basic time series seasonality question

Question

I need to do seasonality analysis on a daily time series by which I mean the following:

• Understand the relation between day of the week and data.

• Use deseasonalized series as an input to the forecasting model.

I am comparing 2 methods for this:

1. Usual dummy variable

   • Do a regression yt= b1D1+b2D2...b5D5 + ut where bi are the regression coefficient and Di are the dummy for day of the week. ut is the residual.

   • Use bi coefficients as an estimate of the average seasonal effect of the day of the week and the residual series as a deseasonalized series for forecasting.

2. Averaging over data

   • Calculate average by the day of the week over all data. Call this average Ai (so 5 total from A1 to A5).
   • Divide each Ai by Average(A1 to A5). Call it Si. This gives an estimate of seasonal effect of each day.
   • To deasoanlize the series, divide the original series by Si.

I am trying to understand the conceptual differences in these two approaches. Is one approach preferable to the other?

Answer 1

Either these two (very simple and very dated) approaches (x11 type) or any one of a number of possible alternative approaches could be correct . Only the data knows for sure.

Daily data can often exhibit some of the following effects and the idea is to identify the important ones .....

Trends, Seasonality, Monthly or Weekly patterns, Level Shifts, Big increases and drops, but not necessarily a trend, Autoregressive behavior (ARIMA), Fixed Day of the month, Seasonal Pulses (Changes in Day of the week effects) , Interventions, Holidays plus before and after and others like day-of-the-month , week-of-the-month. Error variance and/or parameter variance over time can also come into play AND possible response to known external effects .

Both of your approaches implicitly assumes no ARIMA structure which if present can seriously impact tour results. If you post your data in a column oriented CSV file and identify the country and initial date, I will try to help you.

You might want to look at http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/53-capabilities-presentation as it has a presentation of some daily data and the resultant analysis.