I’m trying to understand the example in the book where they use 11 dummy variables for Jan-Nov when they test for monthly seasonality of returns. What exactly are they trying to do here? You have monthly return data from 1979 through end of 2002. You want to see if returns are different for any particular month. They set up this equation: R_t = b0 + b1 Jan_t + b2 Feb_t + … + b11 Nov_t Then they say that each monthly dummy variable is set to 1 if that month occurs! Then I’m lost! What exactly are we doing here? How would I know if January has a statistically different return from other months?
Conceptually 11 regressions are done using one calendar month each . You group the entire set using the dummy variable , so it neatly divides into 11 sets . The effect of only one calendar month are studied to the exclusion of others because the effects of other months is zero when you regress a month’s effect. That helps to pinpoint the particular month(s) whose effect is pronounced as given by a significance test of the mean
The Dummy variable is a Boolean (True/False, 1/0) variable. If Jan - then Jan_t=1, else 0. and so on for every period. Now based on your sales data - when you set up this equation - and find b_Jan, b_Feb and so on… your values pertain to like being a factor model (Factor for Jan=1 when Jan, else =0). Now based on B_Jan, B-Feb, etc. you can determine if the variable is significant based on the t-statistic.
ok, let us break into pieces so I (and any others) can understand it in more detail. 1) What is the dependent variable for this regression? Is it Rt, the monthly return? 2) What are the independent variable(s) in this case?
Do total returns to Index differ by month? Total Returns = Dependent Variable. Intercept = Average Returns of the Index in December. Then you have 11 Dummy Variables representing Jan, Feb, Mar… Nov. Additionally - you have also taken the difference of Returns in Jan against Returns in December on your data. Your regression is Total Returns against (Jan-Dec), (Feb-Dec),(Mar-Dec) … (Nov-Dec). If at the end of the regression - none of Jan-Nov variable coefficients are significant - it means - NO Returns to the Index do not depend on the Month. All the returns are totally explained by December Returns. When it is January - the January Dummy variable=1, all other variables are 0. If the January Coefficient in the regression is significant… you end up with Total Ret = Dec Return + 1(Delta Jan-Dec)
thanks cpk, I think it’s beginning to make sense…Are the independent variables 11 monthly change in returns (not actual returns)? Another thing is that they confused the issue more by still concluding no monthly bias, even though three of the months have statistically significant coefficients! So, I give up.
they mention that the estimated coefficients for the dummy variables shows estimated returned in that month and returns for december at the bottom of Pg 321. The F-Test which signifies are all coefficients equal to 0 or not - is failed. So the coefficients are not statistically significant. there are two levels - 1. if the variable itself is statistically significant. --> T-Test 2. Are any of the variables significant from a totality perspective --> F-Test. If F-Test is not significant - (p-Value is too high) [Given by Significance-F=0.1213] -> and a low F-Value < FCrit of 1.87 --> your dummy variables are not significant -> so total returns is explained quite satisfactorily by the December returns.
Great feedback, thanks.