IntroductionTime series models on financial data often have problems with the stationary assumption of variance on the residuals. It is well known as the heteroscedasticity effect. The heteroscedasticity is represented by a nonconstant value that varies over time.MethodsThe heteroscedasticity effect contained in the basic classical time series model of Autoregressive Integrated Moving Average (ARIMA) can adjust its residuals as the variance model by using Generalized Autoregressive Conditional Heteroscedasticity (GARCH). In improving the model accuracy and overcoming the heteroscedasticity problems, it is proposed a combination model of ARIMA and Feed-Forward Neural Network (FFNN), namely ARIMA-FFNN. The model is built by applying the soft computing method of FFNN to replace the variance model. This soft computing approach is one of the numerical methods that can not be only applied in the theoretical subject but also in the data processing.ResultsIn this research, the accuracy of the time series model using the case study of the exchange rate United States dollar-Indonesia rupiah with a monthly period from January 2001 to May 2021 shows that the best accuracy of the possible models is the model of ARIMA-FFNN, which applies soft computing to obtain the optimal fitted parameters precisely.DiscussionThis result indicates that the ARIMA-FFNN model is better used to approach this exchange rate than the rest model of ARIMA-GARCH and ARIMA-GARCH-FFNN.
IntroductionThe price of crude oil as an essential commodity in the world economy shows a pattern and identifies the component factors that influence it in the short and long term. The long pattern of the price movement of crude oil is identified by a fractionally time series model where the accuracy can still be improved by making a hybrid residual model using a fuzzy time series approach.MethodsTime series data containing long-memory elements can be modified into a stationary model through the autoregressive fractional integrated moving average (ARFIMA). This fractional model can provide better accuracy on long-memory data than the classic autoregressive integrated moving average (ARIMA) model. The long-memory data are indicated by a high level of fluctuation and the autocorrelation value between lags that decreases slowly. However, a more accurate model is proposed as a hybridization time series model with fuzzy time series Markov chain (FTSMC).ResultsThe time series data collected from the monthly period of West Texas Intermediate (WTI) oil price as the standard for world oil prices for the 2003–2021 time period. The data of WTI oil price has a long-memory data pattern to be modeled fractionally, and subsequently their hybrids. The times series model of crude oil price is obtained as the new target model of hybrid ARIMA and ARFIMA with FTSMC, denoted as ARIMA-FTSMC and ARFIMA-FTSMC, respectively.DiscussionThe accuracy model measured by MAE, RMSE, and MAPE shows that the hybrid model of ARIMA-FTSMC has better performance than ARIMA and ARFIMA, but the hybrid model of ARFIMA-FTSMC provides the best accuracy compared to all models. The superiority of the hybrid time series model of ARFIMA-FTSMC on long-memory data provides an opportunity for the hybrid model as the best and more precise forecasting method.
The Indonesian composite stock price index is an indicator of changes in stock prices as a guide for investors to invest in reducing risk. The regression model for Indonesian Composite Index (ICI) has the response variable as stock prices with fluctuation behavior and several financial predictor variables, the model tends to violate the assumptions of normality, homoscedasticity, autocorrelation and multicollinearity. This problem can be overcome by modeling the composite stock price index by using the Artificial Neural Network (ANN) and nonparametric regression of Multivariate Adaptive Regression Spline (MARS). In this study, the time series data from the composite stock price index starting from April 2003 to March 2018 with its predictor variables are crude-oil prices, interest rates, inflation, exchange rates, gold prices, Dow Jones price, and Nikkei 225 Index. The both methods give better goodness of fit, where the coefficient of determination ANN is 0.98925 and the MARS determination coefficient is 0.99427. While based on the Mean Absolute Percentage Error (MAPE) of ANN was obtained 6.16383 and the MAPE value of MARS is 4.51372. This means that the ANN method and nonparametric MARS regression method have good performance to forecast the value of the Indonesian composite stock price index in the future, but in this case of data the nonparametric MARS regression method shows the accuracy of the model is slightly better than ANN.
The number of tourist arrivals forecasting is required for the future development of tourism industry to improve the economic growth. The number tourist arrivals data can be analyzed by building a model so that it will help to find out the number of tourist arrivals in the next period which is through Minangkabau International Airport. The linear model that is used is Seasonal Autoregressive Integrated Moving Average (SARIMA) used and continued to build a nonlinear model of the residual SARIMA model using Artificial Neural Network (ANN). In this research, SARIMA model which obtained is SARIMA (1, 0, 1) (1, 1, 0) 12. But, residual of SARIMA model has not been fulfilled an autocorrelation assumption so that it isproposed a new model of SARIMA-ANN. The residual model of SARIMA is built using the ANN model architecture with 2-2-2-1 network topology. The performance rate of time series model of tourist arrivals which is the data started on January 2012 until March 2019 is measured using Mean Absolute Percentage Error (MAPE). Based on the MAPE value of 17.1770% indicates that the model obtained having good performance to forecast the number of tourist arrivals through Minangkabau International Airport in the future.
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