The history of forecasts allows you to tell how well the AI would have been able to forecarst this stock over time. Future forecasts are more likely to be accurate if past ones are more accurate as it shows the AI has more familiarity with the symbol. The prediction band width is tuned so that half the chart should remain within the band. We do not assume that stock market prices are normally distributed so the price can move far outside this band.
The blue line is the actual share price, while the circles and diamonds are what the AI is trying to predict. These circles and diamonds are different from the blue line because they net out the overal stock market movements. This improves accuracy as the overall market movements are caused by factors outside the individual stock's control such as the pandemic, or interest rate movements