<blockquote>
<p>For example, the response of <span class="math-container">$y_t$</span> to a shock in <span class="math-container">$x_t$</span> should be expected to be different at monthly, quarterly and annual frequencies, right?</p>
</blockquote>
<p>Generally (and usually), yes.</p>
<blockquote>
<p>Or it is that the results should be similar irrespective of the frequency of the data?</p>
</blockquote>
<p>Generally (and usually), no. The answer to your question depends on the underlying data generating process (DGP). You can take an example process and analyze it at different levels of time aggregation analytically to figure out implications for what happens when we look at it using different frequencies. E.g. take a monthly AR(1) process
<span class="math-container">$$
y_t=\varphi_1 y_{t-1}+\varepsilon_t
$$</span>
and see how it behaves when aggregated to quarterly or annually:
<span class="math-container">$$
\sum_{i=1}^{3}y_{t-i+1}=f\left(\sum_{i=1}^{3}y_{t-3-i+1}\right)+u_t
$$</span>
and
<span class="math-container">$$
\sum_{i=1}^{12}y_{t-i+1}=g\left(\sum_{i=1}^{12}y_{t-12-i+1}\right)+v_t
$$</span>
where you need to figure out <span class="math-container">$f(\cdot)$</span> and <span class="math-container">$g(\cdot)$</span> based on the original AR(1) model.</p>

CC BY-SA 4.0
2021-01-22T12:43:27.127Z
Thanks @Richard. I asked this question because papers don't usually say why they are using data of a certain frequency in their research. Any reasons why quarterly data is popular?? I guess the finer the data, the better. But quarterly data is how far we can go...and it is available for most series. Of course some variables are available at monthly frequency...but maybe not for all the variables in our model. Or probably, is it because consumers of economic model like central banks care about Dynamics at annual frequency??
Emmanuel Ameyaw
CC BY-SA 4.0
2021-01-22T13:17:42.383Z
@EmmanuelAmeyaw, data availability might be the key factor here. Regarding the finer, the better, it is often true but not always so. Sometimes it matters that we have a long sample in terms of calendar time, not in terms of sample size. E.g. just sampling the data finer and finer does not help much with estimating long-run relationships.
Richard Hardy
CC BY-SA 4.0
2021-01-21T11:13:37.883Z
2021-01-21T11:13:37.883Z
Richard Hardy
<p>I have read blogs posts that say one should use monthly, quarterly or annual data depending on whether you want to predict monthly, quarterly or annual outcome respectively.</p>
<p>So I guess the same applies to studying the dynamics of two or more variables using a VAR model. For example, the response of <span class="math-container">$y_t$</span> to a shock in <span class="math-container">$x_t$</span> should be expected to be different at monthly, quarterly and annual frequencies, right? It appears so in my experiment in the attached figure.</p>
<p>So saying that &quot;the response of <span class="math-container">$y_t$</span> to a shock in <span class="math-container">$x_t$</span> is positive&quot; is incomplete, I guess. Perhaps, it is better to say, &quot;the response of <span class="math-container">$y_t$</span> to a shock in <span class="math-container">$x_t$</span> is positive at annual frequency, negative at quarterly frequency, and so on&quot;.</p>
<p>Or it is that the results should be similar irrespective of the frequency of the data?</p>
<p><a href="https://i.sstatic.net/qF2Yg.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qF2Yg.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2021-01-10T23:37:37.847Z
how are the different models specified? The inclusion of different numbers of lags can really alter the results
Andrew M
CC BY-SA 4.0
2021-01-11T03:03:50.147Z
Thanks!. Same model, same everything...only data changes. They are all 2-variable VAR(1).
Emmanuel Ameyaw
CC BY-SA 4.0
2021-01-11T22:15:22.977Z
Do you include seasonal dummies? Because you probably should for both the quarterly and monthly data. Also it is important to note that 100 steps ahead is not the same as 100 steps ahead for monthly data or quarterly data i.e. 100 years $\neq$ 100 quarters $\neq$ 100 months
Andrew M
CC BY-SA 4.0
2021-01-11T22:50:58.440Z
Also 1 lag in annual terms would be similar to the 4th lag in quarterly terms of the 12th lag in monthly terms. So doesn't really make much sense to compare identical models. Either way none of the effects are significant either which suggests all your models are pretty poor. Therefore I wouldn't trust the signs on the impacts that you see in the figures.
Andrew M
CC BY-SA 4.0
2021-01-12T23:26:08.343Z
But my question is should I expect similar results using quarterly, monthly, or annual data...after doing all the stuff you have suggested? I mean, is there some statistical proof or evidence that data frequency doesn't matter much for a VAR model if indeed you do all the necessary stuff...seasonality, lag length, etc, appropriately for each model. In others words, which frequency should I choose for my VAR model? Based on what? Based on which frequency I want to forcast? But I am not interested in forcast here, just capturing dynamic relationships. Does data frequency matter?
Emmanuel Ameyaw
CC BY-SA 4.0
2021-01-12T23:48:13.980Z
may I ask though...so we should kinda disregard research papers with insignificant irfs, right? I mean, I see a lot....can I say for example that those models are poor...and used that as a basis to write another paper, hopefully a better one where irfs are significant??. Hmm, Can't we have a good model (based on theory) with insignificant results?? Sims(1972) for example used only money supply and GNP in his model...if I used that model for another dataset and find insignificant results, can I say the model is not good, for example?
Emmanuel Ameyaw
CC BY-SA 4.0
2021-01-21T11:05:44.457Z
Disregarding insignificant findings is a recipy for disaster and among the top reasons for [why most published research findings are false](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124), according to Ioannidis.
Richard Hardy
<macroeconomics><applied-econometrics>
Annual data VS Monthly data VS Quarterly data for a VAR model
Emmanuel Ameyaw
# Annual data VS Monthly data VS Quarterly data for a VAR model

