Autoregressive Fractionally Integrated Moving Average Models Research Articles

Modelling Primary Energy by Long Memory Time Series

This research employs long memory modeling techniques to analyze and forecast global energy data spanning from 1965 to 2022. Focusing on the ARFIMA (Autoregressive Fractionally Integrated Moving Average) model, the study demonstrates its efficacy in predicting energy consumption trends. The evaluation of forecasting results for the subsequent four years reveals a remarkable Mean Absolute Percentage Error (MAPE) below 5%. This outcome underscores the effectiveness of incorporating long memory components in energy modeling, offering a robust approach for accurate and reliable predictions. The findings contribute to the advancement of energy forecasting methodologies, providing valuable insights for policymakers, energy analysts, and researchers in the pursuit of sustainable and informed energy planning

PEMODELAN DATA HARGA CABAI DENGAN PENDEKATAN DERET WAKTU FRAKSIONAL ARFIMA

Long-memory is a type of time series data that has a high correlation between long observation times. This can be seen from the autocorrelation function where the lag falls slowly over a long period. Such long-memory data can be modeled in the form of an Autoregressive Fractionally Integrated Moving Average (ARFIMA). One of the data that meets the long-memory criteria is the monthly chili price from March 2017 to April 2023 as much as 73 data. ARFIMA model selection is done by comparing the AIC and BIC values of each candidate model, so that the best model is ARFIMA (1;0.22785;0), this means that the movement of chili prices is influenced by previous prices in the long term

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.

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.

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.

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

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.

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.

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.

Modelling and forecasting monthly Brent crude oil prices: a long memory and volatility approach

AbstractThe Standard Generalised Autoregressive Conditionally Heteroskedastic (sGARCH) model and the Functional Generalised Autoregressive Conditionally Heteroskedastic (fGARCH) model were applied to study the volatility of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model, which is the primary objective of this study. The other goal of this paper is to expand on the researchers’ previous work by examining long memory and volatilities simultaneously, by using the ARFIMA-sGARCH hybrid model and comparing it against the ARFIMA-fGARCH hybrid model. Consequently, the hybrid models were configured with the monthly Brent crude oil price series for the period from January 1979 to July 2019. These datasets were considered as the global economy is currently facing significant challenges resulting from noticeable volatilities, especially in terms of the Brent crude prices, due to the outbreak of COVID-19. To achieve these goals, an R/S analysis was performed and the aggregated variance and the Higuchi methods were applied to test for the presence of long memory in the dataset. Furthermore, four breaks have been detected: in 1986, 1999, 2005, and 2013 using the Bayes information criterion. In the further section of the paper, the Hurst Exponent and Geweke-Porter-Hudak (GPH) methods were used to estimate the values of fractional differences. Thus, some ARFIMA models were identified using AIC (Akaike Information Criterion), BIC (Schwartz Bayesian Information Criterion), AICc (corrected AIC), and the RMSE (Root Mean Squared Error). In result, the following conclusions were reached: the ARFIMA(2,0.3589648,2)-sGARCH(1,1) model and the ARFIMA(2,0.3589648,2)-fGARCH(1,1) model under normal distribution proved to be the best models, demonstrating the smallest values for these criteria. The calculations conducted herein show that the two models are of the same accuracy level in terms of the RMSE value, which equals 0.08808882, and it is this result that distinguishes our study. In conclusion, these models can be used to predict oil prices more accurately than others.

Fractional Dynamics of PMU Data

Novel dynamics are emerging in the power system due to the new Smart Grid (SG) environment. The high sampling rate of the Phasor Measurement Units (PMUs) enables them to capture the dynamic fluctuations in the power system measurements. Understanding the statistical and dynamic characteristics of the PMU data requires advanced data analytics techniques capable of performing accurate modeling of the power system variables (voltage, frequency, phase angle, and rate of change of frequency (ROCOF)). In this article, we provide evidence of the non-stationarity and fractality of PMU data collected from Europe. We adopt the Autoregressive Fractionally Integrated Moving Average (ARFIMA) models with non-integer differencing parameter to model the short-range and long-range correlations in the PMU data. Furthermore, the goodness-of-fit of the ARFIMA model is confirmed by analyzing the correlation and independence of the model residuals. Anomaly detection is among the promising applications of the PMU ARFIMA models. It is shown that the 2012 Indian blackout is accompanied by a change point in the differencing parameter opening the road to event (anomaly) detection by ARFIMA monitoring.

Forecasting long range dependent time series with exogenous variable using ARFIMAX model

Time series analysis and forecasting is one of the challenging issues of statistical modelling. Modelling of price and forecasting is a vital matter of concern for both the farming community and policy makers, especially in agriculture. Many practical agricultural data, principally commodity price data shows the typical feature of long memory process or long range dependency. For capturing the long memory behavior of the data Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is generally used. Sometimes, in time series data besides the original series, data on some auxiliary or exogenous variables may be available or can be made available with a lower cost; like besides the market prices of commodities, market arrivals for that commodity may be available and it affects the market price of commodities. This type of exogenous variable may be incorporated in existing model to improve the model performance and forecasting accuracy, like Autoregressive Fractionally Integrated Moving Average with exogenous variables (ARFIMAX) model. In the present study undertaken at ICAR-IASRI, New Delhi during 2019, daily maximum and modal price of potato of Agra market of UP, India are taken along with daily market arrival. Both the ARFIMA and ARFIMAX model with market arrival as exogenous variable are applied for the data under study. Comparative studies of the fitted models are employed by using the Relative Mean Absolute Percentage Error (RMAPE) and Root Mean Square Error (RMSE) criteria. We could establish superiority of the ARFIMAX model over the ARFIMA model in terms of modeling and forecasting efficiency.

