Cross correlations between risk-factor return series
Many risk-factor returns are correlated with each other in the same time period. However, in the same way that there tends to be only weak serial correlation within series, there tends to be only weak cross correlation between series in different time periods.
The picture changes dramatically when we look at the absolute values, which are often strongly correlated both within and between series.
In this exercise, you will investigate cross correlations between the daily log-returns of the Dow Jones, FTSE100 and SMI equity indexes. When the function acf() is applied to a multivariate time series, we obtain a matrix of plots with the usual sample acf plots on the diagonal, and plots of the correlations between different series at different lags off the diagonal.
One thing to note here is that the US and European series are slightly out of step. The European markets tend to follow the US, so we see some evidence of cross correlation between US returns on one day and European returns on the next.
This exercise is part of the course
Quantitative Risk Management in R
Exercise instructions
- Make a time series plot of
indexeswithplot.zoo()and a pairwise scatterplot withpairs(). - Calculate the sample correlation matrix of
indexesusingcor(). - Plot the sample autocorrelation functions and cross-correlation functions for
indexesusingacf(). - Plot the sample autocorrelation functions and cross-correlation functions for the absolute values of
indexes.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Make a time series plot of indexes with plot.zoo and a pairwise scatterplot with pairs
___(___)
___(___)
# Calculate the sample correlation matrix of indexes
cor(___)
# Plot the sample acfs and cross-correlation functions for the returns in indexes
acf(___)
# Plot the sample acfs and cross-correlations functions for the absolute values of indexes
___(___)