I have effectively removed weekly/daily seasonality from my time series by subtracting the same time interval a week before. This makes the series mostly stationary, which has been great for modeling it.
However, I have anomalous high/low periods in my data, some of which is from data loss. On these occasions, taking the previous week's difference results in an artificially inflated value.
Is there any precedence for subtracting, instead of simply the previous period's value, some average of the past n previous values? Perhaps a weighted one to privilege more recent periods?