**9. Estimation results**

Within this section, we report the cycle estimates and other parameters of interest under the multivariate unobserved component model by the maximum likelihood method using the Kalman filter. In a second step, we proceed to calculate the c and Beta parameters for the trend, cycle, and seasonal parameters using LLT and State Space model using as instruments the gold, energy, and the financial cycle.

The parameters' estimates for the likelihood estimator are shown in **Table 1**. All the parameters are statistically significant. Global consumption and global inflation are significantly negatively determined by the oil, the gold and the financial cycle, which is confirming the expected result compatible with the theory, as a higher price of commodities have a negative impact on the consumption and enhances the inflation which leads to affecting the global economy negatively. In opposite global investment is significantly positively determined by the oil, the gold, and the financial cycle as the oil, the gold are used as hedge funds by the investors as well as the trading of the stock market which promotes the global economy and affects the cyclicity of the global business cycle within the peak. The long-run global investment elasticity of the global output is the highest equal to 0.119. This is confirming that the three determinants are used as a hedge fund for the investors and the payment system and are consistent with the capital channel of the global system, which means that the commodities are distributed mainly for investment other than consumption. **Figure 6**a–d shows the trend of the global business cycle within the Multivariate Unobserved Components model. The time lag of one period for the global GDP has not pronounced an impact on the cyclicity of the global business cycle, which might be explained as the


*The estimate of the generalized UC model for the global GDP. The estimation result of the generalized UC model is reported. The sample period is 1984:Q 1–2020:Q4. Within the estimation, we are limiting to the standard format of the multivariate unobserved model using the maximum likelihood estimator with the Kalman filter. Source: Own study.*

### **Table 1.**

*Result maximum likelihood estimator with Kalman filter for multivariate unobserved model of the global GDP.*

### **Figure 6**

*a. the residual, actual, and fitted estimation of global GDP with maximum likelihood estimator. b. the residual, actual, and fitted estimation of global consumption with maximum likelihood estimator. c. the residual, actual and fitted estimation of global investment with maximum likelihood estimator. d. the residual, actual and fitted estimation of global inflation with maximum likelihood estimator. Source: Own study.*

*The Global Business Cycle within the New Commodities and the Financial Cycle… DOI: http://dx.doi.org/10.5772/intechopen.111482*

deterministic commodities influence the upswing and downswing of the business cycle. However, basic on the filtering data, it is confirmed that oil has a lag impact on the fluctuation of the business cycle, it reacts as an impulsion for the crisis, compared to the gold and the global financial cycle which react simultaneously with the trend of the global business cycle.

Related to the investment, the inflation, and the consumption the related graph will show the univariate unobserved component model for each variable determined by the oil, the gold, and the financial cycle. According to the main result, we can consider that the determinant oil, gold, and financial cycle was a passive influencer for the global cycle of investment, consumption, and inflation. It is in opposite to the theory; however, it can be explained economically that the macroeconomic aggregate is an endogenous aggregate of the fluctuation of the commodities and not the opposite. However, related to the global business cycle, the commodities are reacting as an intermediary between the global business cycle and the investment, consumption, and inflation. Our result confirms that the long-run relationship between commodities and the business cycle is influenced by the economic condition. The relationship between gold and the financial cycle is stable with significant shifts during peak and recession.
