Hello Fatima 11 years constitute insufficient number of observations.

It all has to do with degrees of freedom. which they are related to the number of

coefficients to be estimated. For a single equation the degrees of freedom is equal to n-k-1. If you were to run a single equation with 11 observations you have 5 degrees of freedom. According to the Central Limit Theorem you need at least 30 observations. With a VAR in five variables you will need at least150 observations.

So my suggestion change your topic. Make sure you have a data set with sufficient observations,

Best.

thank you for your answer

Maybe it is good luck, that you do not have sufficient observations. This means that you are obliged to do more thinking about a careful specification of your model. I think it is unlikely that you have autoregressivity for all your dependent variables. (Because with a lot of data, many econometricians foreget economics or mix-up econometric methods and economic models, "throw" the data into a more or less complicated econometric package and are then unable to interpret the results). Therefore, I recommend to abstain from VAR and try to find a good (theoretical, which can also include common sense) specification of the five equations for your dependent variables. By graphical presentations and correlations with lags, you may find out which functions and transformations of the variables could be adequate. Then you can estimate these functions by a simpler method, e.g. OLS. Even for these estimates 11 observations are few, but there is a chance to get reasonable coefficients (unless you have not too many explaining variables and lags). It is therefore important to concentrate on the most relevant relations. Perhaps, by separately analysing the equations, you may even get more data for some of them.

As stated by the experts, the problem is with the number of degrees of freedom (which is negative in your case). If you consider the simplest lag structure for each of the right hand side variables (that is, just one lag or VAR(1)), for instance, the number of parameters that need to be estimated in the VAR system is 25 (five for each of the equations). Clearly you can not estimate 25 parameters with just 11 data points since your degrees of freedom will be 11-25 = -14

One has to take into account several restrictions of the degrees of freedom. Looking at one (let's take the first) of the equations of a simple (with only a one-year-lag for all variables) linear 5-variables VAR-approach, one has

X1 = c1+a1*X1-1+a2*X2-1+a3*X3-1+etc. There are, therefore, not 5, but 6 coefficients to estimate (in total 30), unless all are homogeneous functions (without a constant, which is not very realistic). Every additional lag increases this number. But what is even more problematic, lags reduce the number of observation. If the Xi are, e.g., data for 2010-2020 (11 years), then you have only 10 data for Xi-1 (i.e. from 2010-2019). The problem may be rather serious, if there is only one longer-term-lag in the model. Assume that there is a lag of 4 years for X2 in the above equations, then the number of (usable) data shrinks to 7 (for all equations, because in a VAR approach this minimum limits the total data set). One can, in principle, solve an equation system with 30 variables, 30 coefficients and 30 data, but (even when you try a sort of least square approach for 35 data) that has nothing to do with statistics. I think with annual (and maybe with quarterly) time series, it is unlikely to get enough data to run a VAR method for a model with more than 2 or 3 variables.

you can convert the yearly data to quarterly data

A conversion of annual (original) data to quarterly data via some assumed seasonal pattern cannot deliver additional information.

it's what i did i convert my data to quarterly data, and eviews accept it but I don't know if it's economically correct

Obviously, it is easy to trick the VAR program, but it is not a feasible procedure. A thinking experiment: Assume, you have data for one year for two variables X and Y and you want to estimate Y=aX+c. This is, of course, not possible. If you produce half-yearly data e.g. by taking the relative length in days for X, one gets X1=181/365*X and X2=184/365*X and coefficients k and (1-k) for Y1 and Y2, you have two equations, which can be solved for a and c. If k=181/365, then, of course, c=0 and a=Y/X. That is not yet a statistical estimate. But if you do a similar calculation for months with Xi=kiX (sum of ki=1) and the same with Y, you get two (apparent) time series and a wonderful estimation for a and c. But this is only a reproduction of the procedure for calculating monthly data. For several annual data, the results will be a mix of the "true" relation between X and Y and the function used to calculate sub-annual data.

By the way, this is not a question of (correct) economics (economics is important for the specification of the model), but of good or wrong statistics. VAR is not an economic model, but a statistical method.

Dear Fatima.

Always consider the degree of freedom for a single equation.

The duration (time) is not sufficient.

But if you converted the data to quarterly data, it okay.

Check the results, I guess it's okay.

Regards

To create quarterly data from annual ones is merely a special form of transformation. And, there cannot be any transformation which can add informational content to an unsufficient data set. Kehinde, you should try it, if you do not believe me. You can e.g. assume a simple linear equation, where Y=sum(aiXi) with i>4, where Xi are (random) time series of length 6 or seven. In your assumed function, you may also use lagged data. You can create, say, T=6 or 7 annual data by simulation. If you wish, you can also add a small random variable with mean zero. If you choose i=5 and no lag and no constant, you have one or two degrees of freedom. Nevertheless, the estimation will likely not function. With lags the degrees of freedom will soon be negative. In all cases, you can of course apply a program that makes quarterly data out of your 6 or 7 annual ones. To get more data, one can even calculate monthly or daily data. Then you can make an estimation on the base of these sub-annual data. The econometric program will not protest, because formally you have enough data. But I think you will rather be surprised by the results. Good luck.

As said in the other answers, there is no solution to your problem if you restrict your analysis to VAR models with 5 variables. If you have one variable of interest, you can consider VAR models in two dimensions with that variable and each of the other ones. If there is no feedback in these VAR models, you can consider a regression of that variable of interest in function of the other ones. But with only 11 observations, you lose 6 degrees of freedom, so you can have only one lag per explanatory variable.

Dear Guy, in principle, you are right, but I think that even an estimation of a single equation with 5 explaining variables for 11 observations is questionable - especially if some of the variables show a trend. This estimation would mean that one wants to find 6 coefficients (including the constant, because one cannot assume a homogenous equation in advance). So there are (formally) 5 degrees of freedom (which is rather small for a good statistical "proof"). If one adds the 5 variables with lag 1, the degree of freedom is reduded to zero*). Good econometric packkages would likely refuse the estimation, but it is possible to find an OLS estimation (e.g. EXCEL-OLS would do it). This is merely the solution of a system of 11 equations for 11 coefficients. Therefore, no randomness is left, and the deviations of the coefficients are zero and R2=1. So, formally, one has a wonderful result (Maybe that some other statical figures would not look as good or would not exist), but it is not acceptable.

In EXCEL-OLS, estimations for negative degrees of freedom would be shown, but the program would suppress as many explaining variables necessary to reach a degree of freedom of zero, i.e. to solve the linear non-random system.

*)In case that all variables are really restricted to 11 annual data (e.g. data from 2010 to 2020), the inclusion of lagged variables means not only an increase of coefficients, but also a reduction of (useable) observations according to the longest lag. If e.g. one has an equation of 4 variables for 2010-2020 plus one of them lagged by 3 years, there are again 6 coefficients to estimate, but the shortest time series is from 2020 to 2017, which restricts the number of observations the program can use to 7. Therefore, only one degree of freedom would be left.