# Annual data VS Monthly data VS Quarterly data for a VAR model

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?

• how are the different models specified? The inclusion of different numbers of lags can really alter the results – Andrew M Jan 10 at 23:37
• Thanks!. Same model, same everything...only data changes. They are all 2-variable VAR(1). – Emmanuel Ameyaw Jan 11 at 3:03
• 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 Jan 11 at 22:15
• 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 Jan 11 at 22:50
• 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 Jan 12 at 23:26

## 1 Answer

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.

• 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 Jan 22 at 12:43
• @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 Jan 22 at 13:17