We analyze the effects on prediction intervals of fitting ARIMA models to series with stochastic trends, when the underlying components are heteroscedastic. We show that ARIMA prediction intervals may be inadequate when only the transitory component is heteroscedastic. In this case, prediction intervals based on the unobserved component models tend to the homoscedastic intervals as the predicti...

The popularity of Bitcoin increased significantly in 2021. is considered to deliver high returns a relatively short period, indicating that bitcoin has volatility. Data with volatility usually violates the Autoregresstive IntegratedinMovinginAverage (ARIMA)in homoscedasticity assumption. Autoregressive Conditional Heteroscedasticity (ARCH) and General (GARCH) model often used overcome problem h...

In this paper, we analyze and predict the number of daily confirmed cases coronavirus (COVID-19) based on two statistical models a deep learning (DL) model; autoregressive integrated moving average (ARIMA), generalized conditional heteroscedasticity (GARCH), stacked long short-term memory neural network (LSTM DNN). We find orders by autocorrelation function partial function, hyperparameters DL ...

Gold investment is considered safer and has less risk than other types of investment. One the important knowledge in investing gold predicting price future through modeling past. The purpose this study to model past so that it can be used predict prices future. world data a time series heteroscedasticity properties, solve problem GARCH. This an asymmetric effect, GARCH used, namely Glosten-Jaga...

In this article, we examine the daily water demand forecasting performance of double seasonal univariate time series models (Holt-Winters, ARIMA and GARCH) based on multi-step ahead forecast mean squared errors. A within-week seasonal cycle and a within-year seasonal cycle are accommodated in the various model speci…cations to capture both seasonalities. We investigate whether combining forecas...

This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE, and some M-type estimators. As an application, we verify the a...