Exercise

# Estimate the random walk model

For a given time series `y`

we can fit the random walk model with a drift by first differencing the data, then fitting the white noise (WN) model to the differenced data using the `arima()`

command with the `order = c(0, 0, 0))`

argument.

The `arima()`

command displays information or output about the fitted model. Under the `Coefficients:`

heading is the estimated drift variable, named the `intercept`

. Its approximate standard error (or s.e.) is provided directly below it. The variance of the WN part of the model is also estimated under the label `sigma^2`

.

Instructions

**100 XP**

- The time series
`random_walk`

has already been loaded, and is shown in the adjoining figure. Use`diff()`

to generate the first difference of the data. Save this to`rw_diff`

. - Use
`ts.plot()`

to plot your differenced data - Use
`arima()`

to fit the WN model for the differenced data. To do so, set the`x`

argument to`rw_diff`

and set the`order`

argument to`c(0, 0, 0)`

. Store the model in`model_wn`

. - Store the
`intercept`

value of`model_wn`

in`int_wn`

. You can obtain this value using`model_wn$coef`

. - Use
`ts.plot()`

to reproduce your original plot of`random_walk`

. - Add the estimated time trend to the adjoining plot with the function
`abline()`

. You can use`int_wn`

as the second argument.