1. I generated 1000 observations from the MA(1) model with parameter 0.7 using the following R function: dataset = arima.sim(n = 1000, list(ma = 0.7)) I then fitted the ARMA(1, 2) model to the data using the function arima(dataset, order = c(1, 0, 2)), which gave the following output:

    Call: arima(x = dataset, order = c(1, 0, 2)) Coefficients: 

2.  ar1 ma1 ma2 intercept 0.7838 -0.0802 -0.5301 0.0430 s.e. 0.2063 0.2107 0.1501 0.0566

3.  sigma^2 estimated as 0.986: log likelihood = -1412.22, aic = 2832.45

4. Because the data have been simulated from an MA(1) model with parameter 0.7, I expected the estimated coefficients of ar1 and ma2 to be close to zero and the estimated coefficient of ma1 to be close to 0.7. Explain why this did not happen?