Fractionally Integrated Moving Average Research Articles

Analyzing the Selective Stock Price Index Using Fractionally Integrated and Heteroskedastic Models

Stock market indices are important tools to measure and compare stock market performance. The Selective Stock Price (SSP) index reflects fluctuations in a set value of financial instruments of Santiago de Chile’s stock exchange. Stock indices also reflect volatility linked to high uncertainty or potential investment risk. However, economic shocks are altering volatility. Evidence of long memory in SSP time series also exists, which implies long-term persistence. In this paper, we studied the volatility of SSP time series from January 2010 to September 2023 using fractionally heteroskedastic models. We considered the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) innovations—the ARFIMA-GARCH model—for SSP log returns, and the fractionally integrated GARCH, or FIGARCH model, was compared with a classical GARCH one. The results show that the ARFIMA-GARCH model performs best in terms of volatility fit and predictive quality. This model allows us to obtain a better understanding of the observed volatility and its behavior, which contributes to more effective investment risk management in the stock market. Moreover, the proposed model detects the influence volatility increments of the SSP index linked to external factors that impact the economic outlook, such as China’s economic slowdown in 2012 and the subprime crisis in 2008.

The seasonal model of chili price movement with the effect of long memory and exogenous variables for improving time series model accuracy

This study aimed to explore big-time series data on agricultural commodities with an autocorrelation model comprising long-term processes, seasonality, and the impact of exogenous variables. Among the agricultural commodities with a large amount of data, chili prices exemplified criteria for long-term memory, seasonality, and the impact of various factors on production as an exogenous variable. These factors included the month preceding the new year and the week before the Eid al-Fitr celebration in Indonesia. To address the factors affecting price fluctuations, the Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) model was used to manage seasonality and long-term memory effects in the big data analysis. It improved with the addition of exogenous variables called SARFIMAX (SARFIMA with exogenous variables is known as SARFIMAX). After comparing the accuracy of both models, it was discovered that the SARFIMAX performed better, indicating the influence of seasonality and previous chili prices for an extended period in conjunction with exogenous variables. The SARFIMAX model gives an improvement in model accuracy by adding the effect of exogenous variables. Consequently, this observation concerning price dynamics established the cornerstone for maintaining the sustainability of chili supply even with the big data case.

Modelling Long Memory Time Series for Groundnut Prices in Andhra Pradesh with Autoregressive Fractionally Integrated Moving Average for Forecasting

Modelling Long Memory Time Series for Groundnut Prices in Andhra Pradesh with Autoregressive Fractionally Integrated Moving Average for Forecasting

Google Trends of political parties in Europe: a fractal exploration

Abstract Google Trends, despite its controversial nature for some authors, can be considered an illustrative tool in exploring the political inclinations of a given audience. In the current European Union context, understanding the views and opinions of the public is of paramount importance. Through the analysis of search trends, Google Trends can provide valuable insights into the popularity of political parties in the context of the European Union along with other jurisdictions and how these trends change over time. Furthermore, by incorporating fractal dimensions and ARFIMA (Autoregressive Fractionally Integrated Moving Average) analysis into the data obtained, it is possible to reveal previously non-evident relationships, thereby providing a more comprehensive understanding of the audience‘s political leanings and their interest in specific political parties. The aim of this exploratory study is to assess the potential of ARFIMA, applied to Google Trends data, in characterizing political parties. Preliminary results indicate that this apparatus can be useful for that purpose.

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

Ethereum Value Forecasting Model using Autoregressive Integrated Moving Average (ARIMA)

The purpose of this study is to test the ability of the ARIMA model to predict the value of Ethereum, especially during economic shocks such as the current COVID-19 pandemic. The population in this study is Ethereum value weekly data for the period January 2017 to December 2020, so there are 208 samples in this study. The results showed that the use of the ARIMA method in predicting the value of Ethereum got poor results, where the forecast value was very much different from the actual value. This is evidenced from the results of the accuracy test using MAPE which got a result of 51.94%. On the other hand, the economic conditions that are experiencing uncertainty due to the COVID-19 pandemic and the emergence of deficit (decentralized finance) in early 2021 have pushed up a very significant increase in the value of Ethereum so that the error standard is higher and reduces the ability of the ARIMA model to predict the value of Ethereum. Further research is recommended to use a more advanced model such as the Autoregressive Fractionally Integrated Moving Average (AFRIMA) in order to obtain a better forecast value.

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.

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.

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.

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.

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.

