# ratio, MSE of basic demand to MSE of aggregated demand for MA(1) process

I have a basic demand series that follow MA(1) process,I've applied non-overlapping aggregation approach and then SES on both basic and aggregated series to obtain forecasts, and then I disaggregated forecasts resulted from aggregated series and finally I calculate ratio of MSEbasic/MSEdagg, where MSEbasic=Var(dt-ft) and MSEdagg=Var(dt-(FT/m), dt is basic series at time t, ft is forecast of basic series, FT is aggregated forecast and m is aggregation level and alpha is smoothing constant. this ratio shows that for highly negative value of Theta, basic approach works better and for the rest of Theta parameter aggregated approach works better, I'm trying to understand why aggregation does not work for high negative Theta,I was wondering if you guide me. bests Roji

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$y_t - y_{t-1} = e_t - \theta e_{t-1}$
More generally, as $\theta$ gets more negative, the correlation between two consecutive $y_t$ gets larger (more positive). Aggregating highly positively correlated series doesn't do as much for you as aggregating less positively correlated series, all other things being equal, which they never are. As a thought experiment, consider a case where the autocorrelation = 1, say, $y_{t+1} = y_t = 0$; clearly no level of aggregation will do you any good when forecasting. Combining this with the suboptimal SES forecasting approach is resulting in the interesting table you've included in the question.