You are given an annual time series with 40 consecutive values and asked to fit a fifth-order autoregressive model. How many comparisons are lost in developing the auto-regressive model?
In order to fit a fifth-order autoregressive model, we need to estimate the coefficients for each lagged value. For a fifth-order model, we would consider the previous five values of the time series as predictors for the current value.
Therefore, for each observation in the time series, we lose comparisons with the previous five observations. Since we have 40 consecutive values, the number of comparisons lost would be:
5 comparisons lost for the first observation
5 comparisons lost for the second observation
...
5 comparisons lost for the 40th observation
Adding up these numbers, we get:
5 + 5 + ... + 5 (40 times) = 5 * 40 = 200
So, we would lose 200 comparisons in developing the autoregressive model.