Wind Put Barrier Options Pricing Based on the Nordix Index

Wind power generators face risks derived from fluctuations in market prices and variability in power production, generated by their high dependence on wind speed. These risks could be hedged using weather financial instruments. In this research, we design and price an up-and-in European wind put barrier option using Monte Carlo simulation. Under the existence of a structured weather market, wind producers may purchase an up-and-in European wind barrier put option to hedge wind fluctuations, allowing them to recover their investments and maximise their profits. We use a wind speed index as the underlying index of the barrier option, which captures risk from wind power generation and the Autoregressive Fractionally Integrated Moving Average (ARFIMA) to model the wind speed. This methodology is applied in the Colombian context, an electricity market affected by the El Niño phenomenon. We find that when the El Niño phenomenon occurs, there are incentives for wind generators to sell their energy to the system because their costs, including the put option price, are lower than the power prices. This research aims at encouraging policymakers and governments to promote renewable energy sources and a financial market to trade options to reduce uncertainty in the electrical system due to climate phenomena.

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.

Should Deep Learning Models be in High Demand, or Should They Simply be a Very Hot Topic? A Comprehensive Study for Exchange Rate Forecasting

Exchange rate movements can significantly impact not only foreign trade, capital flows, and asset portfolio management, but also real economic activity. Therefore, the forecast of exchange rates has always been of great interest among academics, economic agents, and institutions. However, exchange rate series are essentially dynamic and nonlinear in nature and thus, forecasting exchange rates is a difficult task. On the other hand, deep learning models in solving time series forecasting tasks have been proposed in the last half-decade. But the number of formal comparative study in terms of exchange rate forecasting with deep learning models is quite limited. For this purpose, this study applies ten different models (Random Walk, Autoregressive Moving Average, Threshold Autoregression, Autoregressive Fractionally Integrated Moving Average, Support Vector Regression, Multilayer Perceptron, Recurrent Neural Network, Long Short Term Memory, Gated Recurrent Unit and Autoregressive Moving Average-Long Short Term Memory Hybrid Models) and two forecasting modes (recursive and rolling window) to predict three major exchange rate returnsnamely, the Canadian dollar, Australian dollar and British pound against the US Dollar in monthly terms. To evaluate the forecasting performances of the models, we used Model Confidence Set procedure as an advanced test. According to our results, the proposed hybrid model produced the best out-of-sample forecast performance in all samples, without exception.

Long-Range Dependence in Financial Markets: A Moving Average Cluster Entropy Approach.

A perspective is taken on the intangible complexity of economic and social systems by investigating the dynamical processes producing, storing and transmitting information in financial time series. An extensive analysis based on the moving average cluster entropy approach has evidenced market and horizon dependence in highest-frequency data of real world financial assets. The behavior is scrutinized by applying the moving average cluster entropy approach to long-range correlated stochastic processes as the Autoregressive Fractionally Integrated Moving Average (ARFIMA) and Fractional Brownian motion (FBM). An extensive set of series is generated with a broad range of values of the Hurst exponent H and of the autoregressive, differencing and moving average parameters . A systematic relation between moving average cluster entropy and long-range correlation parameters H, d is observed. This study shows that the characteristic behaviour exhibited by the horizon dependence of the cluster entropy is related to long-range positive correlation in financial markets. Specifically, long range positively correlated ARFIMA processes with differencing parameter , and are consistent with moving average cluster entropy results obtained in time series of DJIA, S&P500 and NASDAQ. The findings clearly point to a variability of price returns, consistently with a price dynamics involving multiple temporal scales and, thus, short- and long-run volatility components. An important aspect of the proposed approach is the ability to capture detailed horizon dependence over relatively short horizons (one to twelve months) and thus its relevance to define risk analysis indices.

A new hybrid model for forecasting Brent crude oil price

Received a plethora of attention by both practitioners and researchers, oil price forecasting remains a challenging issue due to the particular characteristics of oil price and its prodigious impact on various economic sectors. Motivated by this issue, the authors aim to introduce a robust hybrid model for reliable forecasting of Brent oil price. For this purpose, the Adaptive Neuro Fuzzy Inference System (ANFIS), Autoregressive Fractionally Integrated Moving Average (ARFIMA), and Markov-switching models are employed in the proposed hybrid model. The cardinal merit of this hybridization lies in the fact that the constituent models are capable of capturing particular features like nonlinearity, lag, and market interrelationships existing in oil price time series. Then, specific weights are assigned to each model to achieve an accurate prediction of the empirical time series. Three weighting scenarios, namely equal weights, error-value-based weights, and genetic algorithm weighting function, are applied. The authors use root mean square error, mean absolute error, and mean absolute percentage error to measure errors. Robustness of results and prediction quality of the hybrid model compared with counterparts are also investigated by Diebold-Mariano test. Finally, numerical results reveal that the hybrid model weighted by genetic algorithm generally outperforms the constituent models, hybrid model with equal weights, and hybrid model weighted based on the error values. Reliable forecasting of crude oil prices is especially beneficial to producer and importer nations to optimize their production and order rates and mitigate the adverse effect of possible shocks.