All the Bitcoin protocol cares about when re-targeting the difficulty is how close we were to 10 minutes per block since the last difficulty change. Anything before that is really irrelevant.
Irrelevant at the most technical level, sure. But irrelevant on a fundamental level? Hardly. You could say that the worldwide number of barrels of oil produced today has no relationship with the number of barrels oil produced yesterday. Technically, this is correct; the events are independent. But ignoring today while trying to predict tomorrow is foolish. The network hashrate has increased unimpeded over the past several years. It may be in a period of slowdown as ASIC makers hit the smallest transistor node sizes available at a decent price, but it would take some kind of miracle for the hashrate to show a significant decrease. And to repeat myself, the network hashrate is what determines the average block time, not the other way around. The hashrate represents real-world resource usage, while the block time is simply a byproduct of those resources. To ignore recent hashrate trends when you're trying to predict future difficulty is to ignore a lot of meaningful data.
To give one example, there is a fairly common thing that has happened with the hashrate, which is that it increases to a peak, then drops, then a week or so later, it rises to the previous peak. This is due to the test-then-ship-then-install procedure followed by ASIC manufacturers. It often takes a week or so for the ASICs to ship to customers and be installed. In this case, a peak is telling you what is soon to come.... perhaps before the next difficulty adjustment. I encourage you to study the charts at Bitcoinwisdom, and to do so on a daily basis. They can tell you a lot more than a single difficulty prediction number can.
If you did want to try to include prior data, how would you determine where to draw the line? Since the beginning of time? Last month? Last 3 difficulty changes? All are arbitrary, and really have no influence on the next change. One may be able to argue that since a bunch of new hardware was just sent out that it'll increase ... however the price/BTC is also an unknown variable that influences difficulty. If it drops, older hardware will be turned off. If it increases, older hardware may be turned on.
Let's say the difficulty has just changed 10 blocks ago.... less than 2 hours. Your app can rely on either the last 9 blocks, or you can rely on a larger dataset telling you that the network hashrate has averaged 280,000-290,000 TH/s during the last month. Which do you think is going to give you a better estimate? If your answer is just "there will be wild swings during the first few blocks after a difficulty re-target" then your app should simply not provide an estimate during that time rather than look like a fool giving an answer based on a tiny sample size. What if the first block is found 10 seconds after the difficulty adjustment, and your app shows a 5000% projected increase? You've got to at least have some sanity checks in there.
Certainly a difficulty estimator could include the fiat price of BTC in its calculations, but only on the margins, and only for extreme swings. Since I stopped mining in March, the hashrate has increased nearly 10-fold. The September 25 difficulty increase represented the addition of an equivalent hashrate to the total network hashrate that existed when I stopped mining in March. (roughly 30,000 TH/s) Obviously all of the hardware that existed in March represents the "older hardware" pretty closely. If we assume that all of that existing older hardware has been turned off since March (unlikely -- but maybe half of it has), but BTC/USD doubles tomorrow and all those old machines are turned back on, it will represent a 10% increase in hashrate. So it would have an effect, but not a huge one. An ideal predictor would have all kinds of information built into it, such as ASIC manufacturer announcements and ship dates.
(Again, apologies for the thread derail... I hope that discussions of difficulty change predictions are interesting enough to earn forbearance.)
