I try to compute a Kalman gain as one of my state variables due to learning dynamics in my model and I see that it can be larger than 1 but I believe that theoretically, it cannot be. Does anyone have an idea if this is theoretically possible?
Thank you!
Are you talking about a univariate example with fixed Kalman matrices? In that case, the gain is just a share of the sum of the overall variances \sigma^2_0/(\sigma^2_0+\sigma^2_1) and must be between 0 and 1. In more complicated cases, that restriction does not hold.