(Asked by: username_0 on 2021-01-10)

I have read blogs posts that say one should use monthly, quarterly or annual data depending on whether you want to predict monthly, quarterly or annual outcome respectively.

So I guess the same applies to studying the dynamics of two or more variables using a VAR model. For example, the response of $y\_t$ to a shock in $x\_t$ should be expected to be different at monthly, quarterly and annual frequencies, right? It appears so in my experiment in the attached figure.

So saying that "the response of $y\_t$ to a shock in $x\_t$ is positive" is incomplete, I guess. Perhaps, it is better to say, "the response of $y\_t$ to a shock in $x\_t$ is positive at annual frequency, negative at quarterly frequency, and so on".

Or it is that the results should be similar irrespective of the frequency of the data?

[![enter image description here](https://i.sstatic.net/qF2Yg.png)](https://i.sstatic.net/qF2Yg.png)

**Tags:** macroeconomics, applied-econometrics

> **Comments:**
> **username_1**: how are the different models specified? The inclusion of different numbers of lags can really alter the results  
> **username_0**: Thanks!. Same model, same everything...only data changes. They are all 2-variable VAR(1).  
> **username_1**: Do you include seasonal dummies? Because you probably should for both the quarterly and monthly data. Also it is important to note that 100 steps ahead is not the same as 100 steps ahead for monthly data or quarterly data i.e. 100 years $\neq$ 100 quarters $\neq$ 100 months  
> **username_1**: Also 1 lag in annual terms would be similar to the 4th lag in quarterly terms of the 12th lag in monthly terms. So doesn't really make much sense to compare identical models. Either way none of the effects are significant either which suggests all your models are pretty poor. Therefore I wouldn't trust the signs on the impacts that you see in the figures.  
> **username_0**: But my question is should I expect similar results using quarterly, monthly, or annual data...after doing all the stuff you have suggested? I mean, is there some statistical proof or evidence that data frequency doesn't matter much for a VAR model if indeed you do all the necessary stuff...seasonality, lag length, etc, appropriately for each model. In others words, which frequency should I choose for my VAR model? Based on what? Based on which frequency I want to forcast? But I am not interested in forcast here, just capturing dynamic relationships. Does data frequency matter?  
> **username_0**: may I ask though...so we should kinda disregard research papers with insignificant irfs, right? I mean, I see a lot....can I say for example that those models are poor...and used that as a basis to write another paper, hopefully a better one where irfs are significant??. Hmm, Can't we have a good model (based on theory) with insignificant results?? Sims(1972) for example used only money supply and GNP in his model...if I used that model for another dataset and find insignificant results, can I say the model is not good, for example?  
> **username_2**: Disregarding insignificant findings is a recipy for disaster and among the top reasons for [why most published research findings are false](https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.0020124), according to Ioannidis.  

---

## 1 answers

### Answer by username_2 on 2021-01-21. Score: 2

> For example, the response of $y\_t$ to a shock in $x\_t$ should be expected to be different at monthly, quarterly and annual frequencies, right?

Generally (and usually), yes.

> Or it is that the results should be similar irrespective of the frequency of the data?

Generally (and usually), no. The answer to your question depends on the underlying data generating process (DGP). You can take an example process and analyze it at different levels of time aggregation analytically to figure out implications for what happens when we look at it using different frequencies. E.g. take a monthly AR(1) process
$$
y\_t=\varphi\_1 y\_{t-1}+\varepsilon\_t
$$
and see how it behaves when aggregated to quarterly or annually:
$$
\sum\_{i=1}^{3}y\_{t-i+1}=f\left(\sum\_{i=1}^{3}y\_{t-3-i+1}\right)+u\_t
$$
and
$$
\sum\_{i=1}^{12}y\_{t-i+1}=g\left(\sum\_{i=1}^{12}y\_{t-12-i+1}\right)+v\_t
$$
where you need to figure out $f(\cdot)$ and $g(\cdot)$ based on the original AR(1) model.

> **Comments:**
> **username_0**: Thanks @Richard. I asked this question because papers don't usually say why they are using data of a certain frequency in their research. Any reasons why quarterly data is popular?? I guess the finer the data, the better. But quarterly data is how far we can go...and it is available for most series. Of course some variables are available at monthly frequency...but maybe not for all the variables in our model. Or probably, is it because consumers of economic model like central banks care about Dynamics at annual frequency??  
> **username_2**: @EmmanuelAmeyaw, data availability might be the key factor here. Regarding the finer, the better, it is often true but not always so. Sometimes it matters that we have a long sample in terms of calendar time, not in terms of sample size. E.g. just sampling the data finer and finer does not help much with estimating long-run relationships.  

---

