Forecasting seasonal components is an important practical problem in finance, where products that are highly exposed to monthly seasonality in consumer prices are traded. For example, one can trade swaps based on a monthly (unknown) index value of the European Harmonised Index of Consumer Prices (HICP). The state of the art method for seasonally adjusting data seems to be X-13ARIMA-SEATS, which is produced by the US Census Bureau.
However, this software seems to have been set up mainly to adjust the data historically for seasonality and other deterministic effects and forecast the entire series into the future. In finance, forecasts of trend values (for consumer price indices, for example) can generally can be observed in the market, but the seasonal component must be forecasted.
Any tips or comments on whether one can extract forecasts of the seasonal components within X-13ARIMA-SEATS would be greatly appreciated