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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.

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  • $\begingroup$ I don't understand what you mean by "gaussian distributed time series". Can you precisely define it? Are you saying that each element of the time series is sampled from 1. the same or 2. possibly different Gaussian? In general, I don't fully understand your problem. Do you have the original time series $X_t$? If not, do you want to estimate it from "noisy" similar time series? I don't understand how subtracting $a$ from $X_t$ gives you any insight. Also, I don't understand how you are going to generate $Y_t$ if you don't have $X_t$. Are you assuming that $Y_t$ is $X_t -a$, for some $a$? $\endgroup$ – nbro Apr 25 at 23:44
  • $\begingroup$ @nbro Thanks for your response. The time series $X_t$ is given, and we know it has a Gaussian distribution, (histogram: Gaussian). So each point in $X_t$ belongs to a gaussian distribution with the same mean and variance. Now if you subtract a from each point in $X_t$ to construct a different series $Y_t$ the mean of the gaussian shifts. For some $a$, the constructed $Y_t$ has 0 mean. What I am asking if you vary $a$ and try to see for what $a$ this is achieved, then use that correctly found a, to generate more data points of $Y_t$, from $X_t$ can I call it as ML? $\endgroup$ – Raunak Dey Apr 27 at 17:40

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