Suppose we have a function $$ y = a \cdot t^b \cdot \exp(-ct) $$ here $t$ is time in days and $y$ is yield per day. Usually $0< t <300$. An asset exists for multiple years, so the yield function $y$ can be applied to the asset multiple times during its lifetime to approximate the daily yield within a year. However, the coefficients $a,b,c$ of the yield function change over the years.
All data points $(t,y)$ from previous years (curves) as well as data points during the current year are available. It is task to predict the total yield of the current year (using historic and up-to-date data) and to predict yields in future years.
What will be the best method to tackle this problem?
I was thinking to fit the curve for each year, and make a machine learning model to give me $a,b,c$ for any inputs $(t,y)$? And use the trend over years to calculate the total yield in future years ?
Has anyone suggestions how to deal with this problem?