisAutoregresive conditional volatility, skewness and kurtosis
www.sciencedirect.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Autoregressive conditional kurtosisAutoregressive conditional kurtosis
academic.oup.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Modeling asymmetry and excess kurtosis in stock return dataModeling asymmetry and excess kurtosis in stock return data
papers.ssrn.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Co‐kurtosis and capital asset pricingCo‐kurtosis and capital asset pricing
onlinelibrary.wiley.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Persistence and kurtosis in GARCH and stochastic volatility modelsPersistence and kurtosis in GARCH and stochastic volatility models
academic.oup.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Kurtosis of GARCH and stochastic volatility models with non-normal innovationsKurtosis of GARCH and stochastic volatility models with non-normal innovations
www.sciencedirect.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

A note on skewness and kurtosis adjusted option pricing models under the Martingale restrictionA note on skewness and kurtosis adjusted option pricing models under the Martingale restriction
www.tandfonline.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Conditional volatility, skewness, and kurtosis: existence, persistence, and comovementsConditional volatility, skewness, and kurtosis: existence, persistence, and comovements
www.sciencedirect.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Do investors dislike kurtosis?Do investors dislike kurtosis?
papers.ssrn.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …

Kurtosis as Peakedness, 1905–2014. Kurtosis as Peakedness, 1905–2014.
www.tandfonline.com [PDF]
This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t …


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