Why Time Series has to be STATIONARY ???
This question choked me up for a long time when I had my first introduction to Time Series. I searched it all over, even took help from fellow kagglers but in vain. Recently, I got a great explanation.
Dependent & Independent data
First of all, let’s clear this. Independent data can be any collection of samples independent of each other. Like Titanic, Household Regression & so on.
Dependent data, as you would have guessed, samples are dependent on each other. Like in Time Series. Here each sample is dependent on other samples present in the data
We must understand a thing, Independence cannot give us an idea of any sort of magnitude or pattern to follow up for prediction
Example-If two numbers are equal, we know their magnitudes are equal but if they are unequal, we don’t have any relation between their magnitudes. Like one can be double of the other,1/2th of the other, or even an imaginary number. But the catch is WE DON’T KNOW the reason behind the inequality!
but for dependency, we can have some idea if we know at least one value. But we have got a problem, dependency can still take many forms. For Example-
Y=a+bX
Y=a+bX²
Y=a+bX³
here Y is dependent on X but each time the dependency takes a different form. But if we say Y is independent of X it can take any form.
Stationarity is just that form/model out of all the dependency models we use to find the relation between the samples in a time series & hence we try to bring our time series in stationary form.
Stationarity & Non-Stationary data
Like in the case of dependence & independence, the same goes for stationarity & non-stationarity. Like for stationarity we know we need constant mean, std & autocorrelation but for non-stationarity, we don’t know anything!! Non-stationarity, as discussed for independent data, can take any form. No fixed norms are present which can model non-stationary data like there exists ARIMA, AR, MA, or any other model for stationary data.
The mean can be double, or triple the previous observations can be 0. The same goes for std & autocorrelation, hence it cannot be modeled & that’s why we convert non-stationary data to stationary first so that we know something about the features of this time series & hence can & apply our different models that I will be explaining in my next article!!!
