For example, I have the following data:
$Y = 366$ measured values
$X = 366$ measured values
$t = [ 1 : 366 ]$, representing the days of the year (index)
So at each $t$ (day), we have value of $Y$ and corresponding value of $X$. When drawing $Y$
and $X$ vs. $t$, it shows a continued curve for $Y$ with disturbances. These disturbances
are caused by the change of $X$ and it is clear that $Y$ is mainly affected by $X$, meaning
that: $Y = f(X)$
This figure is shown here:
This figure shows $Y$ vs. $X$:
My aim is to find this relation between $Y$ and $X$ or in another words: $Y = f(X)$.
What I have tried and think so far is first to smooth the curve $Y$ and from the
smoothed points and smoothed curve, some function may be established.
Then, including the effect of disturbances (up and down) by some function,
may be exponential.
Could you please guide me how can I manipulate this problem to get
a final model $Y = f(X)$.