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”

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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

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