A VAR model is the best. Vector Autoregresive model  can used to identify and analyse the relative contribution of domestic fuel price on inflation.   The model can help detect that a shock in fuel price increases/decreases real output and prices. OR one can conclude using VAR that the increase in Inflation was due to the fact that domestic price of fuel enters the aggregate price index.

thanks a lot sir@ Garikai

ISSUE: Impact measurement

REGRESSION: assume that regression is used. Let Y = inflation; X = fuel price; and t = time period. A simple regression model says that:

Y = B0 + B1X1 + e

B0 = price level without any effect from fuel price; B1 = parameter;  X = independent variable (fuel price); and e = error. The test for impact is the test whether B1 is statistically significant. Inflation is the change in price level (quantitative); fuel price is also quantitative measure monetary unit per unit of fuel, i.e. liter (quantitative). The appropriate test statistics seems to be t-test for the Pearson correlation coefficient:

tr = r(sqrt(n - 2)) / sqrt(1 - r2)

This approach is quite rudimentary, especially in a case of measuring X:Y relationship. "Fuel" may be define as a single factor; however, "domestic price" is comprised of prices of a bundle of goods. Therefore, we may be looking for a model that could account for intermediate effect(s) among the Xs, for example:

Y = B0 + B1X1 + B2X2 + B3X1X2 + e

If the model could capture the non-linear relationship of X1 and X2 with Y, more information can be read from it. The correlation between X1 and X2 may be valuable to the understanding of the interplay among factors that produces Y. See attached.

DIRECT EFFECT: Is the effect of fuel price on domestic price direct? Some prices of consumer goods are directly linked to fuel price and some are not. When speaking of inflation, it might be helpful to differentiate between (i) headline inflation and (ii) core inflation. Fuel price would show significant effect on headline inflation, but for core inflation, the price level may be stable. For example, food production may have effect from price of fuel since the price of fuel affects transportation and the cost of input, i.e. fertilizer, tractor, fuel to run tractor, transport to market, etc. in a local market. However, when reference it to the world's price index of commodity price of the same product, the effect may not be significant. The claim of one-to-one relationship between "domestic price" and fuel price may be misleading. A better tool of measurement must be able to account for other factors (x2, x3, ...) that may mediate "domestic price" relative to changes in fuel price.

REFERENCES: See the attached 2 articles on latent effect measuring models.

http://www.ssicentral.com/lisrel/student.html

Thanku Sir @ Paul Louangrath i will try and if i come with any problem hope you highness will help further 

The VAR model is the best in this case!

thanku sir @sadgui

With due respect to all commentators, I would like to say that you've only two variables in your proposed model. A bivariate VAR model may not capture the dynamic reponse of domestic inflation due to domestic fuel price shock. We need to remember the fact that domestic fuel price is influenced by world price of oil, especially in the oil importing small and open economies. If you're modeling the domestic inflation and fuel price of a small and open economy, you need to add 'world oil price', 'policy interest rate of the most major trading partner', and 'domestic policy interest rate' in the VAR model. You may then estimate the impulse responses of domestic inflation due to these shocks. Identification of these shocks may be performed either by 'Choleskey decomposition method' or by 'AB model (see Amisano and Giannini in 'Topics in Strcutural VAR)'. Hope, it helps.

Correlation does not suggest causation. Inflation is a monetary effect. Rising fuel prices are an expression of inflation, not a cause.