ARFIMA-FIGARCH Model Research Articles

Modeling Long Memory Volatilities of Nigeria Selected Macro Economic Variables with Arfima and Arfima Figarch

The research delved into analysing the stochastic characteristics of Nigeria's Real GDP, the exchange rate of the Naira to US Dollar, and the inflation rate employing Autoregressive fractionally integrated moving average (ARFIMA) and the Autoregressive Fractionally Integrated Moving Average Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) modelling approach. The ability of the hybrid formation of ARFIMA-FIGARCH model with Nigeria macroeconomic variables in modeling the periodicity of long memory volatilities was examined. ARIMA GARCH method of modeling was also employed in analyzing the volatilities of Nigeria selected macroeconomic variables to enrich the study. The efficiency of ARFIMA, ARFIMA FIGARCH and ARIMA GARCH models were evaluated with the forecast evaluation measurements. Results revealed that ARFIMA FIGARCH and ARIMA GARCH models are more adequate in modeling the Inflation rate and the exchange rate while ARFIMA present more adequacies in modeling the RGDP. This result revealed evidence of high volatilities in Nigeria Inflation and the exchange rate of Naira to US dollar

Risks in Major Cryptocurrency Markets: Modeling the Dual Long Memory Property and Structural Breaks

This study estimates the effects of the dual long memory property and structural breaks on the persistence level of six major cryptocurrency markets. We apply the Bai and Perron structural break test, Inclán and Tiao’s iterated cumulative sum of squares (ICSS) algorithm, and the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model, with different distributions. The results show that long memory and structural breaks characterize the conditional volatility of cryptocurrency markets, confirming our hypothesis that ignoring structural breaks leads to an underestimation of the persistence of volatility modeling. The ARFIMA-FIGARCH model, with structural breaks and a skewed Student-t distribution, fits the cryptocurrency market’s price dynamics well.

A Fractional Integration Analysis on Daily FX Implied Volatility: Long Memory Feature and Structural Changes

Purpose - The purpose of this paper is to analyze the dynamic factors of the daily FX implied volatility based on the fractional integration methods focusing on long memory feature and structural changes. Design/methodology/approach - This paper uses the daily FX implied volatility data of the EUR-USD and the JPY-USD exchange rates. For the fractional integration analysis, this paper first applies the basic ARFIMA-FIGARCH model and the Local Whittle method to explore the long memory feature in the implied volatility series. Then, this paper employs the Adaptive-ARFIMA-Adaptive-FIGARCH model with a flexible Fourier form to allow for the structural changes with the long memory feature in the implied volatility series. Findings - This paper finds statistical evidence of the long memory feature in the first two moments of the implied volatility series. And, this paper shows that the structural changes appear to be an important factor and that neglecting the structural changes may lead to an upward bias in the long memory feature of the implied volatility series. Research implications or Originality - The implied volatility has widely been believed to be the market’s best forecast regarding the future volatility in FX markets, and modeling the evolution of the implied volatility is quite important as it has clear implications for the behavior of the exchange rates in FX markets. The Adaptive-ARFIMA-Adaptive-FIGARCH model could be an excellent description for the FX implied volatility series

Do bitcoin and precious metals do any good together? An extreme dependence and risk spillover analysis

The speculative nature of Bitcoin over the last 5 years documents high returns for investors and can also provide optimal returns with a good mix of some assets with hedging abilities. We analyze extreme dependence and risk spillover between Bitcoin and a sample of precious metal commodities comprising of gold, silver, copper, wheat, platinum and palladium over a sample period of April 2013–January 2018 based on daily data. We test the long memory properties of our sampled assets using ARFIMA-FIGARCH model followed by followed by time varying copula framework. Later we use VaR, CoVaR and ΔCoVaR tests to measure risk spillover and resulting asymmetries. Our results contribute towards the existing literature by reporting the hedging ability of gold for Bitcoin and the effect that have on precious metal returns. In this way our results provide insights in both the direction. Our results also document spillover from Bitcoin to precious metal market however in terms of directional spillover from precious metals to Bitcoin, silver remains insensitive to any downside risk spillover. We also report asymmetries in upside and downside ΔCoVaR values, suggesting that extreme changes in returns in either of the market has the potential to affect extreme returns in the other market. Our results have implications for individual investor and fund managers in formulating an optimal portfolio yielding returns with hedge against extreme downward price movements.

