e=arima.sim(n=1000,list(order=c(0,0,0))) e1=lag(e,1) e2=lag(e,2) x1=e-2*e1 x2=e-0.5*e1 x3=e-4/5*e1+16/25*e2 x4=e-5/4*e1+25/16*e2

These are four different time series models that each include a white noise error term e with different lagged terms:

- Model x1 includes a lagged error term e1 with coefficient -2.
- Model x2 includes a lagged error term e1 with coefficient -0.5.
- Model x3 includes lagged error terms e1 with coefficient -4/5 and e2 with coefficient 16/25.
- Model x4 includes lagged error terms e1 with coefficient -5/4 and e2 with coefficient 25/16.

Each of these models is an ARIMA model with a differencing order of 0 and no autoregressive or moving average terms. The lagged error terms are included as exogenous variables in the model to capture any additional dependence on past values of the error term beyond the white noise assumption. The specific lagged terms and coefficients are chosen based on some underlying theory or hypothesis about the data generating process.