key: cord-0719572-wps2ikac authors: Balah, B.; Djeddou, M. title: Forecasting COVID-19 new cases in Algeria using Autoregressive fractionally integrated moving average Models (ARFIMA) date: 2020-05-08 journal: nan DOI: 10.1101/2020.05.03.20089615 sha: c4213fb7b0fdd8926e9e4108726524bc87483677 doc_id: 719572 cord_uid: wps2ikac In this research, an ARFIMA model is proposed to forecast new COVID-19 cases in Algeria two weeks ahead. In the present study, public health database from Algeria health ministry has been used to build an ARFIMA model and used to forecast COVID-19 new cases in Algeria until May 11, 2020. ORCID iD: https://orcid.org/0000-0002-4762-0368 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. In this article, we build an ARFIMA model, and study the behavior and analyze the type of forecast memory (long or short) of this model using COVID-19 new cases in Algeria using two techniques: 1. Maximum likelihood. Long memory models have become increasingly popular as a tool for describing time series. Longterm memory (long-term correlation) in time series is mainly assessed using the exponent from Hurst The ARFIMA model was proposed by Granjer and Joyeux (1980) [4-5-6] , and since then they draw particular attention to the class of ARFIMA models by their flexibility to model many real situations by estimating the parameter d [7] . Hamid et al. [8] recommend that data used should follow a normal distribution, In order to verify this recommendation, the data set is tested using Jarque-Bera normality test, based on the distribution of a combined measure of asymmetry and kurtosis. The stationary of the time series was verified using the Augmented Dickey and Fuller test. Residuals analysis is the most important step to validate the constructed model. In order to check if the residuals are white noise, a Ljung-Box test is applied to the models obtained to verify the effect of homoschedastic, this test remains is a decisive tool for the adaptability of constructed model. Hurst (1951) [3] proposed a useful statistical method for understanding the properties of a studied time series., it is often used to analyze long-term time series correlations [9] [10] . Depending on the H value, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020. If 0.5 < H <1, the autocorrelations are all positive and decrease hyperbolically towards zero, the spectral density exhibits a pole at zero frequency, the series presents all kinds of non-periodic cycles and the process has a persistent form of long memory whose explanation is different from that of short-term persistence. If 0 < H <0.5, the autocorrelations alternate sign and the spectral density, zero at zero, is dominated by the high frequency components. The process is anti-persistent: rising phases tend to be followed by falling phases. According to [3] ; the Hurst exponent is given by Eq. (1) below: Jarque-Bera normality test (Fig.1 ) applied to the time seriese, shows that the series of COVID-19 new cases follows a normal distribution and the risk of rejecting the null hypothesis H 0 is equal to 19.4%. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. PETTITT test was applied on the COVID-19 new cases time series, results showed that data series is not homogeneous, and has an increasing tendency in stairs. The first average is about 17 persons and the second average is 102 persons with March 30, 2020 as the break date (see Figure 2 ). Analysis of the data with Augmented Dickey-Fuller test (ADF) is proof of acceptance of the null hypothesis (H0) and the risk of rejection of the alternative hypothesis (Ha) is less than : 89% for the series of new cases of COVID-19. Therefore, the data series shows the absence of the unit root, therefore it is characterized as non-stationary. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020. Through these three criteria, the Non-linear least squares estimation method, whose ARFIMA model . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 8, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 8, 2020. . https://doi.org/10.1101/2020.05.03.20089615 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted May 8, 2020. . https://doi.org/10.1101/2020.05.03.20089615 doi: medRxiv preprint Climate change, the Hurst phenomenon, and hydrological statistics Some comments on Hurst exponent and the long memory processes on capital markets Hurst's exponent estimation methods. Application to stock market profitability Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation Using SARFIMA Model to Study and Predict the Iran's Oil Supply Preliminary Estimation of ARFIMA Models Multifractal Detrended Analysis Method and Its Application in Financial Markets Assessment of Stochastic Models and a Hybrid Artificial Neural Network-Genetic Algorithm Method in Forecasting Monthly Reservoir Inflow The Hurst phenomenon and the rescaled range statistic