Hi all, this might be a very silly question, but I am a bit rusty and would really appreciate some help.

Before I apply it to a more complex situation, I wanted to understand a simple working example of the kalman filter.

I am trying to implement a forecasting method using Kalman filter for a portfolio of bonds.

lets say I have a distribution of portfolio balances that look like so :

*Editing the series so the distribution is normal.

**(Month) : Balance**

(1) : 1000

(2) : 750

(3) : 1250

(4) : 1000

(5) : ?

Balance change due to maturities and new bonds added to portfolio, so I guess the linear equation would be like so :

Current Month Balance = Prior Month Balance + Change in Bond Volume

My issue is I do not have any observation noise, and a coeffecient of 1 applied as a multiplier to the prior value balances.

When I try to compute what the kalman gain should be, I am a bit confused on what I should use as my inputs, how do I go about computing the predictor/corrector values for Month 5 above without knowing the true balance for that month?

Specifically referring to the lecture notes( Chapter : First look at Kalman Filter), How do I compute

The filtering distribution value, or E(X^|Y) and then further use this to forecast for month 5 by calculating Kalman gain applied to the difference of y-x^