Reduce the effect of excessive zeros

I am working on an autoregression problem where I use sequential LSTM. My target is well defined, but I think I am facing a problem with the features. As the features were non-stationary, then I decided to apply the log-returns to each of them. In other words, if $$F_t$$ is a feature at a certain time $$t$$, then I apply $$\log(\frac{F_t}{F_{t-1}}).$$

$$\Rightarrow$$ Why non-stationary data is hard to analyse?

The property makes it easier to analyse, but produce a lot of zeros when $$F_t = F_{t-1}$$.

As there is lots of zeros, then the predictions tend to be closer to 0. How can I reduce that effect mathematically?