# Thread: estimate an equation recursively

1. ## estimate an equation recursively

Hi,

I have the following equation:

Rt= c + aRt-1 + vt (1)

where Rt are returns at time t, c is a constant, a is the parameter of returns at time t-1 and vt is an error term at time t.

I need to compute adjusted retruns at time t, that is R adjt, as follows

R adjt = vt /(1-a) (2)

Equation (1) must be estimated recursively. I do not really understand what I should do to estimate that equation recursively.

Any suggestions?

Thank you,

fran

2. Originally Posted by fraN
Hi,

I have the following equation:

Rt= c + aRt-1 + vt (1)

where Rt are returns at time t, c is a constant, a is the parameter of returns at time t-1 and vt is an error term at time t.

I need to compute adjusted retruns at time t, that is R adjt, as follows

R adjt = vt /(1-a) (2)

Equation (1) must be estimated recursively. I do not really understand what I should do to estimate that equation recursively.

Any suggestions?

Thank you,

fran
What you have written is almost incomprehensible.

Kalman filter - goole for it

3. Originally Posted by fraN
Hi,
I have the following equation:
Rt= c + aRt-1 + vt (1)
where Rt are returns at time t, c is a constant, a is the parameter of returns at time t-1 and vt is an error term at time t.
I need to compute adjusted retruns at time t, that is R adjt, as follows
R adjt = vt /(1-a) (2)
Equation (1) must be estimated recursively. I do not really understand what I should do to estimate that equation recursively.
Any suggestions?
Thank you,
fran
First Question: Do you understand recursion?

If you do, then plug is some initial value and you will be a 2nd value.
The use the 2nd value to calculate the 3rd value.
It may be necessary to do a 4th and 5th values.
You can determine the difference between the values. For any set of values you should then have enough data to estimate the terminating result.

If you were doing it efficiently -- taking the derivitive or Newton's method would give you what you want.

4. Originally Posted by aidan
First Question: Do you understand recursion?

If you do, then plug is some initial value and you will be a 2nd value.
The use the 2nd value to calculate the 3rd value.
It may be necessary to do a 4th and 5th values.
You can determine the difference between the values. For any set of values you should then have enough data to estimate the terminating result.

If you were doing it efficiently -- taking the derivitive or Newton's method would give you what you want.
You are going off at halfcock, the question is about recursive estimation of a system state from noisey measurements.

CB

5. Thanks Aidan and CB for replying me.

I was wondering whether I have to use the Kalman filter on the Time series of Returns.

If this is the right way, I guess I must use the filtered Returns in equation (1).

Hope my question is comprensible.

Thanks

fran