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I have read some papers on forecasting time series with double seasonality (e. g. hourly data with daily and weekly seasonality). I understand that double seasonal ARIMA can be used for that purpose. However, some researchers instead create a different data set for each weekday and then fit a single seasonal ARIMA model to each data set (e. g. the SARIMA model estimated by a Kalman filter in Lippi et al. (2013): Short-term traffic flow forecasting: An experimental comparison of time-series analysis and supervised learning. IEEE Transactions on Intelligent Transportation Systems). The forecasting results of such an approach seem to be good in most papers but I have not found a theoretical foundation for doing that. It seems weird to me because it disturbs the pattern for the non-seasonal components of the model. For example, the lagged value for the AR(1)-component for the first value of each day is then the value of the last time point on the same weekday from the last week and not the value directly preceding the current time point.

Does anyone have a theoretical justification for such an approach (or a reference to paper discussing this issue)?

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