The Poisson model is typically used for modeling count data, which is data that takes on non-negative integer values. In your case, the dependent variable is the number of days it takes for a company to complete an acquisition, which is a continuous variable that can take on any positive value. Therefore, the Poisson model may not be the most appropriate for your data.

Instead, you could use a linear regression model, which is a common method for modeling the relationship between a dependent variable and one or more independent variables. In your case, the dependent variable would be the number of days it takes for a company to complete an acquisition, and the independent variables could include factors that might affect this, such as the size of the companies involved, the complexity of the acquisition, and so on. You could then use the estimated coefficients from the regression model to predict the number of days it would take for a company to complete an acquisition based on the values of the independent variables.

Another potential approach you could consider is using a survival analysis model. Survival analysis is a branch of statistics that is used to analyze data that involves time-to-event data, such as the time it takes for an event to occur (in this case, the time it takes for an acquisition to be completed). Survival analysis models can account for censoring, which is when an event of interest has not occurred for some of the observations in the data. This could be relevant in your case if there are acquisitions that are still ongoing and have not yet been completed.

Ultimately, the choice of which model to use will depend on the specifics of your data and the research question you are trying to answer. It's always a good idea to try out different models and compare their performance to determine which one is the best fit for your data.

First, you need to convert your discrete data to continuous data. Days are discrete data. Continuous data are typically between 0 and 1. For example, 0.9 or a number with a decimal point example, 3.9. Once you do that, you can use the ARDL model since you said from 1 to 1000 days by changing the year to quarterly. You can also analyse your data annually using the ADRL model. ARDL model is the most appropriate model for quarterly and annual.

If you want to analyse daily, you can use ARCH and GARCH models or any extended ARCH family models, which are appropriate for forecasting and predicting.

I hope it helps you.

Hi again

ARDL model works best with quarterly and annual data analysis, whereas ARCH models work best with high-frequency data such as hourly, daily, and monthly data analysis.

Dear Asrat Araya

Thanks for your kind response. I think time series modeling would not be the case, since the data is disposed as cross section. I have the information of the acquisition process duration for many companies, and some of the regressors are also time invariant and quailitative, for instance: an indicator if the deal is cross-border, an indicator of deal complexity, or if it needs the aproval of regulatory agencies, and others. Some of the independent variables, that represents the acquiror or the deal characteristics, in this model are taken only in the date of the deal announcement.

Dear Avinash Kiran

You are right. In our dataset we have some deals in which the status is marked as "pending" or were abandoned at some point in the process. This could account as censored data in survival analysis. I was already studying this possibility. This approach would give us the probabilities of the event occuring (in our case, is the deal completion), considering that it is duration dependant. This is in line with our objectives.

Perhaps another possibility to understand how such independent factors affect the number of days, is the censored tobit regression. This would complement survival analysis, since it only gives us the harzard ratios or if the occurrence of the event depends on the duration.

Thanks a lot

Dear Alexandre Teixeira Norberto Batista

First, I have never mentioned the word “time series modelling”. It is wrong to mislead readers.

Second, your data is a panel and not time series. In this case, you need panel analytical models and the best model for this are ARDL or ARCH and GARCH Models.

Third, I can provide evidence of dozens of scholarly papers in acquisition and merger literature that uses ARDL or ARCH and GARCH Models.

Fourth Tobit regression: what do you want? Is your question an analytical question or a theoretical question? I will leave it to the readers. Thank you.

Dear Asrat Araya

Forgive my ignorance. I am considering your recommendations. I will try to make myself more clear to explain why I thought that such AR family models would not be suitable:

- We are trying to explain the duration of the acquisition process of public acquirors, considering as regressors the acquiror financial and market characteristics, some characteristics of the deal, and some institutional characteristics of the countries involved.

- Some of the regressors and the dependant variable (duration of the acquisition process) are time invariant: The Y variable are the difference between the date of the acquisition annoucement and the date it was completed, which gives us the number of days required to complete the deal. So, parting from the start date (the announcement) we take the regressors, which are the last information available from that date. For instance, regarding the acquiror accounting and finacial characteristics, we take the last information disclosed, which we consider the last fiscal year (FY0) disclosure. We also consider for the regressors some of the deal characteristics, such as if the target company is public or private, or if it is a cross border acquisition and so on. And that makes us one observation for our analysis.

- Note that this dataset is not necessarly a panel. It is pooled data. Our observations are not gouped across time. That is, a company can annouce an acquisition in a given year and another one 5 years latter.

- About Tobit regression: maybe it works because the duration of the acquisition is a limited dependat variable, with a lower limit of 1 day. Even if we transform it to continuous, it will still have a lower limit. Many of our observations are concentrated at this frequence, which is the minimum time possible to complete the deal.

Once more, thanks for your time and valuable discussion.