forecasting the past

Explaining what happened in the past is as hard as predicting what will happen in the future. Why? Because to predict what will happen in the future you first need to build a model of how things work and to build a model you only have past data to work with.

In fact, it is a common practice to reserve away a certain portion of the past data during the modelling process, and use it to quickly see whether the constructed model has any predictive power. (This eliminates the need to wait for the future to unfold.)

Once you have a good model of the past, you can make predictions about the future.

Those predictions may require you to plug in certain initial conditions which may lie far back in time. In that case, you will need to run your model backwards to predict what may have happened before the beginning of your data set.

Make no mistake. Building a model from past data is a tough business. Each of those past moments was once an amorphous "Now". How they unfolded into each other was a total mystery back then, and it still is.

Ignorance is time-symmetric. Only "Now" is certain. The rest is a matter of speculation.