<p>CPI is a stock while GDP is a flow. Re-sampling of stocks to higher frequencies can be approximated with a number of choices, but probably the most common is linear interpolation. In some contexts filling forward and filling backward are common. But in principle you could fit any function you want through all the points you have and use the values from the function instead. Flows are a bit more complicated because annual flows are the sum of monthly flows. Dividing the annual flow into twelfths across the entire year is analogous to filling forward or filling backward (depending on what month of the year is the date of annual measurement). For example, if GDP is 144 and measured in December of 2018, assigning every month in 2018 a value of 12 is similar to filling backwards. But again, as long as you remember that the flows are supposed to add up across months to equal or approximate annual flows you can you a number of functional forms to approximate them. </p>

<p>This is a big topic. I recommend searching for papers related to "<a href="https://scholar.google.com/scholar?hl=en&amp;as_sdt=0,21&amp;q=interpolate%20time%20series" rel="nofollow noreferrer">interpolated time series</a>". <a href="http://www.math.ucsd.edu/~politis/PAPER/editor.pdf" rel="nofollow noreferrer">Resampling and Subsampling for Financial Time Series</a> by E Paparoditis, DN Politis might be a good, if advanced, place to start. <a href="https://ec.europa.eu/eurostat/ramon/statmanuals/files/KS-DT-05-030-EN.pdf" rel="nofollow noreferrer">Modeling and Forecasting Time Series Sampled at Different Frequencies</a> by Casals, Jerez, and Sotoca is another useful reference. In comparing the effectiveness different methods, <a href="https://res.mdpi.com/water/water-09-00796/article_deploy/water-09-00796-v3.pdf?filename=&amp;attachment=1" rel="nofollow noreferrer">Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment</a> by Lepot, Aubin, and Clemens provides a nice list of methods but doesn't focus on the stock versus flow distinction. </p>

<ol>
<li>Deterministic methods (fill forward or back)</li>
<li>Nearest-neighbor</li>
<li>Polynomial interpolation</li>
<li>Distance weighting methods</li>
<li>Fourier transformation based methods</li>
<li>Regression models</li>
<li>Auto-regressive models</li>
<li>Machine learning based methods</li>
<li>Kernel methods</li>
<li>K-nearest neighbors</li>
<li>Box-Jenkins models</li>
<li>Kriging-based methods</li>
</ol>

CC BY-SA 4.0
2019-01-04T11:13:04.457Z
2019-01-04T11:13:04.457Z
BKay
<p>As there are no other answers, I will offer an informal answer. </p>

<p>Converting from annual to monthly data is effectively inserting information into the series. As a result, the choice of conversion will affect the analysis. It is safer to convert everything to the lowest frequency (annual), as that has much less effect on results.</p>

<p>To convert monthly to annual data, two standard techniques are to either take the latest value (December) or the annual average. It would make sense to have the choice aligned with the methodology for the annual data.</p>

<p>Unfortunately, I do not have books to suggest that cover this topic.</p>

CC BY-SA 4.0
2019-01-04T11:37:04.520Z
To convert monthly to annual for export data, surely the straightforward technique is addition?  I'm assuming here that the data are value of exports for each month.
Adam Bailey
CC BY-SA 4.0
2019-01-05T04:23:11.407Z
Sum of all the months in the year? Sure, but that is just a scaling of the average (12 times the monthly average).
Brian Romanchuk
CC BY-SA 4.0
2019-01-04T03:06:47.543Z
2019-01-04T03:06:47.543Z
Brian Romanchuk
<p>I have annual GDP, annual CPI, monthly exchange rate, and monthly export data. I would like to go for estimation being monthly stock return as the dependent variable. What are the methods to treat the annual figures in to monthly and/or the monthly in to annual? Please, I need your recommendations or books to read?</p>

CC BY-SA 4.0
2019-01-04T03:08:51.397Z
One thing: in the title, you should use “frequencies”, not “dimensions.” The current title is confusing.
Brian Romanchuk
<inflation><gdp><paneldata>
How to treat different frequencies of a time series data?
Enrico Dace
# How to treat different frequencies of a time series data?

(Asked by: username_0 on 2019-01-01)

I have annual GDP, annual CPI, monthly exchange rate, and monthly export data. I would like to go for estimation being monthly stock return as the dependent variable. What are the methods to treat the annual figures in to monthly and/or the monthly in to annual? Please, I need your recommendations or books to read?

**Tags:** inflation, gdp, paneldata
> **Comments:**
> **username_1**: One thing: in the title, you should use “frequencies”, not “dimensions.” The current title is confusing.  

---

## 2 answers

### Answer by username_2 on 2019-01-04. Score: 1 | Accepted answer

CPI is a stock while GDP is a flow. Re-sampling of stocks to higher frequencies can be approximated with a number of choices, but probably the most common is linear interpolation. In some contexts filling forward and filling backward are common. But in principle you could fit any function you want through all the points you have and use the values from the function instead. Flows are a bit more complicated because annual flows are the sum of monthly flows. Dividing the annual flow into twelfths across the entire year is analogous to filling forward or filling backward (depending on what month of the year is the date of annual measurement). For example, if GDP is 144 and measured in December of 2018, assigning every month in 2018 a value of 12 is similar to filling backwards. But again, as long as you remember that the flows are supposed to add up across months to equal or approximate annual flows you can you a number of functional forms to approximate them.

This is a big topic. I recommend searching for papers related to "[interpolated time series](https://scholar.google.com/scholar?hl=en&as_sdt=0,21&q=interpolate%20time%20series)". [Resampling and Subsampling for Financial Time Series](http://www.math.ucsd.edu/~politis/PAPER/editor.pdf) by E Paparoditis, DN Politis might be a good, if advanced, place to start. [Modeling and Forecasting Time Series Sampled at Different Frequencies](https://ec.europa.eu/eurostat/ramon/statmanuals/files/KS-DT-05-030-EN.pdf) by Casals, Jerez, and Sotoca is another useful reference. In comparing the effectiveness different methods, [Interpolation in Time Series: An Introductive Overview of Existing Methods, Their Performance Criteria and Uncertainty Assessment](https://res.mdpi.com/water/water-09-00796/article_deploy/water-09-00796-v3.pdf?filename=&attachment=1) by Lepot, Aubin, and Clemens provides a nice list of methods but doesn't focus on the stock versus flow distinction.

1. Deterministic methods (fill forward or back)
2. Nearest-neighbor
3. Polynomial interpolation
4. Distance weighting methods
5. Fourier transformation based methods
6. Regression models
7. Auto-regressive models
8. Machine learning based methods
9. Kernel methods
10. K-nearest neighbors
11. Box-Jenkins models
12. Kriging-based methods


---

### Answer by username_1 on 2019-01-04. Score: 0

As there are no other answers, I will offer an informal answer.

Converting from annual to monthly data is effectively inserting information into the series. As a result, the choice of conversion will affect the analysis. It is safer to convert everything to the lowest frequency (annual), as that has much less effect on results.

To convert monthly to annual data, two standard techniques are to either take the latest value (December) or the annual average. It would make sense to have the choice aligned with the methodology for the annual data.

Unfortunately, I do not have books to suggest that cover this topic.

> **Comments:**
> **username_3**: To convert monthly to annual for export data, surely the straightforward technique is addition?  I'm assuming here that the data are value of exports for each month.  
> **username_1**: Sum of all the months in the year? Sure, but that is just a scaling of the average (12 times the monthly average).  

---

