Let's say I have a table with 2 columns (data sets), and convert them into 2 graphs.
I have the graph of a stock (=col. 1), and then I simulate using some mathematical model, a prediction of the stock price (=col. 2). So now I have 2 graphs, 1 actual stock price, and 1 'prediction'. So both these graphs are of the same time period. Now how do I find how accurate or 'close' the simulation is to the actual graph, in a number. Is there some formula?
You have to use the underlying data of those two graphs. The first thing you can do is to calculate the correlation between the two columns. Next, you take the square of the correlation, this gives you the R Square of your mathematical model. In essence, it is stating what % of the variance of column 1 is explained by your model in column 2. You could also calculate the standard error of your model by using the function STEYX() in Excel. Once, you have this calculated standard error of the estimate of your model, you can build a 95% confidence interval around your estimate (column 2) by creating a ban of + or - 1.96 standard errors around your estimate (column 2). And, 95% of the actual data points (column 1) should be included within this 95% confidence interval that surrounds your model estimates (column 2).
There are interesting measures of estimating and forecasting accuracy in addition to the Standard Error mentioned above. Two of the most common ones include the Mean Absolute Error (MAE) and the Mean Absolute Percentage Error (MAPE).
Next, you could test the residuals (actual - estimate) of your model to make sure whether your confidence intervals are robust or not. But, that opens up a whole area of statistics that is probably appropriate once you become more familiar with your existing model and the basics associated with it.
