**3. The business cycle and the commodity**

The Schumpeter theory Schumpeter [1] brings an overview of the business cycle, the trend of an economic system. According to Schumpeter [1], the business cycle is a sum of perpetual economic cycles or an overlapping cycle. His main theory is focusing on the business cycle within the process of creative destruction, for which the introduction of innovation boosts investment opportunities and creates economic growth and at the same time decay in the obsolete sector of production. This process is containing an expansion phase and a recession phase where the economy assimilates the innovation across sectors. The commodity prices are involved in the same perspective regarding the demand. Within the expansion phase, the competition for commodities product such as gold and energy tend to increase their prices compared to manufacturing goods, the introduction of innovation as imitation reduces the opportunities for investment to obtain economic rent, decreasing the demand for commodities. Schumpeter is among the economists who reject the frame that the decline in prices might be a result of a slow-down in terms of output and growth, as he explains that within the great recession (1878–1896) for the case of the falling of price due to a decline in the production of gold which result in profit squeeze and the decrease of the investment. From the same perspective as Schumpeter, for the economic phase of the commodities and the manufactured good on the business cycle, we find Prebisch [49], Singer [50], as well as Ocampo [51] and Ocampo and Parra [52] as prominent literature studying the commodities prices and the business cycles.

According to IMF five years ahead forecast for 2017, the expected long-term growth boosted by the boom of the commodity price has been revised down from 4 to 3%. The boom in the commodities prices has an increasing effect in the short run on the real GDP by raising the value and production and lifting the demand for ancillary goods and services. An increase in the investment in the resource sector, such as metal or energy, may raise the potential output, which in turn boosts the financial resource for the investment in the other sector. However, in the long term, commodities boosting growth is a controversial question. According to Corden [53], the positive term trade and income shock associated with the commodity boom shift production out of non-commodity tradable and into the non-tradable service sectors with lower productivity. The global economic crisis starting in 2012 was the result of the boom in commodity prices characterized by unprecedented magnitude and duration, as the price reached the highest level in history, this phase was characterized as a phase of mineral boom. In fact, within the depression of the global economy after the subprime crisis, which slow down the demand for the commodity price, however, the recover for the price was surprisingly fast and the world economy experienced a boom in commodity prices which might be seen as a continuation of 2004–2008. The upswing demand in commodity lifts the resilience of the growth performance of major developing countries and producers' countries. Within the several literatures, it is tempting to believe that there are causality links between the business cycle in terms of output and commodities.

Among many econometric approaches such as the SVAR, UC, and VECM, prove the biased data with low-frequency movement. Fernald [54] noted that low-frequency movement in an hour per capita may bias the VAR model with long-run restriction. Differencing removes the low-frequency movement from the data [55]. In opposite Hamilton [56] affirms that differencing a bounded series may involve misspecification issues by suggesting a filtering approach prior to the estimation model [57]. However, Gospodinov et al. [58] found that filtering the data prior to the estimation removes necessary information to identify these stocks using long-run restrictions.

Within our study, we aim to estimate the model of the Univariate and Multivariate Unobserved Component Model using the HP filtering data and the Band-Pass filtering data. Filtering data, through the selected filters, with a filter window such that cycles are generated at such frequencies. The decomposition method isolates major fluctuations in the deviation of a macroeconomic variable, such as the GDP, around its trend through a combination of detrending procedures and smoothing techniques [59]. Within the literature, determining the long wave is also based on the filtering approach, such as in Baxter and King [60] and Christiano and Fitzgerald [61], the time series is considered as a summation of different frequencies and the filtering approach consists to determine the filter coefficients so as to isolate specific frequencies and to show the course of the pre-specified frequency component in the time domain. The choice of both filters is mentioned in the next section.
