My question is why do we have to choose the first lags in any time series forecasting?
My question can be answered by the autoregression but the answer I am looking for is a rational answer. I will explain that in few words. For example, the correlation between the current and the lags in the daily forecasting could be high but this is not the case in the monthly (bearing in mind the seasonal cycles) or in the annual time series. Mostly the AR and MA are done according to the ACF and PACF which are linear correlation while the relation is not linear at all taking the streamflow as an example. I do know there is a seasonal AR and so on. But my question is can we have another method? another type of forecasting? of course data-driven methods are included as they mostly being implemented according to the AR in general.
Does the rainfall of the current day has any relation (Markov) with the previous days?? of course no! So, doing that for the daily rainfall is completely wrong but it can be applied for streamflow for example.
Again the question is why do we choose first lags and not only the seasonal lags (i.e. one year cycle) for example?
Thanks
Sorry, in my opinion the question is not correct, in many cases the best model can be pure SAR or SMA models, and in these cases first lags are not chosen. For example see in this paper Section 5.2:
Article Gibbs sampling for SARMA models
On one side we may have dynamic model specifications with lags of the dependent and independent variables. Lags are determined with the help of AIC and SC.
On the other hand autoregressive schemes (of order one AR(1) or with more lags AR(p))) refers to the relation of the dependent with itself lagged one period (due to consumption habit say in a demand model, a cobweb case in a supply model, or inaction and circularity more generally). Similarly moving average schemes refer to influences of other explanatory variables on Y (with adequate lags in an MA(q)).
The ARMA specification is a mixture.
ACF and PACF determine (being careful) the AR, MA or ARMA schemes.
Seasonal autoregressive moving average (SARMA) specifications may also follow in case of seasonality being present in the model specification. This becomes more complicated with Bayesian inference.
I agree with Ayman Amin , there are planty of methods that does not require first lag. Today, it is very common to researches to relly on "premade" methodologies, that are in the trend. But they may be not the best choice for the problem you are adressing to. And the usage of the wron methodology may lead to very distintct results. Once i read a research that built four different models for agricultural productivity related to family generations. Each model found a complete different result!
Your model should always be in harmony with the theory of the field you are working on, and have to be treated carefully.
In more then one ocasion I found that a simple Least Square model, without any lag, was the best solution.
That was the case for forecasting Turkey exports, on a problem posted by Celil Aydin.
You can check the debate around that topic on this link:
https://www.researchgate.net/post/About_forecasting_time_series_data
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