Adding two data sets, monthly and quarterly?

[tomadom]

I'm not sure if I've posted in the right section so please let me know if so.

I have two data sets that I want to add together. Both $ values.
The problem is that one is Daily data and the other is Quarterly data.

I am trying to picture how to do this. It wouldn't make sense to just add the quarterly figures to the end of quarter figures in the daily data but I was thinking that if I interpolate the quarterly data for the individual corresponding days, in a linear fashion (y = mx+b) then it can fill in the gaps between the quarterly data to make daily data? Or, should I be using a more curved relationship between the quarterly data to fill in for the daily values (Cubic Spline Interpolation), and if so Why? Would that work or is there something I'm not considering?

I've attached a file to show the two data sets in a picture form.

 

[Ken Abbott]

Dangerous to spline unless you have a very strong prior that that is how the data really behaves. You could Brownian Bridge the quarterly data, but it looks like you don't have too much history so your variance assumption would have to be too strong.

 

[Daniel Duffy]

GIGO

There are many interpolators; Cubic splines overshoot etc. The best ones we found were West-Hagan, Hyman 89 and Akima.

Depends what you want; nice plots or something else.

http://finmod.co.za/Monotone Convex Interpolation.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.529.9594&rep=rep1&type=pdf

linear fashion (y = mx+b) then it can fill in the gaps between the quarterly data to make daily data?
The accuracy will almost surely be very unreliable.. Good "linear interpolation error".

 

[tomadom]

I genuinely feel that in the absence of any real reason to assume that the data follows a certain pattern I should probably use straight lines as I have shown bridging the Quarterly data above. But I'm going to program all this using C++ so I just wanted to make sure I wasn't missing a major point. Just a linear bridge between quarterly figures may be all I need here.

I'll look up Brownian Bridge.

I'm really just trying to get the best interpretation of economic data I can. The appearance of the chart isn't so important.

Thanks for the replies. If anyone else would like to comment please do so as I'm interested in all perspectives here.