Econometrics:

When dealing with time series data, it is often useful to include in the regression variables that account for seasons and/or trends. Assume we have data at the quarterly frequency. We could create seasonal dummy variables such as (only showing first 4 observations) 0 S1 S2 = S3 $4 0 1 0 0 0 0 0 In this set-up si takes a value of 1 for the first quarter and so on. Explain how you could specify your regression model in order to take into account those. seasonal effects. Be specific about your X matrix and the matrix containing the seasonal variables, S. You can use the following generic specification to start your discussion (be specific about the components of S and X) Y = S8 + X + e Interpret the OLS coefficient B. The FWL theorem will be useful. When dealing with time series data, it is often useful to include in the regression variables that account for seasons and/or trends. Assume we have data at the quarterly frequency. We could create seasonal dummy variables such as (only showing first 4 observations) 0 S1 S2 = S3 $4 0 1 0 0 0 0 0 In this set-up si takes a value of 1 for the first quarter and so on. Explain how you could specify your regression model in order to take into account those. seasonal effects. Be specific about your X matrix and the matrix containing the seasonal variables, S. You can use the following generic specification to start your discussion (be specific about the components of S and X) Y = S8 + X + e Interpret the OLS coefficient B. The FWL theorem will be useful