Exercise

# Simulate the random walk model with a drift

A random walk (RW) need not wander about zero, it can have an upward or downward trajectory, i.e., a drift or time trend. This is done by including an intercept in the RW model, which corresponds to the slope of the RW time trend.

For an alternative formulation, you can take the cumulative sum of a constant mean white noise (WN) series, such that the mean corresponds to the slope of the RW time trend.

To simulate data from the RW model with a drift you again use the `arima.sim()`

function with the `model = list(order = c(0, 1, 0))`

argument. This time, you should add the additional argument `mean = ...`

to specify the drift variable, or the intercept.

Instructions

**100 XP**

- Use
`arima.sim()`

to generate another RW model. Set the`model`

argument equal to`list(order = c(0, 1, 0))`

to generate a RW-type model and set`n`

equal to`100`

to produce 100 observations. Set the`mean`

argument to`1`

to produce a drift. Save this to`rw_drift`

. - Use
`ts.plot()`

to plot your`rw_drift`

data. - Use
`diff()`

to calculate the first difference of your`rw_drift`

data. Save this as`rw_drift_diff`

. - Use another call to
`ts.plot()`

to plot`rw_drift_diff`

.