Poor Regression Model Predicts Correct

[Toni2]

Hi all,

I wonder if someone can help on this. I have run with OLS this model

y=1.0527x - 0.082

where 

y= IOS (percentages)

x = Bank Rate (percentages)

When i plot y versus x and add the line the model doesn't fit the data due to low R2 and the outliers (please see the graph in the attached file)

However, when I see the back testing (yellow line in the graph in the attached line) the model almost perfectly fits the data which i am struggled to understand or explain

If the model is not correct how can correctly predict the data ?

My first thought is that since the Bank Rate is stable we might have violation of OLS assumptions but again how the back testing is almost correct?

Thanks,

Antonis

[PGStats]

The R2 looks bad because you don't have enough contrast in your data (in the second half of the time series), which makes the error (the unexplained part of the signal) look large compared to the part of the signal explained by your model. You should be able to make a better assessment of the fit if you replot the second half of the time series and rescale the y axis.

[Toni2]

Hi, thank you for your response. I am going to have a look on this.

[gcjfernandez]

Your data is autocorrelated (timeseries) with interruption (significant time shifts). This violate OLS assumptions. Treat this as a time series problem. Use PROC ARIMA or PROC ESM from SAS ETS.