To do risk calculations, you need to answer 4 questions:

The 4th you've already answered, as you said you want to calculate VaR. And it sounds like you've also answered the 1st question, as you said you have 7 variables, which I take to mean you have 7 risk factors.

The impact of the lack of data on the accuracy of the VaR will depend on 2 & 3, as well as part of the 4th question, namely the percentile at which you're calculating the VaR.

To answer question 2, you have to specify a model for the risk factors (like jointly log-normal, or the empirical distribution, etc). Your risk factors are basically a vector of random variables X & you have some model for X.

The model will likely have some parameters that are estimated based on the data. Depending on your model for the behavior of the risk factors, this may or may not be enough data to accurately estimate the parameters. You can think of the inaccuracy as error bars around the parameter estimates.

As for whether or not the parameter estimation is sufficiently accurate, that depends on your answers to questions 3 & 4. The answer to question 3 is some pricing function V which gives the market value of your portfolio as a function of the risk factor vector X. This function might be very simple or very complex, depending on the positions in your portfolio. How the inaccuracy of the para

You ultimately need to calculate the P&L distribution. So, basically, your risk factors are a vector of random variables X with distribution given by your model, and your pricing function is V, and you need the distribution of V(X). Then, you want to estimate the accuracy of the VaR, namely your calculation of a percentile of V(X) based on the inaccuracy of the parameters you estimated to estimate the distribution of X. Whether or not you have sufficient data will depend on the amount of error you can tolerate in your percentile estimation.

Dear Harvey J Stein

Thank you for your answer.

I found this rule:

Since VAR uses (equation-by-equation) OLS estimation, the number of parameters in one equation cannot be greater than the number of data points used in the estimation, which is the sample size T minus the lag length p.

Then the condition is K*p+1⩽T−p

Can I use this rule for my model?

Thank you

In this case, the following two approaches might be appropriate: (i) using the lasso for estimating a large VAR. This method has become popular recently in literature because it allows for a large number of variables relative to the time series length; (ii) Bayesian VAR. This approach deals with the problem of over-parameterization, given the limited number of time-series observations.