Simulate data from a MA(1) model

Consider the MA(1) model $$Y_t = 0.05 + \epsilon_t + \theta \epsilon_{t-1},$$ with $|\theta| < 0$ and $\epsilon_t ~$ $iid$ $N(0,(0.1)^2)$.

In this exercise, you will simulate 250 observations from the above model. You can use the arima.sim() function in R to simulate a moving average or autoregressive process (see documentation). Furthermore, you should specify the following arguments for arima.sim:

The model argument should contain a list that indicates the type of model that you would like to simulate from. For a MA(1) model with $\theta = 0.3$, for example, you should set the model argument to list(ma = 0.3).
n specifies the number of observations to simulate.

If you take a close look at the documentation of arima, you will notice that there is no constant included in the model. This means that you will need to add the constant $0.05$ yourself.

Simulate 250 observations from the above MA(1) model with $\theta = 0.5$ and the constant $0.05$. Assign the result to ma1_sim.

Exercise

Simulate data from a MA(1) model

Instructions