I use CIR to forecasting.After finish estimation, we get a group parameter {K,theta,sigma,lamda}then for forcasting, you should take the mean value for next period. r(t)=r(t-1)+E(dt)=r(t-1)+k(theta-r(t-1))dt=k*theta*dt+(1-kdt)r(t-1)so first term is cconstant, and basically is very flat, like falt linear. No mean reversion. Any wrong with me?Thank you

What method did you use to estimate your parameters? What set of data did you use? Your parameters are driven by the data you chose to callibrate your model.

I use MLE with UKF and historical 10 year full term structure data. I don't think any wrong with estimation.Problem is when I forcasting, can I calculate mean value directly E[r(t)]=r(t-1)+E[dr(t)] or should I simulate 1000 value, then take the mean?If tried first method, it doesn't work. Future 10 years forecasting seems very flat, no mean reversion.

Sorry, some typo. I take mean directly, and forecasting 10y weekly data, all of them are very flat.

In case you are trying to forecast the term structure of interest rates, CIR offers a closed end (formula) solution to estimate the term structure. You do not necessarily need to simulate the interest rate paths to estimate the term structure. In case you are trying to forecast the short term rates for 10 years going forward you should be simulating the interest rate paths, which should be converging towards your long term mean rate and depending on what your initial rate is relative to the long-term mean and the estimated speed of mean reversion, your conversion will either be profound or not.

You are right. But I still confuse.I need forcasting quartely CMT 10y from next period to future 10 years (so 40 numbers)And I already get the parameters.So if we let current cmt10y is r0, how to get r1?r1=r0+E(dr(0)); r2=r1+E(dr(1))..... Use this way, r1..r40 nearly flat.My question is this method is wrong or not?

Try playing around with your parameters (increase volatility and mean reversion speed) and see how sensitive your simulation is. In general, it is not uncommon to observe a slow convergence speed, in particular when your delta time is 30 days (1 month). I found that reducing delta time (to weekly or daily), makes the process more dynamic.