Are the white noise model or the random walk model stationary?

The white noise (WN) and random walk (RW) models are very closely related. However, only the RW is always non-stationary, both with and without a drift term. This is a simulation exercise to highlight the differences.

Recall that if we start with a mean zero WN process and compute its running or cumulative sum, the result is a RW process. The cumsum() function will make this transformation for you. Similarly, if we create a WN process, but change its mean from zero, and then compute its cumulative sum, the result is a RW process with a drift.

This exercise is part of the course

Time Series Analysis in R

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Exercise instructions

Use arima.sim() to generate a WN model. Set the model argument equal to list(order = c(0, 0, 0)) to generate a WN-type model and set n equal to 100 to produce 100 observations. Save this to white_noise.
Use the cumsum() function on white_noise to quickly convert your WN model to RW data. Save this to random_walk.
Use a similar call toarima.sim() to generate a second WN model. Keep all arguments the same, but this time set the mean argument to 0.4. Save this to wn_drift.
Use another call to cumsum() to convert your wn_drift data to RW. Save this as rw_drift.
Enter the pre-written code to plot all four series for comparison.

Hands-on interactive exercise

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

# Use arima.sim() to generate WN data
white_noise <- 

# Use cumsum() to convert your WN data to RW
random_walk <- 
  
# Use arima.sim() to generate WN drift data
wn_drift <- 
  
# Use cumsum() to convert your WN drift data to RW
rw_drift <- 

# Plot all four data objects
plot.ts(cbind(white_noise, random_walk, wn_drift, rw_drift))

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