A seasonal ARIMA model was fifitted to a monthly time series. A summary of the

fifitted model and some residual diagnostics are given below.

Write down the mathematical equation of the fifitted model in operator form. Is there

evidence that the model is not adequate? If so, suggest a modifification of the model that

may lead to a better fifit.

Call : arima (x = y, order = c(2, 1, 1), seasonal = list (order = c(0, 1, 0), period = 12) Coefficients : ar1 ar2 mal 0. 8498 -0. 4475 0. 5438 s. e. 0. 0508 0. 0482 0. 0466 sigma*2 estimated as 1.582: log likelihood = -803.8, aic = 1615.61 Standardized Residuals 1 3 -3 100 200 300 400 500 Time ACF of Residuals ACF 0.0 0.4 0.8 10 15 20 25 Lag p values for Ljung-Box statistic p value 0.0 0.4 0.8 O O 5 10 15 20 lag