outlier detection in time serie without using windows
You can try to remove trend and seasonality and check whether the time series is stationary. If it is, you can calculate mean ($\mu$) and standard deviation ($\sigma$). Now for each data point, you calculate the distance from the mean ($\|y-\mu\|$) and check if it exceeds some threshold. The default value for threshold is $3 \sigma$ what comes from three-sigma rule motivated by the assumption about the normality of the data (residuals after time series decomposition in our case). You can choose any threshold which is reasonable for you. One solution is to find the distribution of the data and derive a rule for this particular distribution.