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title: "linear regression with ARMA noise"
output: html_document
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## Linear regression with ARMA noise

Simulate data from a linear regression with ARMA noise in the following way: 
- Create an exogenous variable $x_t$ - either simulate this randomly, or pick deterministic values for example using some function of t
- Simulate the noise terms $\epsilon_t$ using an ARMA(p,q) model, where you choose $p$ and $q$ (make sure it is stationary)
- Calculate $y_t$ from $x_t$ and $\epsilon_t$

Now fit a regression model with ARMA noise to the simulated data, and including parameter estimation and model checking. You can try out various models - both the true model used for simulation, but also other models - and compare them using AIC.