Exercise

# Simulate the white noise model

The white noise (WN) model is a basic time series model. It is also a basis for the more elaborate models we will consider. We will focus on the simplest form of WN, independent and identically distributed data.

The arima.sim() function can be used to simulate data from a variety of time series models. ARIMA is an abbreviation for the autoregressive integrated moving average class of models we will consider throughout this course.

An **ARIMA(p, d, q)** model has three parts, the autoregressive order `p`

, the order of integration (or differencing) `d`

, and the moving average order `q`

. We will detail each of these parts soon, but for now we note that the **ARIMA(0, 0, 0)** model, i.e., with all of these components zero, is simply the WN model.

In this exercise, you will practice simulating a basic WN model.

Instructions

**100 XP**

- Use
`arima.sim()`

to simulate from the WN model with`list(order = c(0, 0, 0))`

. Set the`n`

argument equal to`100`

to produce 100 observations. Save this data as`white_noise`

. - Plot your
`white_noise`

object using`ts.plot()`

. - Replicate your original call to
`arima.sim()`

but this time set the`mean`

argument to`100`

and the`sd`

argument to`10`

. Save this data as`white_noise_2`

. - Plot your
`white_noise_2`

object with another call to`ts.plot()`

.