**Table 3.**

Including 12 lags in the lag exclusion test or lag length criteria about deciding the maximum number of lags to be used in our VARs, we get an estimated fitting lag length denoted by an asterisk. We select 2, 11, 3, 2, 10, and 2 lags, respectively, as

**Dummies AL B&H KS MNE NM SRB** d\_2007 d\_2007 d\_2008 d\_2008 d\_2008 d\_2008 d\_2013 d\_2008 d\_2010 d\_2010 d\_2010 d\_2010 d\_2009 d\_2011 d\_2012 d\_2012 d\_2012 d\_2011 d\_2013 d\_2013 d\_2013 d\_2013 d\_2016

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

**AL B&H KS MNE NM SRB** 0.979149 0.981038 0.975064 0.918688 0.987044 0.948791 0.917381 0.981038 0.975064 0.918688 0.987044 0.948791 0.814555 0.963392 0.927706 0.868723 0.979839 0.868408 0.814555 0.963392 0.927706 0.868723 0.979839 0.868408 0.383119 0.962341 0.725579 0.846442 0.943445 0.654013

All inverse roots of the characteristic polynomial are <1, as seen in **Table 2**,

We have reached significant results, and based on the stationarity assessed so far, we can infer that impulse response standard errors are valid (**Table 3**). The largest inverse root of the AR characteristic polynomial is 0.987044. The correlograms of short-term error correlations of the estimated VARs suggest no autocorrelation. The entire lines lie within the 2 standard error bounds, showing at first lags another backup to the suggestion of missing autocorrelation in nonnoticeable continual wave sinusoidal. Based on 95% significance level, the null hypothesis, which states there is no autocorrelation of residuals in our estimated VARs, cannot be rejected. It has *p* values of 44.15, 33.37, 86.14, 91.67, 76.31, and 96.69%, respectively, for lag orders up to 2, 11, 3, 2, 10, and 2 lags. Therefore, there is no indication, based on the LM tests, that there is the autocorrelation of errors.

To generate a forecast, we can use known values or forecasted values. Using the

known values for forecasting is static forecasting. In case we proceed using the predicted values from regression, then it is dynamic forecasting. There are two types of simulation processes. One is a deterministic simulation, where we get only one value for the solution, which does not respond to innovations. It calculates under the current set of assumptions or known facts without any shocks

the appropriate lag length for our VAR models.

*VAR satisfies the stability condition. Source: Authors' calculation. \**

*No root lies outside the unit circle in Table 2.*

*Root of characteristic polynomial.*

confirming the stationarity of the VARs.

**4.1 Forecasting models**

**224**

*Source: Authors' calculation.*

*Dichotomous variables.*

**Table 1.**

**Table 2.**

*VAR residual serial correlation LM tests.*

introduced, which is called the baseline. Deterministic simulation ignores the fact that relationships do not hold exactly, because of random disturbances and estimated coefficients, which are not known or predetermined values. We should account for these sources of uncertainty by using stochastic simulations. **Figure 1** performs gdp\_gap and inflation stochastic simulations for static solution model simulators for period 2017m01 till 2017m12.

Forecasting performance of the static solution performs very well, both in terms of the fit and small standard error bounds, coming as a result of de facto one period ahead forecast.

It uses actual instead of forecasted lagged values over the forecast period. The blue lines portray the actual data for both gdp\_gap and inflation, while the green lines represent the forecasting performance of the stochastic-static model. As seen in **Figure 1**, both predictions are very close to the real data and within the confidence bands, except in the 5th month for the North Macedonia GDP. The red lines show the upper and lower bounds of the stochastic-static solution model simulator. The comovement is noticeable for both variables. Including bootstrapped errors and coefficient uncertainty, we get forecast measures (**Table 4**).

Analyzing **Table 4**, the first thing we notice is low RMSE for all WB 6 countries. The RMSEs for gdp\_gap and inflation are 0.1979 and 0.3768, respectively. Theil's coefficient U1, which measures the forecast accuracy, is acceptable for all variables of the VAR models.
