Initially, before apply arma model stationarity conditions must hold. According to that,time series data must have same variance and mean with normal distribution. If raw data is not normal then box cox transformation is employed. Afterwards using difference stationarity of mean also may be ensured. My questions are:
How do we assume the distribution of raw data at first ( for instance all points are normal distributed with different mean and variance belong to relevant time?)
Box-Cox transformation may not be successful to convert non normal data into normal data. However at least to make variance constant mostly used method I have ever seen is again box cox. I mean although box cox fails to make raw data normal significantly it is capable of stabilizing variance significantly. How does box cox method stabilize variance could you provide me with the analytical proof?
After we have applied box cox to make variance constant we may try to make mean stationary using dickey fuller test but this test employs t statistics which means power transformed data using box cox must be normal( as we have seen in regression we can involve t or f tests because of normality of data). As I said before box cox may fails to make data normal but always used at least make variance constant thus how do we proceed to apply dickey fuller t test after we applied box cox method to stabilize variance and have obtained not significantly normalized data?