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Load & Plot Gold Data

#Load-&-Plot-Gold-Data
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Time Series of Daily Gold Returns

#Time-Series-of-Daily-Gold-Returns
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Looking at Daily Returns Histogram 2015 - 2018

#Looking-at-Daily-Returns-Histogram-2015---2018
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Looking at Daily Returns Histogram since May 2018

#Looking-at-Daily-Returns-Histogram-since-May-2018
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Looking at Standard Deviations

#Looking-at-Standard-Deviations

Standard Deviation 2015 -2018

#Standard-Deviation-2015--2018
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Standard Deviation since May 2018

#Standard-Deviation-since-May-2018
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Testing statistical significance

#Testing-statistical-significance

Hypothesis Test

H0 :σx2 = σy2 versus H1 :σx2 != σy2

Sx2/Sy2 ∼ Fn−1,m−1

PH0 {F1−α/2,n−1,m−1 ≤ Sx2/Sy2 ≤ Fα/2,n−1,m−1} = 1 − α

Thus, a significance level α test of H0 against H1 is to

accept H0 if F1−α/2,n−1,m−1 < Sx2/Sy2 < Fα/2,n−1,m−1

reject H0 otherwise

Significance level α = 5 %

For 2015 - 2018 dataset

#For-2015---2018-dataset

Levene test

#Levene-test
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The Levene test tests the null hypothesis that all input samples are from populations with equal variances.

=> Result here does not rejct H0 since p-value is above significance level of 5%

It can not be infered that there is a difference between the variances in the population.

ANOVA

#ANOVA

ANOVA is used to compare the means of three or more samples

An ANOVA will provide an F-statistic which can, along with degrees of freedom, be used to calculate a p value.

ANOVAs assume independence of observations, homogeneity of variances and normally distributed observations within groups.

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=> Result here does not rejct H0 since p-value is way above significance level of 5%

-> under H0 we obtain the test statistic from this sample with 99.9 %

For May - Aug 2018 dataset

#For-May---Aug-2018-dataset

Levene test

#Levene-test
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=> Result here does reject H0 since p-value is below significance level of 5%

ANOVA

#ANOVA
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Ambiguous results -> small dataset: ANOVA is very sensitive to distributional assumptions => less robust than Levene