# Forecast accuracy of simulation vs empirical measurement

I want to compare how well a simulated curve approximates the "real" curve measured on empirical data.

More in detail: I have empirical data, let's say for simplicity the worldwide population per year for the last 200 years. I measure a curve that is mostly increasing with 1 data point for each year. Now I also have a model with some parameters that I use to simulate the same curve. For the simulation I only use the starting point (population at the first year) as well as some universal parameters that I can estimate from any time span in the empirical data and that don't change in time. So I end up with two curves, the real one and the simulated one. Now I want to quantify how accurate my simulation is compared to the empirical data.

How would I approach this apart from plotting both curves on top of each other? Are measures like Mean absolute percentage error or scaled errors the right way?

As I am very new to this topic I apologize if this is perhaps a very trivial or stupid question

So because you are discrete for both the curves you can just calculate: $$MSE = \frac {1}{n}\sum_{poins} (y_i-y_j)^2$$ where $$i$$ and $$j$$ denote first and second curve.