ARFIMA Research Articles

A Fractional ARIMA (ARFIMA) Model in the Analysis of Historical Crude Oil Prices

We investigate historical data for crude oil prices using autoregressive fractionally integrated moving average (ARFIMA) models to determine whether shocks in the series have transitory or permanent effects. Our best specification is an ARFIMA(2,d,2) with an estimated value of d around 0.4, but its confidence interval is wide and does not allow us to either reject the I(0) or the I(1) hypotheses. This high level of uncertainty may be due to the presence of breaks or non-linear trends in the data.

Bayesian estimation of fractional difference parameter in ARFIMA models and its application

Recognizing and presenting the appropriate model is of particular importance to examine the statistical models for fitting time series data. Among time series models widely used in the analysis of economic, meteorological, geographical, and financial data is Auto Regressive Fractionally Integrated Moving Average (ARFIMA) model. In this model, and other time series models, the parameters of model are estimated by assuming that the average of data is constant. In this article, while investigating the behavior of ARFIMA model, Bayesian estimation of the fractional difference parameter (d) was presented considering the appropriate prior distribution. To check the efficiency of the proposed Bayesian estimation, using simulation and Akaike information criterion (AIC) it is shown that Bayesian estimation performs better compared to other methods. Finally, using a real data set and assuming a suitable prior distribution for the fractional difference parameter (d), shows that ARFIMA (0, d,0) is a suitable model for these data. The goodness of fit of the ARFIMA model was evaluated according to the Bayesian estimation of parameters.

The hybrid model of autoregressive integrated moving average and fuzzy time series Markov chain on long-memory data

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.

Time Analysis of an Emergent Infection Spread Among Healthcare Workers: Lessons Learned from Early Wave of SARS-CoV-2.

To find whether an emergent airborne infection is more likely to spread among healthcare workers (HCW) based on data of SARS-CoV-2 and whether the number of new cases of such airborne viral disease can be predicted using a method traditionally used in weather forecasting called Autoregressive Fractionally Integrated Moving Average (ARFIMA). We analyzed SARS-CoV-2 spread among HCWs based on outpatient nasopharyngeal swabs for real-time polymerase chain reaction(RT-PCR) tests and compared it to non-HCW in the first and the second wave of the pandemic. We also generated an ARFIMA model based on weekly case numbers from February 2020 to April 2021 and tested it on data from May to July 2021. Our analysis of 8998 tests in the 15 months period showed a rapid rise in positive RT-PCR tests among HCWs during the first wave of pandemic. In the second wave, however, positive patients were more commonly non-HCWs. The ARFIMA model showed a long-memory pattern for SARS-CoV-2 (seven months) and predicted future new cases with an average error of ±1.9 cases per week. Our data indicate that the virus rapidly spread among HCWs during the first wave of the pandemic. Review of published literature showed that this was the case in multiple other areas as well. We therefore suggest strict policies early in the emergence of a new infection to protect HCWs and prevent spreading to the general public. The ARFIMA model can be a valuable forecasting tool to predict the number of new cases in advance and assist in efficient planning.

Analysis of Precious Metal Price Movements Using Long Memory Model and Fuzzy Time Series Markov Chain

Precious metals occur naturally and have a high resistance to corrosion or oxidation. These natural resources are used as investment instruments to protect wealth values, such as gold, silver, and palladium. Price movements need to be understood when investing, and it is achieved through a time series model that predicts future prices. Also, autoregressive fractional integrated moving average (ARFIMA) is used to model price movements with long memory effects, while fuzzy time series Markov chain (FTSMC) is employed for performing numerical approach. It was observed that gold price movement has a long memory effect; therefore, it is eligible to be formed into the ARFIMA model. However, the silver and palladium prices do not contain a long memory effect, which means their movements are only formed through the FTSMC numerical model. The ARFIMA modeling results show that the gold price long memory model has the best accuracy with the smallest error value and also demonstrates excellent goodness of fit. Furthermore, the gold price long memory model movement has long-term stability compared to other precious metals. This provides an investment advantage because it is a stable asset, easy to liquidate in cash, free of interest, has an emergency fund role, and protects wealth’s value.

