If you provide a plot with the time series you have and illustrate how the break occurs, it will be easier to answer. The assumptions about et are not really plausible. I would apply log to both sales and price first. Perhaps, for sales you can use sqrt instead of logs.

But the major issue here is in how you understand the intercept break. So the first step is visual analysis.

Also, one approach to test your hypothesis is to conduct an MC experiment where you know the data generation process and then check if your estimates really correspond to the true parameters you used to generate data (this approach has been successful in crashing the belief in a number of well-known methods). You can google for it, but it is known that replacing missing data with dummies leads to biases, and it was demonstrated using an MC experiment.

If you provide a plot with the time series you have and illustrate how the break occurs, it will be easier to answer. The assumptions about et are not really plausible. I would apply log to both sales and price first. Perhaps, for sales you can use sqrt instead of logs.

But the major issue here is in how you understand the intercept break. So the first step is visual analysis.

Also, one approach to test your hypothesis is to conduct an MC experiment where you know the data generation process and then check if your estimates really correspond to the true parameters you used to generate data (this approach has been successful in crashing the belief in a number of well-known methods). You can google for it, but it is known that replacing missing data with dummies leads to biases, and it was demonstrated using an MC experiment.

Yunqing ma , of course you can, what the break (the dummy) is saying is that there was some important change in the dynamics that was permanent or transitory. This change could have affected the level or the slope of one or both series in your models, so you may try to experiment including the break dummies with and without interactions with your variables. I believe that you need to have a strong theoretical, statistical and/or phenomenological argument for including the dummies, since, as you said, the results will be different depending on how do you include the dummy terms. In your case, I would particularly also suggest a SVAR (structural VAR), decomposing from prices to sales.

I would recommend applying a (Markov Switching) MS-VAR as opposed to integrating a dummy - esp if it is difficult to confirm with certainty that the break was attributed to either cyclical or structural forces.

I agree with Elvis Munyaradzi Ganyaupfu , when you have a structural break you should also break your data and estimate separate equations or use switching models that permit the coefficients of your variables to change before and after the break.

Dear Yunqing.

Markov Switching will be the best option in this case.

Regards

One shoud never take breaks in time series data merely as an obstacle for a trouble-less econometric estimation. Such a break can deliver valuable information (unless it is only due to a change in the statistical data capture procedure or redefinition). Therefore, one should always try to find out the reasons for this break. I do not find it feasible to exclude this information by automatically setting dummies. By the way, I think, the specification of your equations are not based on theoretical considerations. And it is not clear, how the variables are measured (absolute values or indices, logs, percentage changes?) and what periodicity they have.

Thank you very much, guys. I really appreciate it. Anton Rainer Kehinde Mary Bello Chiraz Karamti Elvis Munyaradzi Ganyaupfu Rolando Gonzales Andrey Davydenko

Here is a bit more information and my research goal.

1. The Sales_t represents a supermarket's weekly volume sales in a category, say, beverage drinks, and the price is the average weekly price of that category.

2. I have two years of data and the frequency is at the week level.

3. You can assume the only seasonality I have is around holiday weeks.

Actually, I only use VAR model to estimate price elasticity (I know I can use log-log form) and it is not the final goal of my research. The final goal is to explain these elasticities derived from many VAR models across stores and categories by regressing them on other variables.

So, what I need is just an unbiased estimate of the irf by correcting any biasedness potentially caused by breaks. No need fancy methods. For example, if I can determine the break date by using something like OLR test and then incorporate the correct form of the break into the model...it's perfect.

But the problem is I'm not sure whether what I did was methodologically correct i.e., the way I put dummies...As I said, even I put the step dummy into the price equation, the lag of price in the equation is still nonstationary because it has a break. So I thought putting an interaction would do the trick.

Sorry about it if I said anything illogical, I'm not an econometrics major...Thank you!

Dear Yunqin,

Thanks for the detailed information you shared. Based on your response above, I am not sure if I am correct that you have already chosen to use a VAR model for estimation ONLY, and not any other method? If that is correct, please recall that selection of the estimation method is guided by nature and statistical properties of data/series. It is in the same line of methodological logic that I do not understand what you regard as a "fancy method" - your advice in respect of these questions can guide us in providing suggestions to meeting your study's empirical goals. Thank you

Elvis Munyaradzi Ganyaupfu Thank you very much for your time and help.

Yes, I understand what you said. Let me clarify.

The initial reason I chose VAR:

Those papers are quite old, like 10 - 20 yrs ago. They did not mention MS-VAR and neither did they explicitly specify what they did in their VAR models when coming across breaking series. I thought I might just follow the conventions..but need to figure out what to do with these breaking series.

Why I plan to stick to VAR:

Thank you! I'm happy to hear any suggestions!

I doubt, whether your Salest-equation is realistic, in principle. When I go to a supermarket, I mostly by several products. In general, for my decision to buy something, the price of the two past weeks is of no interest. Often I do not know these prices. It is the current price, which is important. But even if I know that it is higher then that of other supermarkets nearby, I would not buy at the competitor, unless the price difference is rather high. If a price has been excessively increased in comparison to the weeks before (in all supermarkets), my decision depends on my expectations of the future prices. You may think-over your Pricest-equation, too.

To be short: I think that you should take a simple equation like Salest=f(Pricet). But you should proceed according to Andrey's proposals before estimating.

Anton Rainer This is inspiring.

So you're suggesting it is the lead of the price of the supermarket and competitors that do the difference...

As a person who shops grocery for like only 5 mins every trip...I would never think of this..thank you...