Exercise

# Simulate the random walk model

The random walk (RW) model is also a basic time series model. It is the cumulative sum (or integration) of a mean zero white noise (WN) series, such that the first difference series of a RW is a WN series. Note for reference that the RW model is an **ARIMA(0, 1, 0)** model, in which the middle entry of 1 indicates that the model's order of integration is 1.

The `arima.sim()`

function can be used to simulate data from the RW by including the `model = list(order = c(0, 1, 0))`

argument. We also need to specify a series length `n`

. Finally, you can specify a `sd`

for the series (increments), where the default value is 1.

Instructions

**100 XP**

- Use
`arima.sim()`

to generate a 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. Save this to`random_walk`

. - Use
`ts.plot()`

to plot your`random_walk`

data. - Use
`diff()`

to calculate the first difference of your`random_walk`

data. Save this as`random_walk_diff`

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

to plot`random_walk_diff`

.