Testing for the Long Memory and Multiple Structural Breaks in Consumer ETFs

Abstract This research examines the consumer exchange-traded funds (ETFs) in several industries based on long memory and multiple structural breaks. The autoregressive fractionally integrated moving average (ARFIMA) model indicates that consumer ETF returns in the media, consumer service, food and beverage, and consumer goods industries can be accurately predicted. The autoregressive fractionally integrated moving average and fractionally integrated generalized autoregressive conditional heteroskedasticity (ARFIMA-FIGARCH) model reveals that only the gaming and consumer goods industries have a long memory in volatility. This study establishes that through the iterated cumulative sum square test, multiple structural breaks exist in consumer ETF industries. Results prove that the consumer goods industry has a long memory and multiple structural breaks. Finally, the structural breaks in consumer ETFs have strong asymmetrical effects, indicating that all of the consumer ETF industries are generally unstable. Keywords: The Long Memory, Multiple Structural Breaks, Consumer ETFs, Iterated Cumulative Sums Squares Test.

Dynamic Asymmetric Effect of Currency Risk Pricing of Exchange Rate on Equity Markets: A Regime-Switching Based C-Vine Copulas Method

This paper investigates whether currency risk is priced differently in the different sectors (industrial, financial, and basic materials) of equity markets in a sample of developed United States of America (USA) and developing economies (Brazil, India, Poland, and South Africa). The paper makes use of the following techniques: (i) Univariate Autoregressive Fractionally Integrated Moving Average and Exponential General Autoregressive Conditional Heteroskedastic (ARFIMA-EGARCH), (ii) the Markov Switching method (MS), and (iii) the Canonical Vine Copulas (C-Vine) techniques. Using a sample of daily data made of the foreign exchange rate against the domestic currency and equity market sectors; our findings show that there is an asymmetry effect between equity markets and the foreign exchange rate: there is a heterogeneous, strong, and positive dependence between the two. Higher equity prices are associated with depreciation of local currencies, according to US dollar (USD) exchange rates. In addition, we find that the selected emerging economies are pricing a positive and considerable currency risk. The pricing of currency risk has a varied effect in both regimes representing the states of the economy. In fact, when currency risk pricing has a beneficial impact on certain sectors of the economy, investors predict better returns.

Adaptive Reservoir Management by Reforming the Zone-based Hedging Rules against Multi-year Droughts

In this study, the zone-based hedging rule, which is the main operating policy adopted from multipurpose reservoirs in Korea is adjusted to reflect the multi-year droughts caused by climate change. Annual synthetic inflow series with different magnitudes of long memory were generated using the autoregressive fractional integrated moving average (ARFIMA) model. The generated inflow series were then disaggregated into 10-day series and utilized as input variables to derive the alternative hedging rules. The alternative hedging rules from this study were used in adaptive reservoir management by newly updated information. Finally, the performance of the suggested policy is measured in terms of frequency and magnitude under the historical inflow series. As a result, adaptive reservoir management demonstrated improvements in the following terms of the frequency of critical failures (water deficit ratio greater than 30%): 6.14% of the simulation period in the status quo (SQ) policy, and 2.99% in the adaptive management. However, the overall reliability of the reservoir during the simulation horizon was better when operated with the SQ policy (41.19%) than the results from adaptive management (26.42%). Because this result is in a good agreement with the original objective of the hedging rules, the adaptive policy suggested in this study holds promise and may be utilized in further reservoir management with an increase of potential drought risk from climate change.

Consistent order selection for ARFIMA processes

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model can be any real number, this consistency result is valid for short memory, long memory and nonstationary time series. This paper further extends the consistency of the BIC to ARFIMA models with conditional heteroscedastic errors, thereby extending its applications to encompass many real-life situations. Finite-sample implications of the theoretical results are illustrated via numerical examples.

