(i) First, I would build a model that fits the historical data well, then secondly, I would use the model to forecast the future. In terms of models that I might use, I may use the Random Walk Model or I might choose to use Autocorrelation.
(iii) According to the textbook, the problem with time series data is that the residuals are often correlated with nearby residuals, a property called autocorrelation . The most frequent type of autocorrelation is positive autocorrelation. For example, if residuals separated by one month are correlated—called lag 1 autocorrelation—in a positive direction, then an over prediction in January, say, will likely lead to an overestimate in February, and an underestimate in January will likely lead to an under prediction in February. If this autocorrelation is large, serious prediction errors can occur if it isn't dealt with appropriately. The numerical measure developed to check for lag 1 autocorrelation is called the Durbin-Watson statistic, and it is quoted automatically in the regression output of many statistical software packages. The Durbin-Watson (DW) statistic is scaled to be between 0 and 4. Values close to 2 indicate very little lag 1 autocorrelation, values below 2 indicate positive autocorrelation, and values above 2 indicate negative autocorrelation. (iv) I would use a Runs Test to determine if there are too many or too few runs in the series—and if either is the case, then the null hypothesis of randomness can be rejected.
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