Forecasting stationary data that has no trend/seasonality

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SUMMARY

The discussion centers on forecasting a stationary variable, specifically the number of warranty claims received daily over 53 days, using the ARIMA model. The data exhibits no trend or seasonality, leading to the conclusion that ARIMA(1,0,1) is a suitable model based on autocorrelation function (ACF) and partial autocorrelation function (PACF) plots. However, participants express skepticism about ARIMA's effectiveness for this particular dataset, questioning if alternative forecasting methods may yield better results.

PREREQUISITES
  • Understanding of time series analysis
  • Familiarity with ARIMA modeling techniques
  • Knowledge of autocorrelation and partial autocorrelation functions
  • Experience with statistical software for modeling (e.g., R or Python)
NEXT STEPS
  • Explore alternative forecasting methods such as Exponential Smoothing State Space Model (ETS)
  • Learn about the application of Seasonal Decomposition of Time Series (STL) for stationary data
  • Investigate the use of machine learning techniques for time series forecasting, such as LSTM networks
  • Study the implications of model selection criteria like AIC and BIC in time series analysis
USEFUL FOR

Data scientists, statisticians, and analysts involved in time series forecasting, particularly those working with stationary data without trends or seasonality.

Deimantas
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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.
 

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