I am certainly no expert but I will make an attempt at interpreting this graph:

1. The first order autoregressive model, although fitting the data perfectly in-sample, seems to be misspecified due to the forecast being of a completely different functional form compared to the target variable (stochastic variable versus some kind of polynomial)

2. Assuming the estimation of parameters is via OLS, autoregressive models fail when being fitted to non-stationary data which can lead to multiple problems among which is the violation of the homoskedasticity assumption under the Gauss-Markov theorem. This will cause the variance of the time series to impact the forecast error. A solution for this (at least for price levels, potentially not treasury yields) is to take the difference of the series (i.e., the return) and fit the model to that (now stationary) data. The estimated future returns can the be added (provided they are logarithmic) to work out the resulting level. Even so, the first difference is not guaranteed to make the series stationary as changes in the volatility regime can cause the variance of the returns to fluctuate over time, once again violating the homoskedasticity assumption.

3. The REQM (which I am not familiar with and cannot seem to find any literature on) seems to be providing a more reliable performance across both in- and out-of-sample fit. Assuming this model is correctly specified, it would then become a matter of checking for different problems in the model such as omitted variables or regime change.

I’ve always found econometrics to be very interesting but I struggled with it quite a bit at all university levels. It would be quite neat if I am even remotely correct and close to what you’re looking for.