Modelling the dynamics of stock market in the gulf cooperation council countries: evidence on persistence to shocks

This study examines the statistical properties required to model the dynamics of both the returns and volatility series of the daily stock market returns in six Gulf Cooperation Council countries, namely Bahrain, Oman, Kuwait, Qatar, Saudi Arabia, and the United Arab Emirates, under different financial and economic circumstances. The empirical investigation is conducted using daily data from June 1, 2005 to July 1, 2019. The analysis is conducted using a set of double long-memory specifications with some significant features such as long-range dependencies, asymmetries in conditional variances, non-linearity, and multiple seasonality or time-varying correlations. Our study indicates that the joint dual long-memory process can adequately estimate long-memory dynamics in returns and volatility. The in-sample diagnostic tests as well as out-of-sample forecasting results demonstrate the prevalence of the Autoregressive Fractionally Integrated Moving Average and Hyperbolic Asymmetric Power Autoregressive Conditional Heteroskedasticity modeling process over other competing models in fitting the first and the second conditional moments of the market returns. Moreover, the empirical results show that the proposed model offers an interesting framework to describe the long-range dependence in returns and seasonal persistence to shocks in conditional volatility and strongly support the estimation of dynamic returns that allow for time-varying correlations. A noteworthy finding is that the long-memory dependencies in the conditional variance processes of stock market returns appear important, asymmetric, and differ in their volatility responses to unexpected shocks. Our evidence suggests that these markets are not completely efficient in processing regional news, thus providing a sound alternative for regional portfolio diversification.

Forecasting price of Indian mustard (Brassica juncea) using long memory time series model incorporating exogenous variable

The objective of present study was to investigate the efficiency of Autoregressive fractionally integrated movingaverage model with exogenous input (ARFIMAX) in forecasting price of Indian mustard [Brassica juncea (L.) Czern.& Coss]. The daily modal price and arrival data of mustard for two major markets of India, viz. Bharatpur and Agrawere collected during 2008–2018 from AGMARKNET and used for the present investigation. It was observed thateach of the price series under consideration is stationary but autocorrelation function of both the series decay in ahyperbolic pattern. This indicates possible presence of long memory in the price data. Moreover, the significant result of correlation between price and arrival indicate that arrival data could be used as exogenous variable to model and forecast the price for both markets. Accordingly, Autoregressive fractionally integrated moving average (ARFIMA) and ARFIMAX models were applied to obtain the forecasts. The forecast evaluation was carried out with the help of Relative mean absolute percentage error (RMAPE) and Root mean square error (RMSE). The residuals of the fitted models were used for diagnosis checking as well as to investigate the adequacy of developed model. To this end, a comparative study has also been made between the fitted ARFIMAX model and ARFIMA model for both in-sample and out-of-sample data to identify the best fitted model in order to forecast future prices. The model has demonstrated a good performance in terms of explained variability and predicting power.

A hybrid ARFIMA-fuzzy time series (FTS) model for forecasting daily cases of Covid-19 in Iraq

Most time series are characterized in practice that they consist of two components, linear and non-linear, and when making predictions, the single models are not sufficient to model these series. Recently several linear, non-linear and hybrid models have been proposed for prediction, In this research, a new hybrid model was proposed based on the combination of the linear model Auto-Regressive Fractionally Integrated Moving Average (ARFIMA) with the non-linear model fuzzy time series model (FTS). The proposed hybrid model analyzes the linear component of the specified time series using the ARFIMA model, calculates the estimated values, and then calculates the residuals for this model by subtracting the estimated values from the original time series. The nonlinear component is analyzed using the (FTS) model for the computed residuals, which inherently contain the nonlinear patterns of the time series. The final values for the prediction by applying the} {hybrid model (ARFIMA-FTS) are obtained by combining the predictions of the (ARFIMA) model of the original series with the predictions of the model (FTS) for the residual series. The new hybrid model was used to predict those infected with the Covid-19 virus in Iraq for the period from 24/2/2020 to 11/8/2021. The proposed model was more efficient in the prediction process than the single (ARFIMA) model using a number of comparison criteria, including (RMSE), (MAPE) and (MAE). The final results showed that the proposed model has the ability to predict time series that contain linear and nonlinear components

Розроблення програмного та алгоритмічного забезпечення для прогнозування курсу криптовалют з використанням методів фрактального аналізу

