## 2 Related Works
The monthly data spans from January 2000 to December 2017 for the training set, and the last twelve observations from January to December 2018 are used as a test set to obtain the out-of-sample forecast and for validation. In the experimental setup, generalized autoregressive conditional heteroskedasticity (GARCH) and generalized autoregressive conditional heteroscedasticity with exogenous variable (GARCHX) models are applied to capture heteroscedasticity and nonlinearity in the conditional variance of ARMAX. Appropriate GARCH and GARCHX models are selected based on minimum Akaike information criterion (AIC), BIC, and HQ (Hannan and Quinn) criteria. The stochastic linear autoregressive moving average with exogenous variable with GARCH (ARMAX-GARCH) and ARMAX-GARCHX hybrid models are compared with individual models and evaluated using error measures such as MAE, MAPE, and RMSE. In the research, the hybrid model ARMAX-GARCHX is perceived to be more effective than other rival single and twin hybrid models for the data under study. [PERSON] et al. [20] determined the best model to forecast the unemployment rate in selected Asian countries. In the study, the ARIMA-ARNN hybrid model is proposed against the reference models ARIMA, ANN, SVM, and hybrid combinations such as ARIMA-ANN and ARIMA-SVM. Unemployment data from seven developing Asian countries--Iran, Sri Lanka, Bangladesh, Pakistan, Indonesia, China, and India--is used and comes from the FRED financial index database. In the experimental setup, the ARIMA model is fitted for each selected country using criteria such as AIC and log-likelihood to select the best model. Subsequently, the ARIMA residuals are modeled using ARNN, which allows the residual nonlinearities present in the data to be captured. The \"predict\" package of the R-Studio environment is used to fit the ARIMA model, and graphical analysis techniques, such as autocorrelation function (ACF) and partial autocorrelation function (PACF) plots, are used to determine the optimal parameters of the ARIMA model. Once the best ARIMA model for each country has been selected, the results of the ARIMA and ARNN models are combined to generate accurate forecasts of the unemployment rate. Furthermore, performance metrics such as MAE, MAPE, and RMSE are used to evaluate the quality of the models. The results show that the hybrid ARIMA-ARNN model outperformed competitors for developing economies in Asia. [PERSON]. [21] investigated the unemployment rate forecast in the United States, the United Kingdom, France, and Italy. To do this, he proposed a hybrid LSTM-GRU model, which combines the long short-term memory (LSTM) with gated recurrent unit (GRU) methodologies, two algorithms widely used in deep learning for time series forecasts that used a data set of the monthly unemployment rate from January 1983 to May 2022 for the four countries mentioned, obtained from the OECD website. The data was divided into training and test sets at a ratio of 70% and 30%, respectively. The data were normalized between 0 and 1 using the min-max scaler. The model architecture consists of an LSTM layer with 128 hidden neurons, a GRU layer with 64 hidden neurons, and a dense layer with one output neuron. The LSTM-GRU hybrid model better predicted the unemployment rate for the United States, the United Kingdom, and France, except Italy, where the GRU model alone performed better. The results indicated that the hybrid model was more effective in most cases. Finally, [PERSON]. [PERSON] et al. [22] determined the best model to forecast the unemployment rate in selected European countries, specifically France, Spain, Belgium, Turkey, Italy, and Germany. Monthly unemployment rate data from the FRED economic data set, available online, were used. Classic models such as ARIMA and machine learning models such as ANN and SVM were considered. Furthermore, hybrid approaches such as ARIMA-ARNN, ARIMA-ANN, and ARIMA-SVM were proposed.