The first letter, x in this case, specifies a particular time series. This is a common part of notation in statistics. The number in brackets is the time at which the estimate is made. The number in parentheses is the leadtime for making the forecast. In practice the most common leadtime is one period.
Business cycles are an example of irregular repetition.
If people behave consistently over time in a given situation requiring forecasts, that implies their acceptance of some loss function. The Law of Large Numbers says that averages over larger and larger samples are more and more likely to be accurate. Averaging lets certain types of changes cancel each other out. That is good if the changes are random noise. Noise is a succesion of changes that are unrelated.