The work created software and algorithmic support for modeling and forecasting the Bitcoin cryptocurrency using the ARFIMA (AutoRegressive Fractionally Integrated Moving Average) fractal model. Time series forecasting models (autoregressive, fractal) were analyzed. The selection of the most appropriate parameters of the selected fractal model was also carried out to maximize accuracy in view of the RMSE metric. The series were analyzed for trend, seasonality, white noise, non-stationarity and long-term memory. The Hurst indicators were studied and the algorithm for choosing the optimal parameter d of fractal differentiation of the ARFIMA model was adapted. The choice of software tools for implementing algorithms and forecasting models using the Python programming language version 3.6.5 using the pandas version 1.1.3 and numpy version 1.19.2 libraries is justified. In order to forecast the time series, the programming language R version 4.1.3 was used, along with the forecast version 8.16 and arfima version 1.8.0 libraries. The software implementation of the ARFIMA fractal model was carried out. Transferred the application to the Google Colab cloud service using Google Drive storage for storing data and forecasting results. The results of comparing the effectiveness of the created fractal model with the same model with automatic selection of parameters, as well as with the most appropriate autoregression model on different sizes of training and test data were obtained. It was established that a larger amount of both training and test data clearly favors fractal models, since in this case there is a long-lasting effect, that is, a pronounced long memory in the second time series. The result is a software system that can be used by investors and ordinary people to analyze and forecast their chosen cryptocurrency using a modern fractal modeling approach. It is important to always check the data and clean up anomalous deviations that cause error in the prediction estimate.

Lesson (un)replicated: Predicting levels of political violence in Afghan administrative units per month using ARFIMA and ICEWS data

Abstract The aim of the present article is to evaluate the use of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model in predicting spatially and temporally localized political violent events using the Integrated Crisis Early Warning System (ICEWS). The performance of the ARFIMA model is compared to that of a naïve model in reference to two common relevant hypotheses: the ARFIMA model would outperform a naïve model and the rate of outperformance would deteriorate the higher the level of spatial aggregation. This analytical strategy is used to predict political violent events in Afghanistan. The analysis consists of three parts. The first is a replication of Yonamine’s study for the period beginning in April 2010 and ending in March 2012. The second part compares the results to those of Yonamine. The comparison was used to assess the validity of the conclusions drawn in the original study, which was based on the Global Database of Events, Language, and Tone, for the implementation of this approach to ICEWS data. Building on the conclusions of this comparison, the third part uses Yonamine’s approach to predict violent events in Afghanistan over a significantly longer period of time (January 1995–August 2021). The conclusions provide an assessment of the utility of short-term localized forecasting.

A Random walk down the Dhaka Stock Exchange lane

Market efficiency has always been a matter of keen interest to the researchers of finance. Since the advancement of this concept, researchers are consistently investigating the market efficiency of different financial markets. Bangladesh, being one of the emerging economies, has also attracted the attention of many researchers. The researchers have investigated the realities regarding the market efficiency of both the stock exchanges of the country. Most of their investigations reveal that the Dhaka Stock Exchange (DSE) and the Chittagong Stock Exchange (CSE) are inefficient. This research, however, did not stop at revisiting market efficiency alone. Whether the return series follows a long-memory process, has also been tested. Besides, non-parametric tests have also been conducted to confirm the results of the parametric tests and vice versa. It generated a more reliable estimate of market efficiency for the period under study. Results of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model confirm that the return series does not follow a long memory process, and any shock in the system will eventually vanish. The findings of other tests (the run test, the Augmented Dickey-Fuller (ADF) test, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, and the Kolmogorov-Smirnov (K-S) test) suggest that the return series of the DSE are time-series stationary, non-normal, and do not follow a random walk. Given these results, we must echo the prior researchers to conclude that the stock market of Bangladesh is not efficient for the period of 2015 to 2020. These findings add new knowledge to the existing knowledge pool about market efficiency and long memory of the stock market of Bangladesh.

