Elastic Regression fitting good mean and bad variance
Your model actually looks pretty good. What it sounds like you are asking to do is to overfit your model. I would not recommend that you do that. You can do that by finding more variables that you can input into the model, fitting extra polynomial terms or anything else like that, fitting a neural network will potentially do it for you too. However, you generally want to smooth your predictions out, like what you have.

One thing that you could try is to add an autocorrelation term. That might cause your model to behave as you intend. With negative autocorrelation your predicted values will have a tendency to bounce back and forth around the mean. But I wouldn't recommend doing that, your performance will probably suffer, just judging by the graph that you provided.