COMPARISON OF ARIMA AND GARMA'S PERFORMANCE ON DATA ON POSITIVE COVID-19 CASES IN INDONESIA

The development of methods in statistics, one of which is used for prediction, is overgrowing. So it requires further analysis related to the goodness of the method. One of the comparisons made to the goodness of this model can be seen by applying it to actual cases around us. The real case still being faced by people worldwide, including in Indonesia, is Covid-19. Therefore, research comparing the autoregressive integrated moving average (ARIMA) and the Gegenbauer autoregressive moving average (GARMA) method in positive confirmed cases of Covid-19 in Indonesia is essential. Based on the results of this research analysis, it was found that the best model with the Aikake's Information Criterion measure of goodness that was used to predict positive confirmed cases of Covid-19 in Indonesia was the Gegenbauer autoregressive moving average (GARMA) model

Advancement of Fractionally Differenced Gegenbauer Processes with Long Memory

The class of long memory time series models involving Gegenbauer processes is investigated in detail in terms of formulation, parameter estimation, prediction and testing. Corresponding truncated AR (autoregressive) and MA (moving average) approximations driven by Gaussian white noise are analysed through state space modelling and Kalman filtering to assess the viability of estimating techniques . The optimal approximation option is employed to proceed with the estimation of model parameters. The resulting mean square errors are validated by the predictive accuracy to establish an optimal lag order through a large scale simulation study. It is shown that the use of this newly established lag order for a real data application provides benchmarks which are comparable and mostly better than a number of existing results in the literature. It is followed by an execution of this technique to extract and assess seasonal models through a Monte Carlo experiment. Thereafter empirical applications were provided. The above approach has been extended to model fractionally differenced Gegenbauer processes with conditional heteroskedastic errors and models with seasonality. Potential applications are provided. In addition, quasi-likelihood type ratio tests have been developed for testing unit roots, stationarity versus non-stationarity and Gegenbauer long memory versus standard long memory

GARMA, HAR and rules of thumb for modelling realized volatility

This paper features an analysis of the relative effectiveness, in terms of the Adjusted R-Square, of a variety of methods of modelling realized volatility (RV), namely the use of Gegenbauer processes in Auto-Regressive Moving Average format, GARMA, as opposed to Heterogenous Auto-Regressive HAR models and simple rules of thumb. The analysis is applied to two data sets that feature the RV of the S&P500 index, as sampled at 5 min intervals, provided by the OxfordMan RV database. The GARMA model does perform slightly better than the HAR model, but both models are matched by a simple rule of thumb regression model based on the application of lags of squared, cubed and quartic, demeaned daily returns

Periodic Long Memory GARCH models

A distinguishing feature of the intra-day time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type due mainly to time-of-the-day phenomena. In this work we introduce a model able to describe the empirical evidence given by this periodic longmemory behaviour. The model, named PLM-GARCH (Periodic Long Memory GARCH), represents a natural extension of the FIGARCH model proposed for modelling long-range persistence of the volatility of financial time series. Periodic long memory versions of EGARCH (PLM-EGARCH) models are also considered. Some properties and characteristics of the models are given and an estimation procedure based on quasi maximum likelihood is established. Further possible extensions of the model to take into account multiple sources of periodic long-memory behaviour are suggested. Some empirical applications on intra-day financial time series are also provided

Forecasting electricity spot market prices with a k-factor GIGARCH process

URL des Documents de travail :http://ces.univ-paris1.fr/cesdp/CESFramDP2007.htmParu dans Applied Energy, 86, 4 (2009) 505-510.Documents de travail du Centre d'Economie de la Sorbonne 2007.58 - ISSN : 1955-611XIn this article, we investigate conditional mean and variance forecasts using a dynamic model following a k-factor GIGARCH process. We are particularly interested in calculating the conditional variance of the prediction error. We apply this method to electricity prices and test spot prices forecasts until one month ahead forecast. We conclude that the k-factor GIGARCH process is a suitable tool to forecast spot prices, using the classical RMSE criteria.On donne l'expression analytique de la prévision en moyenne et en variance issue d'un processus GIGARCH à k-facteur. Les propriétés probabilistes sont données. Une application aux prix spot d'électricité sur le marché allemand est fourni

Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models

We review the multiple frequency Gegenbauer autoregressive moving average model, which is able to reproduce a wide range of autocorrelation functions. Extending the result of Chung (1996a), we propose the asymptotic distributions for a conditional sum of squares estimator of the model parameters. The parameters that determine the cycle lengths are asymptotically independent, converging at rate T for finite cycles. This result does not hold generally, most notably for the differencing parameters associated with the cycle lengths. Remaining parameters are typically not independent and converge at the standard rate of T1/2. We present simulation results to explore small sample properties of the estimator, which strongly support most distributional results while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume

A prospective study of the k-factor Gegenbauer processes with heteroscedastic errors and an application to inflation rates

We investigate some statistical properties of the new k-factor Gegenbauer process with heteroscedastic noises One of the goals of the paper is to give tools which permit to use this model to explain the behaviour of certain data sets in finance and in macroeconomics. Monte Carlo experiments are provided to calibrate the theoretical properties. Applications on consumer price indexes and inflation rates are done;GIGARCH process – estimation theory – Inflation rates – prices indexes.