Exercise

# Characteristics of financial time series

Daily financial asset returns typically share many characteristics. Returns over one day are typically small, and their average is close to zero. At the same time, their variances and standard deviations can be relatively large. Over the course of a few years, several very large returns (in magnitude) are typically observed. These relative outliers happen on only a handful of days, but they account for the most substantial movements in asset prices. Because of these extreme returns, the distribution of daily asset returns is not normal, but heavy-tailed, and sometimes skewed. In general, individual stock returns typically have even greater variability and more extreme observations than index returns.

In this exercise, you'll work with the `eu_percentreturns`

dataset, which is the percentage returns calculated from your `eu_stocks`

data. For each of the four indices contained in your data, you'll calculate the sample mean, variance, and standard deviation.

Notice that the average daily return is about 0, while the standard deviation is about 1 percentage point. Also apply the hist() and qqnorm() functions to make histograms and normal quantile plots, respectively, for each of the indices.

Instructions

**100 XP**

- Use colMeans() to calculate the sample mean for each column in your
`eu_percentreturns`

data. - Use apply() to calculate the sample variance for each index. Leave the
`MARGIN`

argument at`2`

and set the`FUN`

argument to`var`

. - Use another call to
`apply()`

to calculate the standard deviation for each index. Keep the`MARGIN`

argument at`2`

but this time set the`FUN`

argument to`sd`

. - Use a third call to
`apply()`

to display a histogram of percent returns for each index. - Use a final call to
`apply()`

to display normal quantile plots for each index.