The Comparison between ARIMA and ARFIMA Model to Forecast Kijang Emas (Gold) Prices in Malaysia using MAE, RMSE and MAPE

Gold is known as the most valuable commodity in the world because it is a universal currency recognized by every single bank across the globe. Thus, many people were interested in investing gold since gold market was always steadier compared to other investment (Khamis and Awang, 2020). However, the credibility of gold was questionable due to the changes in gold prices caused by a variety of circumstances (Henriksen, 2018). Hence, information on the inflation of gold prices were needed to understand the trend in order to plan for the future in accordance with international gold price standards. The aim of this study was to identify the trend of Kijang Emas monthly average prices in Malaysia from the year 2010 to 2021, to determine the best fit time series model for Kijang Emas prices in Malaysia and using univariate time series models to forecast Kijang Emas prices in Malaysia. The ARIMA and ARFIMA models were used in this study to model and forecast the prices of gold (Kijang Emas) in Malaysia. Each of the actual monthly Kijang Emas prices for 2021 were found to be within the 95% predicted intervals for both the ARIMA and ARFIMA models. The performances for each model were checked by considering the values of MAE, RMSE and MAPE. From the findings, all the MAE, RMSE and MAPE values showed that the ARFIMA model emerged as the better model in forecasting the Kijang Emas prices in Malaysia compared to the ARIMA model.

Forecasting of New Cases of COVID-19 in Nigeria Using Autoregressive Fractionally Integrated Moving Average Models

The emergence of global pandemic known as COVID-19 has impacted significantly on human lives and measures have been taken by government all over the world to minimize the rate of spread of the virus, one of which is by enforcing lockdown. In this study, Autoregressive fractionally integrated moving average (ARFIMA) Models was used to model and forecast what the daily new cases of COVID-19 would have been ten days after the lockdown was eased in Nigeria and compare to the actual new cases for the period when the lockdown was eased. The proposed model ARFIMA model was compared with ARIMA (1, 0, 0), and ARIMA (1, 0, 1) and found to outperform the classical ARIMA models based on AIC and BIC values. The results show that the rate of spread of COVID-19 would have been significantly less if the strict lockdown had continued. ARFIMA model was further used to model what new cases of COVID-19 would be ten days ahead starting from 31st of August 2020. Therefore, this study recommends that government should further enforce measures to reduce the spread of the virus if business must continue as usual.

FORECASTING FRESH WATER AND MARINE FISH PRODUCTION IN MALAYSIA USING ARIMA AND ARFIMA MODELS

Malaysia is surrounded by sea, rivers and lakes which provide natural sources of fish for human consumption. Hence, fish is one source of protein supply to the country and fishery is a sub-sector that contribute to the national gross domestic product. Since fish forecasting is crucial in fisheries management for managers and scientists, time series modelling can be one useful tool. Time series modelling have been used in many fields of studies including the fields of fisheries. In a previous research, the ARIMA and ARFIMA models were used to model marine fish production in Malaysia and the ARFIMA model emerged to be a better forecast model. In this study, we consider fitting the ARIMA and ARFIMA to both the marine and freshwater fish production in Malaysia. The process of model fitting was done using the “ITSM 2000, version 7.0” software. The performance of the models were evaluated using the mean absolute error, root mean square error and mean absolute percentage error. It was found in this study that the selection of the best fit model depends on the forecast accuracy measures used.

Directional dependency and coastal framework geology: implications for barrier island resilience

Barrier island transgression is influenced by the alongshore variation in beach and dune morphology, which determines the amount of sediment moved landward through wash-over. While several studies have demonstrated how variations in dune morphology affect island response to storms, the reasons for that variation and the implications for island management remain unclear. This paper builds on previous research by demonstrating that paleo-channels in the irregular framework geology can have a directional influence on alongshore beach and dune morphology. The influence of relict paleo-channels on beach and dune morphology on Padre Island National Seashore, Texas, was quantified by isolating the long-range dependence (LRD) parameter in autoregressive fractionally integrated moving average (ARFIMA) models, originally developed for stock market economic forecasting. ARFIMA models were fit across ∼250 unique spatial scales and a moving window approach was used to examine how LRD varied with computational scale and location along the island. The resulting LRD matrices were plotted by latitude to place the results in the context of previously identified variations in the framework geology. Results indicate that the LRD is not constant alongshore for all surface morphometrics. Many flares in the LRD plots correlate to relict infilled paleo-channels, indicating that the framework geology has a significant influence on the morphology of Padre Island National Seashore (PAIS). Barrier island surface morphology LRD is strongest at large paleo-channels and decreases to the north. The spatial patterns in LRD surface morphometrics and framework geology variations demonstrate that the influence of paleo-channels can be asymmetric (i.e., affecting beach–dune morphology preferentially in one direction alongshore) where the alongshore sediment transport gradient was unidirectional during island development. The asymmetric influence of framework geology on coastal morphology has long-term implications for coastal management activities because it dictates the long-term behavior of a barrier island. Coastal management projects should first seek to assess the framework geology and understand how it influences coastal processes in order to more effectively balance long-term natural variability with short-term societal pressure.

Prediction intervals in the ARFIMA model using bootstrap G

This paper presents a bootstrap resampling scheme to build pre-diction intervals for future values in fractionally autoregressive movingaverage (ARFIMA) models. Standard techniques to calculate forecastintervals rely on the assumption of normality of the data and do nottake into account the uncertainty associated with parameter estima-tion. Bootstrap procedures, as nonparametric methods, can overcomethese diculties. In this paper, we test two bootstrap prediction in-tervals based on the nonparametric bootstrap in the residuals of theARFIMA model. In this paper, two bootstrap prediction intervals areproposed based on the nonparametric bootstrap in the residuals ofthe ARFIMA model. The rst one is the well known percentile boot-strap, (Thombs and Schucany, 1990; Pascual et al., 2004), never usedfor ARFIMA models to the knowlegde of the authors. For the secondapproach, the intervals are calculated using the quantiles of the empir-ical distribution of the bootstrap prediction errors (Masarotto, 1990;Bisaglia e Grigoletto, 2001). The intervals are compared, througha Monte Carlo experiment, to the asymptotic interval, under Gaus-sian and non-Gaussian error distributions. The results show that thebootstrap intervals present coverage rates closer to the nominal levelassumed, when compared to the asymptotic standard method. An ap-plication to real data of temperature in New York city is also presentedto illustrate the procedures.