Deseasonalizing Data

[ulas alk]

Hi Everyone,

I have a model as follows:

S(t) = a + B1*S(t-1) + B2*Smax + B3*Month2 + B4*Month3 + ...... + B13*Month12 + B14*Week1 + B15*Week2 + B16*Week3 + epsilon

St: Price
St-1: Lag price
Smax: Max price up to that point
Month1 ... Month12: Dummy variable. (Month1 is equal to 1 if in month 1 etc.)
Week1 .... Week4: Dummy variable (Week1 is equal to 1 if in first week of the month etc)


My code is as follows:

regress St Month2 ...... Month12 Week1 Week2 Week3
predict eSt, resid

regress St_1 Month2 ...... Month12 Week1 Week2 Week3
predict eSt_1, resid

regress Smax Month2 ...... Month12 Week1 Week2 Week3
predict eSmax, resid

regress eSt eSt1 eSmax


1. My first question is that can I use this model even though I have two different dummy variables? (Week and month)
2. Also, how should I interpret these coefficients? I mean are the coefficients of est1 and eSmax deseasonalized model's coefficients? or do I need a further step?

Thanks for your helps and time in advance.

Best

[Clyde Schechter]

1. My first question is that can I use this model even though I have two different dummy variables? (Week and month)

I don't really get the question. The answer seems to me to be so clearly "yes" that I don't understand why you are raising it as a question. So I have the feeling I'm missing something here. You can put, in effect, as many different sets of indicator (dummy) variables into a model as you like (well, within the limits of memory and what Stata's matrices will handle.)

2. Also, how should I interpret these coefficients? I mean are the coefficients of est1 and eSmax deseasonalized model's coefficients? or do I need a further step?

It depends on what you mean by "deseasonalized." It's an odd approach. What you have done here is categorized each observation by which month of the year it occurs in and by which week within month. So you are modeling out periodic effects on the outcome that have a duration of a month and recur annually. That is, you are treating January 1885 as being equivalent to January 2017. That's not unusual. What does strike meas unusual is the further classification into weeks 1 through 4 of the month. This is modeling out periodic effects on the outcome that have a duration of about a month and recur weekly. You are treating Week 1 of March 2017 as equivalent to Week 1 of December 1885. There's nothing necessarily wrong with that if there really are effects like that operating in your data. But I've not seen it before. (Then again, this looks like some kind of economic or financial analysis, so it's out of my domain and I wouldn't necessarily see things like this. In my line of work, epidemiology, this would be bizarre.) There is another minor point: only non-leap year February fits into 4 weeks. Any other month will have dates that do not fit your four week classification. How did you handle those?

[ulas alk]

Dear Clyde,

Thanks a lot for your reply. For February and the other months that have more than 4 weeks,I am ignoring those. So there is nothing wrong with this approach in my case but thank you for your comment and warning. This might be easily and error in any other similar case. Regarding your confusion,

Of course I know that I can use more than one dummy but my questions are as follows:

1. For two dummy case, can I use this approach to get the residuals? or should I get residuals by regressing dependent and independent variables on each dummy separately? I think my approach is correct (regressing dependent and independent variables on both dummies together for each dependent and independent variable) but could not be quite sure though.

2. Are these coefficients deseasonalized coefficients or should I do a further estimation? I mean you understood what I am trying to do correctly. I know My model is a bit odd but trying to find out something. In this case, should I do a further estimation? Can I interpret these coefficients as deseasonalized coefficients?

Thanks again for your valuable comments.

Best,
Ulas

[Clyde Schechter]

Of course I know that I can use more than one dummy...

Yes, I suspected as much, which is why I said I felt like I was missing something. I'm sorry if I came off condescending or insulting--that was not my intent at all.

1. I also think your approach is correct, given your explanation.

2. Yes, I would consider the coefficients of the other variables to be de-seasonalized (with this definition of seasonality). I don't know what additional estimations you have in mind, so I can't really comment on that.

[ulas alk]

Thank you so much for your help. I did not take it as insulting, I just tried to express that my intent was a bit different. Your comments helped me a lot!