Problem 1 (i) First, I would institute a copy that fits the literal axioms well-behaved, then secondly, I would use the copy to forecast the forthcoming. In conditions of copys that I authority use, I may use the Random Walk Copy or I authority select to use Autocorrelation. (ii) (iii) According to the textbook, the total after a while duration course axioms is that the residuals are generally correlated after a while nearby residuals, a nature particularized autocorrelation .
The most general form of autocorrelation is absolute autocorrelation. For illustration, if residuals divided by one month are correlated—determined lag 1 autocorrelation—in a absolute address, then an balance foretelling in January, say, gain slight bring to an balanceestimate in February, and an subordinaterate in January gain slight bring to an subordinate foretelling in February. If this autocorrelation is abundant, thoughtful foretelling errors can take-place if it isn't dealt after a while justly.
The numerical gauge familiar to impede for lag 1 autocorrelation is particularized the Durbin-Watson statistic, and it is quoted automatically in the retrogression output of frequent statistical software packages. The Durbin-Watson (DW) statistic is scaled to be betwixt 0 and 4. Values bar to 2 evince very short lag 1 autocorrelation, values underneath 2 evince absolute autocorrelation, and values aloft 2 evince indirect autocorrelation. (iv) I would use a Runs Test to particularize if there are too frequent or too few runs in the course—and if either is the condition, then the vain theory of randomness can be uncommon.