Forecasting stationary data that has no trend/seasonality

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Homework Statement



We've got a random variable that appears to have no trend/seasonality, is stationary, and we want to forecast it.
The variable is number of warranty claims received each day, 53 days, so we've got 53 values, and we want to forecast the values of the upcoming 5 days.

2. The attempt at a solution

I'm trying to model the data using ARIMA model.
1.png


Judging from the autocorrelation plots, the data is stationary, so no differencing should be done. Judging from the ACF and PACF plots, our best bet would be AR(1), MA(1) or ARIMA(1,0,1). All yield similar results:
results1.png
results2.png
forecast.png


Is there no better way to forecast this variable? ARIMA does not seem like a good forecasting option in this case. The data has no apparent trends/seasonalities and is stationary. What method would be best to forecast such data?
 
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ARIMA is a very powerful and general method for modeling time series. I don't know what you might try that would be better.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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