DISAGGREGATE - a general procedure for interpolation

[fadimohamed]

Dear tom,
with respect to the constant, as mentioned in the dissagregate.src, the constant is used only in (model=AR1), is it meant here the linear model or is it meant (tsmodel=AR1)?

[TomDoan]

Sorry. Yes, it means TSMODEL=AR1.

[TomDoan]

As for Stock and Watson's research memorandum "Distribution of quarterly values of GDP/GDI across months within the quarter
Background", is there a replication here?

http://www.princeton.edu/~mwatson/mgdp_gdi.html

This does one of the examples (distributing Government expenditures). It needs the updated version of @DISAGGREGATE (from the beginning of the thread) since it needs the new MAINTAIN=WEIGHTEDSUM option.

ratscode.rpf

Program file

(3.19 KiB) Downloaded 14 times

DISTRIBUTE_GDP_GDI_INPUT.xls

Data file

(268.5 KiB) Downloaded 13 times

[fadimohamed]

Dear tom,

assuming i dont have the day of the week effect, would you provide me a plain example of how to interpolate data from
monthly to weekly?

thanks for your help

[TomDoan]

I don't have one. Do you have an example from the literature where anyone has done this?

[fadimohamed]

i have reviewed the literature for interpolating monthly data to weekly but unfortunately all what i have found is just mentioning briefly
without a concrete methodology,

as you mentioned before

You can't use @DISAGGREGATE to do monthly to weekly. That procedure is designed to handle only frequencies which are a fixed number of subperiods. The same underlying idea can be used from monthly to weekly, but you have to figure out how you want to handle the weeks that split across months. There are many ways that one could do that, since for some data sets, there are day-of-the-week effects, so Saturday and Sunday might need different weights than the weekdays. If there are day-of-the-week effects, the input monthly data may or may not have already been adjusted for those, which makes the weight handling in the disaggregation more complicated.

so how can i handle the weekly missing data points without affecting monthly real data?

thanks

[TomDoan]

i have reviewed the literature for interpolating monthly data to weekly but unfortunately all what i have found is just mentioning briefly
without a concrete methodology,

as you mentioned before

You can't use @DISAGGREGATE to do monthly to weekly. That procedure is designed to handle only frequencies which are a fixed number of subperiods. The same underlying idea can be used from monthly to weekly, but you have to figure out how you want to handle the weeks that split across months. There are many ways that one could do that, since for some data sets, there are day-of-the-week effects, so Saturday and Sunday might need different weights than the weekdays. If there are day-of-the-week effects, the input monthly data may or may not have already been adjusted for those, which makes the weight handling in the disaggregation more complicated.

so how can i handle the weekly missing data points without affecting monthly real data?

thanks

The way DISAGGREGATE works is to set up a state-space model for the higher frequency. The measurement equation has one valid observation each quarter (for monthly to quarterly) in the final month which says that Q is equal to (with no error) either the average or the sum of the unobserved monthly data. For weekly to monthly, you can create a similar state-space model for the unobservable weeks. The problem is the handling of the measurement equation. When should M be observed? That will depend upon the timing of the weekly data---it can't be until the last week which has days within that month. And how is the monthly data supposedly constructed from the weekly? Anything you do there will be based upon some assumption of how the underlying daily data would work. If you say Month=2/7 x week1 + week2 + week3 + week4 + week5 + 1/7 x week6 for a month that has one day off one end and two off the other, then you are implicitly assuming that the days in a week are roughly equal. For how many economic data series is that a reasonable assumption? Are the data at the daily level affected by holidays? It's your data, you'll have to figure out how you want to handle that.

If someone didn't describe any concrete methodology, I would speculate that they simply used something like what the RATS DATA instruction does, which is to take a week which spans the boundary between two months and takes a weighted average of the monthly numbers based upon the number of days in each month, that is,

(3 x Jan + 4 x Feb) / 7 if the week ends February 4

That's rather crude, but it's the best that can be done without making assumptions about the time series behavior of the underlying weekly data.