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I am learning about the ARIMA model and trying to implement it and had some questions. From my understanding, ARIMA forecasts better for short-term projections rather than long-term projections (is this true or false)? I am implementing the ARIMA to make a 6 month projection on a daily basis. Would I get better results if I predict one day, then retrain the model including that day, then predicting the next day, and then retraining, and so on?

EDIT: Thanks for the responses. Sorry if I wasn't being clear. I am using the ARIMAX model, and I have about 30 exogenous variables. I know what the actual values are for the endogenous variable, even for the 6 month projection period. I want to test how well my model performs on this 6 month period. So what I meant by retraining is that after I make a prediction for the next day using n samples, I would retrain on n+1 samples, where the new sample is using the actual value for the endogenous variable as opposed to the prediction.

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    $\begingroup$ Essentially all forecasting methods do better in the short-term.... The only exceptions are whenever the long-term state or value is inevitable, and here predictive success is a property of the phenomenon, rather than a mark for the method. So, I don't expect to be around in 2113, but I'm very uncertain about 2033. $\endgroup$ – Nick Cox Nov 29 '13 at 10:26
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ARIMA models are univariate so the only information they use is the history of the series. Essentially, they tell you how the variable will react to previous stochastic variation. When you start forecasting with them you no longer have any 'noise' in them because your model will not add in error terms (and nor should it). So what you'll see is that the forecast will quickly decay to the constant term/trend in your ARIMA model. Re-estimating the model won't help because you're not adding any new information about the underlying process.

Over 180+ forecast periods you'll need to add in more explanatory variables to get anything more than a trend line out of your model. For instance, you might include macroeconomic projections as an input, which would give you some dynamics over a 6 month period.

Update: If you are going for in-sample predictive power then using all the data will give you a better fit, so yes it will improve. The underlying question is what you want to achieve. If you're trying to understand the causative factors explaining the dependent variable then a few extra observations aren't going to overturn your theoretical priors. If you want forecasting power then you want to use as much data as possible to estimate your model. Of course you need to be wary of overfitting, which I guess is why you want to check the estimation against a sub-sampled model. If you're seeing a lot of change in your coefficients as you increase the sample size and they don't stabilise that's indicating your model's mis-specified.

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  • $\begingroup$ Thanks for updating your response. I am just interested in forecasting power just to see how well the model performs. I am a bit confused how I could run into overfitting problems, since I am not training on the data points that I want to predict. $\endgroup$ – user34864 Nov 30 '13 at 2:42
  • $\begingroup$ Overfitting occurs when your model has a lot of parameters relative to the number of observations and starts to fit the noise as well as the signal. That can happen even when you're not estimating using the data you want to predict. Information criteria such as the Akaike and Schwarz are useful for pruning your general model back to something appropriately parsimonious. $\endgroup$ – jmz Dec 1 '13 at 13:06
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User Rauparaha made an short but informative comment about ARIMA-models.

You could use other variables is transfer function / ARIMAX-model, but the problem is that after some point you would have to forecast values for the explanatory variables.

We found out that MAPE for electricity consumption could be 15-20 percent when using only series own history but when you include number of customers and temperature you can get 2-3 percent MAPE. Only problem is that weather forecasts for long run will decay quickly and after a week or two you do not have any extra information which would be useful.

Regards,

Analyst

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