I have a gaussian distributed time series ($X_t$) with some parameters in my experiment. Suppose I want to know the mean $\mu$. If I define another time series $Y_t$ such that $Y_t=X_t-a$ for all $t$. Now say I vary this parameter $a$ and generate altogether different time series for each $a$, say $Y_t(a)$. I look at the mean of $Y_t$ for each $a$. The value of a, where I get the mean of $Y_t$ closest to $0$, will be my estimate of $\mu$. Say I will eventually use this learnt value of $\mu$ to generate $Y_t$ as my final goal. Can this be called ML? I am using some training data of $X_t$ to learn about its parameter and then using test data of $X_t$ to generate $Y_t$.
Now why am I working so hard on this simple problem? Well, actually I am not. I am doing something else, which will have lots of parameters in the time series and will be used to generate other time series after similar parameter extraction. That will be too complicated to discuss here. I just wanted to clear my basics using an over-simplified example. I am a new to ML, and help is appreciated.