This morning I woke up wondering (this could be due to the fact that last night I didn't get much sleep): since cross-validation seems to be the cornerstone of proper time-series forecasting, what are the models I should "normally" cross-validate against?
I came up with a few (easy) ones, but I soon realized they were all but special cases of ARIMA models. So I'm now wondering, and this is the actual question, what forecasting models does the Box-Jenknins approach already incorporate?
Let me put it this way:
- Mean = ARIMA(0,0,0) with constant
- Naive = ARIMA(0,1,0)
- Drift = ARIMA(0,1,0) with constant
- Simple Exponential Smoothing = ARIMA(0,1,1)
- Holt's Exponential Smoothing = ARIMA(0,2,2)
- Damped Holt's = ARIMA(0,1,2)
- Additive Holt-Winters: SARIMA(0,1,m+1)(0,1,0)m
What else can be added to the previous list? Is there a way to do moving average or least squares regression "the ARIMA way"? Also how do other simple models (say ARIMA(0,0,1), ARIMA(1,0,0), ARIMA(1,1,1), ARIMA(1,0,1), etc.) translate?
Please note that, at least for starters, I'm not interested in what ARIMA models cannot do. Right now I only want to focus on what they can do.
I know that understanding what each "building block" in an ARIMA model does should answer all of the above questions, but for some reason I have difficulties figuring that out. So I dediced to try a "reverse engineering" kind of approach.