Exercises

  1. Random Walk without Drift

    • Set the seed of R's RNG to \(111\).
    • Generate \(100\) normally distributed random numbers with mean \(0\) and standard deviation \(1\) and save your results in a variable wn.
    • Calculate the random walk without drift and save it in the variable rw_wo_drift.
    • Plot the random walk as a dashed red line.
    • Take a look at your neighbour's display. It should show the same result as yours.

  2. Random Walk with Drift

    • Generate \(100\) normally distributed random numbers with mean \(0\) and standard deviation \(1\) and save your results in a variable wn_drift.
    • Calculate the random walk with drift, use \(\mu = 0.2\), and save it in the variable rw_drift.
    • Use your results from the first exercise and visualize both random walks in one plot with colors and linetypes of your choice.
    • Add a legend to the plot.

  3. Portmanteau Tests

    • Use the function Box.test() to calculate the Box - Pierce and Ljung - Box test statistic for both random walks.
    • Make a decision by using the functions output.
    • Use the diff() function to compute the lagged differences of the random walk without drift. Calculate the Box - Pierce and Ljung - Box test statistic for the differenced time series.
    • What kind of stochastic process is the result of a differenced random walk without drift?