Modellin inflation and exchange rate with VAR
...ions about which model is more plausible into the real world. Now we will perform all steps that we mentioned above. 1. Specifying the number of lags that should be included into our VAR model. According to the VAR theory we should be careful with specifying the number of lags. Our VAR model contains 3 equations and each of them will be explained (we should remember that the feature of the VAR model is that all variables are endogenous) with lagged values of three variables respectively. Hence, every additional lag will subtract 9 degrees of freedom. The decision rule is to compare the different values of the Akaike and Schwarz criteria in the different VAR specifications, their lowest value is preferred. Other approach [Jonston, DiNardo, 1997] is to make the likelihood ratio test statistic. We accomplish both of them. The results are in the Appendix 1. Here we will present only the comparison table: Order of VAR Akaike criteria Schwarz criteria 2 -13.47915 -12.69114 3 -13.10864 -11.97227 4 -12.53664 -11.04527 5 -12.02424 -10.17103 6 -11.61653 -9.394475 7 -11.15351 -8.555426 8 -10.40251 -7.421032 9 -9.794483 -6.422046 10 -9.206702 -5.435574 The results of the likelihood ratio test are presented in the excel-file (app_project.xls, worksheet: appendix1). We can say for sure that the lower number of lags is more preferable that the big ones. Economic theory doesn’t explain precisely the relationship between the variables within the different time intervals, therefore we will use the common approach in this problem. The analog research of Dmytro Holod tells us that the appropriate number of lags is three. 2. Determining the order of integration of our time-series. At first we will analyze the visual values of our time series (Appendix 2). We see that taking the logarithm of the data saved the trends and behavior of our data. It also made it more convenient to work with because of the reducing the tremendous differences of the adjacent values. Hence, we won’t go back to our original data and will work with modified (logarithmic) data. Further analysis shows that there is a trend, which is a strong hint to the nonstationarity of the time serious. We will perform the ADF (Augmented Dickey-Fuller) test in order to investigate the order of integration, we will also analyze the correlograms. According to the analysis of correlograms we can tell that all our time series are nonstationary in the levels and seems to be stationary in the differences. We perform the ADF test with 2 lagged differences of the first differences of our time-series. Here is a result table with MacKinnon critical values: Time-series ADF Test Statistic 1% Critical Value 5% Critical Value 10% Critical Value D(LN_CPI) -3.231129 -3.5653 -2.9202 -2.5977 D(LN_EXR) -3.790664 -3.5653 -2.9202 -2.5977 D(LN_M2) -4.345315 -3.5653 -2.9202 -2.5977 We see that D(LN_EXR) and D(LN_M2) shows the unit root, hence the LN_EXR and LN_M2 are integrated of order I(1). Within the 5% critical value we can say that LN_CPI is also integrated of order I(1). The graphs of the differences of the time series are also provided in the Appendix 2. We will run the VAR in the first differences. 3. Checking our model for cointegration and modifying the VAR into VEC According to the theory the linear combination of the nanstationary time series with the same order of integration could produce a white noise disturbance term. We should be thoughtful for such kind of relations and determine whether they are present or not. After our VAR is built we can say that it has a long-run equilibrium (see Appendix 1, Characteristic Polynomial Roots Graph) in every equation, but if we establish the cointegration between our time series we could say that besides the long-run equilibrium of the separate equations our model is supplemented with long-run relations between equations. Our time series are integrated of order I(1) in levels, hence we should test our model ...