# 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.

This is a part of the course

## “Time Series Analysis in R”

### Exercise instructions

- 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()`

.

### Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

```
# Simulate a WN model with list(order = c(0, 0, 0))
white_noise <- arima.sim(model = ___, n = ___)
# Plot your white_noise data
# Simulate from the WN model with: mean = 100, sd = 10
white_noise_2 <- arima.sim(model = ___, n = ___, mean = ___, sd = ___)
# Plot your white_noise_2 data
```

This exercise is part of the course

## Time Series Analysis in R

Learn the core techniques necessary to extract meaningful insights from time series data.

In this chapter, you will conduct some trend spotting, and learn the white noise (WN) model, the random walk (RW) model, and the definition of stationary processes.

Exercise 1: Trend spotting!Exercise 2: Random or not random?Exercise 3: Name that trendExercise 4: Removing trends in variability via the logarithmic transformationExercise 5: Removing trends in level by differencingExercise 6: Removing seasonal trends with seasonal differencingExercise 7: The white noise (WN) modelExercise 8: Simulate the white noise modelExercise 9: Estimate the white noise modelExercise 10: The random walk (RW) modelExercise 11: Simulate the random walk modelExercise 12: Simulate the random walk model with a driftExercise 13: Estimate the random walk modelExercise 14: Stationary processesExercise 15: Stationary or not?Exercise 16: Are the white noise model or the random walk model stationary?### What is DataCamp?

Learn the data skills you need online at your own pace—from non-coding essentials to data science and machine learning.