# Relatively low MAE, but also low R-squared? Why

I am testing forecasts against against realized values with a number of observations of 4000.

When I calculate the mean MAE, its relatively low. Around 10% deviation to the original variable.

However, when I regress the forecasts against the realized values I get an r-squared value of 0.06...

Is there any rationale behind this?

How this can be?

Extrem outliners? Or extrem bias? Or something else?

The MAE is calculated as $mean(abs(y_{real,t+1} - y_{predict,t+1}))$. The t+1 indicating that I only forecast and compare one-step-ahead forecasts.

and the regression is simply calculated by MATLAB with the function regstats,which regress $y_{real}$ over $y_{predict}$.

I do the regression during the mincer-zarnowitz test. It completely fails.

This is the plot:

• You need to provide us with the expressions for a) the calculation of MAE b) the regression equation of forecasts on realized values – Alecos Papadopoulos Jan 7 '17 at 18:51
• Also, are you examining one-step-ahead forecasts only? – Alecos Papadopoulos Jan 7 '17 at 18:55
• yes. Only one-step-ahead forecasts – Alexander De Beur Jan 7 '17 at 19:37
• Could you show a plot of the data? Visualizing your problem can be really helpfull to see what is going on. – Pieter Jan 7 '17 at 19:44
• Your data points are not really independent... If you want to assess your model fairly you should probably sample the data to get rid of the temporal dependency. – Pieter Jan 7 '17 at 20:03