First of all, if you have this strong proof it means that your design research match with method and tools, and if you are trying to find out others methods it could be incorrect because you didn't designed in advanced, and attempt tentative method and tool essentially are wrong approach, so why are you seeking something else not designed?

Thank you for your quick answer. I was seeking for alternatives because I wanted to make sure that this is the right method. I know there can be used different time lag lenghts for autocorrelation and there is also a possibility to use trend analysis i guess.

It is not fully clear to me what you are modelling, can you give more informations on the data you have? it seems interesting. Besides that:

-) in general, you can't state in advance that the model you chose is the best, you should try all alternative models, which is impossible.

-) If you know well what you are modelling you can often rule out models which make no sense

-) watch residuals ! If they are uncorrelated and homoskedastic you are on a good way

-) beware of R^2 !! If interested on predictions i suggest you score models (e.g.)  looking at residuals of out of the sample forecasts.

Thanks for your interest in this subject.

I have data per day of the amount of people visiting shopping centers.

I can split the file by shopping centers and make models of each center, with the predictors: day of the week, month in the year, weather variables and economic variables.

I can see that in some centres the residuals are correlated because they show trends. This suggests that a lineair regression model cannot be used. Using a AR(1) model increases R-Square and doesnt violate the uncorrelated residual assumption, because all Durbin-watson values are close to 2,0.

Problem is actually, there can still be trends observed when plotting the residuals of the AR(1) model over time, so I guess I have non-stationary series. That is where ARIMA(p,d,q) (with d=1 for a lineair trend) comes in right? I'm not sure about this and how to use this correctly (using SPSS).

Thanx again!

So, you may try with something like this (simplified version) which adds to the linear model an autoregressive term. 

y_i = b0 + b1*x_i + b_2*y_(i-1) + eps_i 

The autoregressive term was already added, still i can see non-stationarity (so not just temporary fluctuations, but trends or no full recovery after a random shock), which are ignored with the autogregressive b_2*y_(i-1) term right?

yes, if you see non stationarity in residuals you must add something else to your model

Check the sample ACF and PCAF and determine your model by the lags out of 95% bound;

Fit the ARMA(p,q);

Test the residuals to se if it's white noise;

select different model and compare AICC.

Thank you Chenying,

i knew that's an option, but the real challenge is to make this for 100 different cases. I can do your method 100 times but that is very time-consuming and maybe there will be more cases in the future.

Hi Joost,

if I understand your problem correctly, your problem is the high number of shopping centers, which would be too much for modeling individually, right? You might use a Principal Component Analysis first. Transforming the 100 time series into their principal components, you could run your time series analysis based on the important principal components first. This way you very likely won't need to regress on 100 but rather on 5-15 time series.

Regarding the stochastic term, in my mind, graphical analysis tells you more than statistical tests. Look at the time series of the errors, usually you get an idea whether, they are non-stationary. The augmented Dickey-Fuller test also helps very much (although it is not perfect either for small sample size). If your time series is non-stationary, you should differentiate it.

The "best" orders of your ARMA(p,q) model cannot be derived easily. You might take a look at the ACF and the PACF, like Chenying said, but be careful with the interpretation! It takes a lot of experience to see this from the ACF and PACF, its not as easy. I would rather use them as an indication of the maximum values of p and q and from then on try different ps and ds. Better use one or more information criteria for your decision: AIC; BIC; HQC.