## 3 Material and Methods
### Spuriousness in the Analysis Results
#### 3.2.2 Autocorrelation  
Autocorrelation occurs when error terms are correlated with each other. This correlation can be of two types: positive autocorrelation (where error terms move in the same direction) and negative autocorrelation (where error terms move in opposite directions). This problem is typically encountered in time series data and is rarely observed in cross-sectional data. It can be represented by the following equation [46; 52]:  
\[E\left(u_{i}u_{j}\right)=0 \tag{3}\]  
From Equation (3), it can be observed that the more the error terms are correlated with each other, the greater the impact on the accuracy of the equation. The causes of autocorrelation arise from three factors: (1) the inappropriate selection of independent variables, leading to error terms being correlated through these incorrect variables; (2) errors in defining the mathematical function or a misunderstanding of the principles involved; and (3) pure autocorrelation, arising naturally within the model itself. Effects of Autocorrelation  
The variance is not minimized, preventing the achievement of the efficiency property. The model lacks consistency due to bias still present in the model. Forecast values will exhibit higher-than-normal error rates. Detecting Autocorrelation  
Autocorrelation can be tested through several methods, with the most popular being the Durbin-Watson test. However, this test has limitations; it is appropriate only for data where the error terms exhibit a first-order regressive level. The model should present a conception value and should not be the first difference in the dependent variable (Lagged Dependent Variables). The testing procedure involves comparing the Durbin-Watson statistic to the critical values using the Durbin-Watson table, which shows the distribution of the statistic \(\hat{d}\) between \(d_{L}\) and \(d_{U}\) The results are interpreted as follows: \(\rho=-1\) and \(\hat{d}=4\) indicates Perfect Negative Correlation, \(\rho=0\) and \(\hat{d}=2\) indicates Autocorrelation, and \(\rho=+1\), \(\hat{d}=0\) indicates Perfect Positive Correlation. Methods for Resolving Autocorrelation  
The most severe case of autocorrelation is known as Pure Autocorrelation, which arises when the disturbance variables are correlated with one another. In this research, the Cochrane-Orcutt Iterative Method was selected to address the issue of autocorrelation. The process is carried out step-by-step, starting with the first-round residuals and then checking whether the problem still persists. If the issue remains, the process continues to the second-round residuals. However, if the problem cannot be resolved even after further iterations, the model must be revised immediately, as it will no longer be usable. The details of this process are as follows:  
\[Y_{t}-\hat{\beta}Y_{t-1}=\left(\alpha-\hat{\beta}\alpha\right)+\left(\beta X_ {t}-\hat{\beta}\beta X_{t-1}\right)+\varepsilon_{t}^{*} \tag{4}\]  
From Equation (4), the error term is tested using the Durbin-Watson Test. If the test result allows for the acceptance of \(H_{0}\), it indicates that there is no autocorrelation, and the calculation process will stop. However, if the test result leads to the rejection of \(H_{0}\), it implies that autocorrelation still exists. Therefore, it is necessary to calculate the \(\varepsilon,\rho\) value at a higher order. Multicollinearity occurs when independent variables are highly correlated with each other. The higher the correlation, the more it affects the model's ability to explain the variation in the dependent variable. However, it is common for independent variables to exhibit some degree of correlation within the model. The issue arises when this correlation becomes strong enough to cause problems in the model. Specifically, if the correlation is imperfect multicollinearity, the model can still proceed; however, if it is perfect multicollinearity, it severely affects the analysis, leading to spurious relationships in the model.