Using days to bridge data (different frequency)

[tomadom]

I'm trying to understand the merits and flaws of the days I choose to bridge two data sets. I have already posted and addressed the issue of the method used. I'm now looking at the days.

Task: Converting Monthly data to daily data (for the purpose of this exercise I will use a linear approach).
The days I choose to count in each month to generate data for is what is important for this question.

Method: I have Quantlib (C++ quant library) and have tested other data sets such as stock data to see if they strictly adhere to the Business days for a given calendar (say Australia() in my case). And they don't . Days appear in that data set which are holidays but trading went ahead.. I think it will be rather difficult to find a robust way of adhering to the public holidays in each year so I have chosen another method.

Quantlib allows you to find Weekdays() for each day in each reference month. So I thought if I was going to turn monthly data into daily data (using a linear method, but that's not relevant), then I just adhere to adding days for weekdays and not weekends.

What's the best approach here? Is my method considered plausible?
Thanks

 

[yetanotherquant]

To be true I only vaguely understand what you want (though I read your post several times).
Generally, it depends on the kind of data you want to interpolate.
So you want to linearly interpolate stock prices (from monthly to daily), don't you?
If yes, it is a bad idea, as the volatility is not linear in time and secondly, (intra)day-tails (relative to the scale) are much heavier than monly.
But first of all - what do you do it for?! Daily OHLC prices are available for free from Yahoo.Finance.

P.S.
A better idea may be to find a suitable model in continuous time. Then, theoretically(!), you can fit it to whatever data and then up- or downscale as you want.

 

[Ken Abbott]

PM me. I had had to solve this problem. I know of two different approaches to doing this. One is closed-form, the other is Monte Carlo based.

 

[IntoDarkness]

like ken said, use a brownian bridge. its closed form

 

[tomadom]

Hi. Thanks for the replies. I think, from your answers, that there are two issues here.

All I was originally asking is whether or not I should count the weekends when converting monthly to daily data (not stock data but economic data). I have assumed that I would because figures such as 'Consumption' and 'Government spending' all accumulate over time.
(this is in the absence of any information about whether that monthly data covers weekends as well).

The second matter is how to bridge the data when I convert monthly to daily. I will have 20-30 days in which to find values for. I chose linear because I feel that I can't really assume anything else unless I have a strong prior. Maybe a Continuous compounding curve between the start and end of the month to cover the 20-30 days I'm converting to would be a good idea too. Not sure. Any assumptions though will affect figures such as 'Rate of Change' in data over say 12 months or 365 days. So I have to be careful. Maybe some of you can highlight some arguments about this.
I will be doing this with both Stock Data and Economic Data. They will be handled differently to each other.

My original question took the long way to ask a relatively simple question. In turn, I've invoked another important question which some of you have answered above.

 

[Ken Abbott]

Weekends don't count unless they are trading days (which they usually aren't.)

 

[tomadom]

Does this also apply to economic data such as 'Consumption expenditure' and other national accounts data?

The reason I ask is that 'Consumption' continues on weekends and could show a varying rate of growth if such data was extracted on a weekend.

Trading data I understand.