In my opinion, minimum number of observations to conduct  an empirical panel data aalysis or to develop an empirical model should be more than 50, at least not less 30. More observations you use, more accurate results you will obtain.

Saganga - Hi. - I am not certain of your goals, but the 40 observations of which you speak would not be independent, so please keep that in mind.

If you are looking at a time series application, or trying to get an acceptable accuracy on a regression coefficient, or an estimated total using prediction (which is not time series forecasting, but deals with a current data sample and regressor data on the population), then in any case, you need to estimate what is needed to attain the desired accuracy, as measured by standard errors, of whatever interests you. Keep in mind that nonsampling error, such as measurement error, is a huge concern. Scatterplots may help identify measurement error.

For the cases of prediction for a total or for regression coefficient estimation, preliminary work could estimate the MSE, which for WLS is really going to be your estimated variance of the random factors of the estimated residuals. (This is the square of STDI, in a WLS application of SAS PROC REG, by the way.) For instance, section 5 in the first linked paper below, and Eq 2 in the second linked paper below. For an estimate of the regression coefficient for the classical ratio estimator (CRE), look at the square root of V(b) in section 5 of the first paper. You need a big enough n (sample size) there to obtain the standard error of b that you want. If you are estimating totals, the second paper covers that, for the model-based CRE, which is rather robust.

https://www.researchgate.net/publication/261474159_Some_Proposed_Optional_Estimators_for_Totals_and_their_Relative_Standard_Errors_for_a_set_of_Weekly_Quasi-Cutoff_Sample_Establishment_Surveys

https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

Article Some Proposed Optional Estimators for Totals and their Relat...

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

You have a repeated measures or  multilevel design where occasions (level 1 -n ) are nested within companies (at level 2 -m)- there will tend to be dependency between occasions so you will not have as much information as you might think ( ie not  n * m)

Software for design:

Raudenbush, S. W., et al. (2011). Optimal Design Software for Multi-level and Longitudinal Research (Version 3.01) [Software]. Available from www.wtgrantfoundation.org.

Documentation:

Spybrook, J., et al. (2011). Optimal Design for Longitudinal and Multilevel Research: Documentation for the Optimal Design Software Version 3.0. Available from www.wtgrantfoundation.org.

These can be freely accessed at

http://sitemaker.umich.edu/group-based/optimal_design_software

You can also use Bill Brown et al's simulation software as a sandpit to try out a range of different sizes of occasions and individuals

http://www.bristol.ac.uk/cmm/software/mlpowsim/

For an example where there are not a large number of units at either level see

https://www.researchgate.net/publication/256443368_Stylised_fact_or_situated_messiness_The_diverse_effects_of_increasing_debt_on_national_economic_growth

and for a recent technical paper covering key analysis issues see

https://www.researchgate.net/publication/233756428_Explaining_Fixed_Effects_Random_Effects_modelling_of_Time-Series_Cross-Sectional_and_Panel_Data

Article Stylised fact or situated messiness? The diverse effects of ...

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...