I am finding it difficult to interpret the following Impulse response and variance decomposition graphs-basically studying the effect of currencies on each other(I know the results from the Granger causality test,but how do we interpret the graphs below?) What do they mean and represent-what is your conclusion when you see these graphs and how do you reach this conclusion ?
Impulse response plots represent what they are named after - the response of a variable given an impulse in another variable.
In your first graph you plot the impulse-response of EUR to EUR. At the initial period, a positive shock on EUR will obviously lead the EUR to go up by the shock amount - thus the initial value of one. The decay in the plot illustrates that, as time passes, the effects of a shock in EUR today decay to 0. (Typically to be expected in stationary VAR models - think of the stationary AR definition..)
Similarly, when GBP goes up by 1 unit of measurement, EUR goes down by about 1/2 on the next period, but the impact of a shock on GBP today on future EUR goes to 0 fast. Pretty much the same with JPY.
The IR of GBP to EUR shows a different pattern - a shock to EUR causes GBP to go down in the near future, but the effect of such shock is mean reverting to 0.
Variance decomposition shows how much a shock to one variable impacts the (variance of the) forecast error of a different one - in your case, 50% of the variance in the forecast error of GBP seems to be explained by a unit shock in EUR. The variance in the forecast error of all other variables is completely explained by the variable alone, i.e, the orthogonal shocks to other variables in the system do not increase the variance of your forecast error.
Maybe you would like to check this link - it expands on what I believe you are looking for.