First of all, What I know is that the i.d.d cannot be applied at each observation and another observation is not the same because at each time point that data point can be any possible value at that point but not the same as the next or previous or other periods.

So most of what I learned in Regression on the Time series is that it is okay if the estimator is not the function of time or to say that the true parameter that we interest in is not varied through time.

What is the difference? what techniques we can use to estimate the time series data? (Can be any techniques not limited to regression)

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    $\begingroup$ There are many things to consider that can be quite subtle. For example it is possible to "naively" use methods designed for i.i.d data and still get un-biased estimators with incorrect variance (GEE). These variances can then be "corrected" to account for the correlation in the data the naive method ignored. Similarly if you have a rich enough covariate set you can render the model residulas i.i.d - for example including "dynamic" time-varying covariates in your model, including lagged responses. This shows that i.i.d is an assumption based on the condtioning set and the model. $\endgroup$ – dandar Feb 13 at 23:26

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