Suppose a wise-sense stationary univariate time series has relatively strong auto-correlation of lag-length of 1, say, around -0.7

Then how would it affect the forecast?

Conversely, if a stochastic process were to be IID, then due to a law of large number, $E[X] = {1 \over N} \sum X$ as N gets large and thus you could say that the "best guess" of the next data point given the previous data points up until now is simply the mean average of the previous points.

But if such a strong auto-correlation were to be present, then I believe it's possible to come up with a "best guess" that's even more accurate than simply using the mean average of the previous points.

I was thinking of an autoregressive model but what are some common methods?


An ARIMA model is simply a weighted average of the past. It answers the double question: How many period (k)should I use to compute a weighted average and precisely what are the k weights. It answers the maiden's prayer to determine how to adjust to previous values (and previous values ALONE) in order to come up with a "best guess" for future periods.


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