Exercise

# Simulated ARIMA

Before analyzing actual time series data, you should try working with a slightly more complicated model.

Here, we generated 250 observations from the ARIMA(2,1,0) model with drift given by $$Y_t = 1 + 1.5 Y_{t-1} - .75 Y_{t-2} + W_t\,$$ where \(Y_t = \nabla X_t = X_{t} - X_{t-1}\).

You will use the established techniques to fit a model to the data.

The astsa package is preloaded and the generated data are in `x`

. The series `x`

and the detrended series `y <- diff(x)`

have been plotted.

Instructions

**100 XP**

- Plot the sample ACF and PACF using
`acf2()`

of the differenced data`diff(x)`

to determine a model. - Fit an ARIMA(2,1,0) model using
`sarima()`

to the generated data. Examine the t-table and other output information to assess the model fit.