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I am new to time series analysis. I try to use data (biweekly return of a portfolio) from 2010/01-2016/12 to obtain an ARIMA(4,1,1) model, by using auto.arima in forecast library. Next, I apply this model to data from 2017/07 to 2018/10, as out sample test. I split in this way, as I don't have the data from 2017/01 to 2017/06. the actual return and estimated return with ARIMA

Basically, I am OK with this fitting, but I have doubt on the beginning of this plot, from 2017/07 to 2017/11. As I don't have preceding data points before 2017/07, should I ignore the beginning part?

Chuck

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Typically, once you've fit an ARIMA model on training data set, you then apply to the time period coming right after that period. If the time series is not stationary (which is usually the case in most real world business problems) then your model won't work on data that too many steps into the future (see this blog for details on why that is the case).

If you purpose is to simply to learn time series models, I recommend you split the data you have from 2010/01-2016/12 into a train set of 2010-2015 and 2016 as a test set, or maybe 2010~2014 as a train set and test on 2015~2016.

If you have your heart set on somehow modeling the data in 2017~2018, then you might want to try direct multistep forecasting, given the data step you have. But then you will need something other than auto.arima to pull that off.

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    $\begingroup$ Hi Alex, Thanks. That blog is very helpful. But I think the return data should be stationary, having constant mean and variance. Especially, it is portfolio return (having more than 20 securities), instead of a return of a specific security. But I agree that I need retrain the model whenever I need prediction. Many people do this way. At first, I don't understand it. However after reading this blog, all my puzzles are solved. $\endgroup$
    – Chuck
    Commented Oct 25, 2018 at 7:29

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