The impact of COVID-19 on global stock markets: early linear and non-linear evidence for Italy

The scientific community still struggles to understand the magnitude of the worldwide infections and deaths induced by COVID-19, partly ignoring the financial consequences. In this paper, using the autoregressive fractionally integrated moving average (ARFIMA)—general autoregressive conditional heteroskedasticity (GARCH) model, we quantify and show the impact of the COVID-19 spread in Italy, utilizing data for the stock market. Using information criteria and forecasting accuracy measures, we show that the COVID-19 confirmed cases contribute with statistically significant information to the modeling of volatility, and also increase the forecasting ability of the volatility of the Italian stock market index, leading to a decrease in the mean stock index.

Examination of Long Memory in Indian Stock Market: A Sectoral Juxtaposition

One of the situations encountered in time series analysis is long-range dependence, also known as Long memory. We investigated the presence of long memory in the Indian sectoral indices returns and investigated whether the long memory behaviour is affected by the data frequency. We applied the autoregressive fractionally integrated moving average (ARFIMA) models to 13 sectoral indices of the National Stock Exchange of India and examined the long memory in daily, monthly and quarterly return series. The results indicate the persistence in daily return series and anti-persistence in monthly and quarterly return series. Thus, we conclude that the frequency of data does have a significant effect on the behaviour of long memory patterns. The results will be helpful for present and potential investors, institutional investors, portfolio managers and policymakers to understand the dynamic nature of long memory in the Indian stock market.

A hybrid autoregressive fractionally integrated moving average and nonlinear autoregressive neural network model for short-term traffic flow prediction

Intelligent traffic control and guidance system is an effective way to solve urban traffic congestion, improve road capacity and guarantee drivers' travel safety, while short-term traffic flow prediction is the core of intelligent traffic control and guidance system. To investigate the long-term memory and the dynamic feature of short-time traffic flow time series, a hybrid model was proposed by integrating autoregressive fractionally integrated moving average (ARFIMA) model and nonlinear autoregressive (NAR) neural network model to predict short-time traffic flow, in which ARFIMA model can address the long-term memory of linear component and NAR neural network can accommodate the dynamic feature of nonlinear residual component. First, the ARFIMA model was employed to predict the linear component of traffic flow, and the results were compared with those of autoregressive integrated moving average (ARIMA) model. Next, the NAR neural network model was adopted to forecast the nonlinear residual components, and the weighted results were considered as the predicted flow of the hybrid model. The proposed hybrid model was validated by using the cross-sectional traffic flow data in California freeways obtained from the open-access PeMS database. The results showed that the ARFIMA model considering the long-term memory can effectively predict the short-term traffic flow, and the prediction accuracy of the hybrid model is better than that of the singular models. The findings provide an alternative for the short-term traffic flow prediction with lower error and higher accuracy.

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems.

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

PEMODELAN AUTOREGRESSIVE FRACTIONALLY INTEGRATED MOVING AVERAGE DENGAN EFEK EXPONENTIAL GARCH (ARFIMA-EGARCH) UNTUK PREDIKSI HARGA BERAS DI KOTA SEMARANG

Time series data is a type of data that is often used to estimate future values. Long memory phenomenon often occurs in time series data. Long memory is a condition that shows a strong correlation between observations even though they are quite far away. This phenomenon can be overcome by modeling time series data using the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. This model is characterized by a fractional difference value. ARFIMA (Autoregressive Fractional Integrated Moving Average) model assumes that the residuals are normally distributed, mutually independent, and homogeneous. However, usually in financial data, the residual variants are not constant. This can be overcome by modeling variants. Standard equipment that can be used to model variants is the ARCH / GARCH (Auto Regressive Conditional Heteroscedasticity / Generalized Auto Regressive Conditional Heteroscedasticity) model. Another phenomenon that often occurs in GARCH models is the leverage effect on the residuals of the model. EGARCH (Exponential General Auto Regessive Conditional Heteroscedasticity) is a development of the GARCH model that is appropriate for data that has an leverage effect. The implementation of this model is by modeling financial data, so this study takes 136 monthly data on rice prices in Semarang City from January 2009 to April 2020. The purpose of this study is to create a long memory data forecasting model using the Exponential method. Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). The best model obtained is ARFIMA (1, d, 1) EGARCH (1,1) which is capable of forecasting with a MAPE value of 3.37%.Keyword : Rice price, forecasting , long memory, leverage effect, GARCH, EGARCH