Combined Methodology for Linear Time Series Forecasting

Time series forecasting is an important type of quantitative model used to predict future values given a series of past observations for which the generation process is unknown. Two of the most well‐known methods for the modeling of linear time series are the autoregressive integrated moving average (ARIMA) and the autoregressive fractionally integrated moving average (ARFIMA). For different datasets, the number of past observations necessary for an accurate prediction may vary. Short and long memory dependency problems require different handling, with the ARIMA model being limited to the first, while the ARFIMA model was specifically developed for the latter. Preprocessing techniques and modification on specific components of these models are common approaches used to tackle the memory dependency problem in order to improve their accuracy. However, such solutions are specific to certain datasets. This paper proposes a new method that combines the short and long memory characteristics of the two aforementioned models in order to keep a low accumulative error in several different scenarios. Twelve public time series datasets were used to compare the performance of the proposed method with the original models. The results were also compared with two alternative methods from the literature used to deal with datasets of different memory dependencies. The new approach presented a lower error for the majority of the experiments, failing only for the datasets that contain a large number of features. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

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.

Pattern interdependent network of cross-correlation in multivariate time series

Cross-correlation of a bivariate time series induces interdependencies between local patterns in the two series, which cooperatively exhibit in turn the structure of the cross-correlation. However, this structure is lost in the procedure of statistical average in time series analysis. In this paper a new concept called pattern interdependent network is proposed to display the structure of cross-correlation, in which the nodes are unique local patterns and the linkages are co-occurring frequencies of the unique local patterns in the series. The performance is illustrated by the bivariate series generated with the Gaussian process and the auto-regressive fractionally integrated moving average (ARFIMA) model. It is found that the cross-correlation and the scaling behaviors dominate the pattern of backbone structure (the set of the nodes and the set of linkages) and the symmetry of the network, respectively. The ARFIMA model can reproduce the structural behaviors of cross-correlations in U.S. stock markets. This concept provides us with a new method for detecting the structure of couplings between time series in various fields, such as clinical pathological signals.

Fractional ARIMA with an improved cuckoo search optimization for the efficient Short-term power load forecasting

Short-term power load forecasting plays a key role in power supply systems. Many methods have been used in short-term power load forecasting during the past years. A new short-term power load forecasting method is proposed in this study. First, the study represents a Fractional Auto-regressive Integrated Moving Average (FARIMA) model based on long-range dependence (LRD). The LRD model is governed by the Hurst exponent, which shows whether the model exhibits the LRD or not. Then, the study employs Cuckoo Search (CS) algorithm based on two parameters dynamic adjustment for parameter optimization of the forecasting model. As test problem, we use the real power consumption data, and test it for different forecasting models. Our results indicate that the FARIMA model and the improved optimization algorithm show relatively high accuracy and effectiveness in forecasting short-term power load.

On long memory origins and forecast horizons

AbstractMost long memory forecasting studies assume that long memory is generated by the fractional difference operator. We argue that the most cited theoretical arguments for the presence of long memory do not imply the fractional difference operator and assess the performance of the autoregressive fractionally integrated moving average (ARFIMA) model when forecasting series with long memory generated by nonfractional models. We find that ARFIMA models dominate in forecast performance regardless of the long memory generating mechanism and forecast horizon. Nonetheless, forecasting uncertainty at the shortest forecast horizon could make short memory models provide suitable forecast performance, particularly for smaller degrees of memory. Additionally, we analyze the forecasting performance of the heterogeneous autoregressive (HAR) model, which imposes restrictions on high‐order AR models. We find that the structure imposed by the HAR model produces better short and medium horizon forecasts than unconstrained AR models of the same order. Our results have implications for, among others, climate econometrics and financial econometrics models dealing with long memory series at different forecast horizons.

Bayesian Inference for ARFIMA Models

This article develops practical methods for Bayesian inference in the autoregressive fractionally integrated moving average (ARFIMA) model using the exact likelihood function, any proper prior distribution, and time series that may have thousands of observations. These methods utilize sequentially adaptive Bayesian learning, a sequential Monte Carlo algorithm that can exploit massively parallel desktop computing with graphics processing units (GPUs). The article identifies and solves several problems in the computation of the likelihood function that apparently have not been addressed in the literature. Four applications illustrate the utility of the approach. The most ambitious is an ARFIMA(2,d,2) model for the Campito tree ring time series (length 5405), for which the methods developed in the article provide an essentially uncorrelated sample of size 16,384 from the exact posterior distribution in under four hours. Less ambitious applications take as little as 4 minutes without exploiting GPUs.

Statistical modelling for forecasting volatility in potato prices using ARFIMA-FIGARCH model

This paper investigates the presence of long memory both in mean and volatility in the potato prices in Agra and Amritsar markets of India, using the Autoregressive fractionally integrated moving average (ARFIMA) and Fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models. Long memory tests are carried out both for the returns and squared return series. The results of GPH estimator indicate the existence of long memory in the price data.The ARFIMA model with error following FIGARCH process is fitted to return prices of potato for each of the two markets. At the end, the forecasting performance of fitted ARFIMA-FIGARCH models are carried out in terms of RMAPE and RMSE and the residuals are also examined to check adequacy of the fitted models.