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I am given two time series of prices between 2009 and 2013. Price series A is weekly data, series B is monthly data. I would like to compare some basic descriptive statistics of these two time series data (such as mean, standard deviation etc).

Intuitively, I just wonder if the period sampling difference should be of any concern.... What could be some potential problems, and if there are ways to reduce the impact....

I guess the other way to put it is that, should I just pick the month-end numbers of series A to match the frequency of series B. I am not sure about this approach because the quality of statistics might be compromised for series A.

Thank you so much!

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  • $\begingroup$ How are the weekly data and monthly data computed? Also, what effect does the number of business days in the time period have on the calculation? $\endgroup$ – Wayne Nov 13 '13 at 22:26
  • $\begingroup$ At the very least, it's important to recognize and understand the concept of aliasing. $\endgroup$ – cardinal Nov 14 '13 at 2:42
  • $\begingroup$ Prices of what? $\endgroup$ – Matthew Gunn May 24 '16 at 5:44
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The sampling difference is a problem. To compare apples-to-apples, both series need to be based on the same frequency and timing. In this case, if Series B is based on the last day of each month, then Series A also needs to be based on the same days. If you can't get daily data for Series A then you may need to interpolate on the weekly data.

If seasonality is involved, then using weekly data is an even bigger problem. The main seasonality issue with weekly data is that there aren't 52 weeks in a year. Using 365 days per year and 7 days a week gives 52.14 weeks per year. That's not an integer number, which means that when a year ends, the associated week may or may not end. As result, all calculations have to be modified to reflect that. Monthly data has exactly 12 months per year. Each month may not have the same number of days, but that is typically understood for monthly data.

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Choosing between weekly and monthly data is called time binning not sampling. Oversampling has its merits when looking for signals or time series.

In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than the Nyquist rate. Theoretically a bandwidth-limited signal can be perfectly reconstructed if sampled above the Nyquist rate, which is twice the highest frequency in the signal. Oversampling improves resolution, reduces noise and helps avoid aliasing and phase distortion by relaxing anti-aliasing filter performance requirements.

The Nyqvist rate is essentially the minimum sampling frequency to reconstruct a signal of frequency $1/T$, where $T$ is the period of the signal. So, the minimum sampling frequency would be $F_s = 2/T = 2*B$

In this case, oversampling will be done on a random signal.

If multiple samples are taken of the same quantity with uncorrelated noise added to each sample, then averaging N samples reduces the noise power by a factor of 1/N.

This means that time binning your data will reduce noise. First, hypothesize how small the signal is then decided whether is better to sample weekly data or monthly.

Source

I am a hobbyist statistician so maybe someone else can give a better answer.

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