How can i do Probabilistic time series forecasting?

I have an univariate time series data (eg. 17/10/2017 4:30 6328.22; 17/10/2017 5:00 6590.45; 17/10/2017 5:30 7078.27; 17/10/2017 6:00 7553.67; 17/10/2017 6:30 7828.64)

How can i do probabilistic forecast using this time series data such as quantile, interval, density and also visualise as the attached file

Answer 1

[Shivam Lahoti]

Hi israt,

In MATLAB, probabilistic forecasting can be approached using two primary functions: 'forecast' and 'simulate'. The 'forecast' function is designed to work with fitted time series models, such as ARIMA, to generate not only point forecasts but also prediction intervals. These intervals provide a range within which future values are expected to fall with a specified probability, offering a straightforward method to assess forecast uncertainty.

The 'simulate' function generates many forecasted paths, each showing a possible future influenced by the model's uncertainty, creating a forecast density that maps out a wide range of potential trajectories for the time series.

The 'quantile' function measures uncertainty in the simulated paths by calculating key percentiles, such as the 5th, 50th, and 95th, to gauge forecast variability. This enhances probabilistic forecasts and informs decision-making.

To understand more about the above-mentioned functions, have a look at the following documentation. They have similar examples to your use case.

https://www.mathworks.com/help/econ/arima.forecast.html

https://www.mathworks.com/help/econ/varm.simulate.html

https://www.mathworks.com/help/matlab/ref/quantile.html

I hope this helps.

Regards,

Shivam.