Stock Returns and Long-Range Dependence

This study throws more light on the long memory behaviour of stock returns on the Ghana stock Exchange (GSE). The researchers examined the long memory of stock returns and volatility prioritizing the weak form efficiency of the Efficient Market Hypothesis. The estimates employed are based on the daily closing prices of seven stocks on the Ghana Stock Exchange. The results of the ARFIMA-FIGARCH model suggest that the stock returns are characterized by a predictable component; this demonstrates a complete departure from the Efficient Market Hypothesis suggesting that relevant market information was only partially reflected in the changes in stock prices. This pattern of time dependence in stock returns may allow for past information to be used to improve the predictability of future returns.

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.

Long memory mean and volatility models of platinum and palladium price return series under heavy tailed distributions

South Africa is a cornucopia of the platinum group metals particularly platinum and palladium. These metals have many unique physical and chemical characteristics which render them indispensable to technology and industry, the markets and the medical field. In this paper we carry out a holistic investigation on long memory (LM), structural breaks and stylized facts in platinum and palladium return and volatility series. To investigate LM we employed a wide range of methods based on time domain, Fourier and wavelet based techniques while we attend to the dual LM phenomenon using ARFIMA–FIGARCH type models, namely FIGARCH, ARFIMA–FIEGARCH, ARFIMA–FIAPARCH and ARFIMA–HYGARCH models. Our results suggests that platinum and palladium returns are mean reverting while volatility exhibited strong LM. Using the Akaike information criterion (AIC) the ARFIMA–FIAPARCH model under the Student distribution was adjudged to be the best model in the case of platinum returns although the ARCH-effect was slightly significant while using the Schwarz information criterion (SIC) the ARFIMA–FIAPARCH under the Normal Distribution outperforms all the other models. Further, the ARFIMA–FIEGARCH under the Skewed Student distribution model and ARFIMA–HYGARCH under the Normal distribution models were able to capture the ARCH-effect. In the case of palladium based on both the AIC and SIC, the ARFIMA–FIAPARCH under the GED distribution model is selected although the ARCH-effect was slightly significant. Also, ARFIMA–FIEGARCH under the GED and ARFIMA–HYGARCH under the normal distribution models were able to capture the ARCH-effect. The best models with respect to prediction excluded the ARFIMA–FIGARCH model and were dominated by the ARFIMA–FIAPARCH model under Non-normal error distributions indicating the importance of asymmetry and heavy tailed error distributions.

Estimating Long Memory Volatility Using High-Frequency Data of Asian Stock Markets

This article analyzed the presence of long memory in volatility in 5 Asian equity indices namely SENSEX, CNIA, NIKKEI225, KO11 and FTSTI, using 5 minutes intraday return series ranging from 05-jan-2015 to 06-Aug-2015. The study employed ARFIMA-FIGARCH model and ARFIMA-APARCH model and compared them with GARCH (1,1) model and APARACH(1,1) in terms of in-sample forecast accuracy. The results confirmed the presence of long memory in both the return and volatility series for all the five markets under study. Among the group, CNIA and STI showed most persistence in both the return and conditional volatility. In terms of forecast measures, the long-memory GARCH models were found to be performing better compared to the short-memory GARCH models.

Arfima-Figarch vs. Arfima-Hygarch: Case Study ETF Returns of Emerging Asian Countries

This research investigate the long memory returns for ETF returns index of seven Asian countries in Emerging Markets Equities during 2008-2013 periods. Those ETFs are Wisdom Tree Indian Rupee Fund (ICN), Market Vectors Indonesia Index (IDX), iShares MSCI Malaysia Index Fund (EWM), Market Vectors Russia ETF (RSX), and iShares MSCI Thailand Investable Market Index Fund (THD), SPDR S&P China ETF (GXC), and Market Vectors Vietnam ETF (VNM). The ARFIMA, ARFIMA-FIGARCH, and ARFIMA-HYGARCH models were estimated. The empirical results of log-likelihood information criterion analyses, the statistics supports ARFIMA-HYGARCH model instead of ARFIMA and ARFIMA-FIGARCH models.

Long memory and structural breaks in the returns and volatility of gold: evidence from Turkey

This article examines the long-memory properties and structural breaks in spot and futures gold returns and volatility in Turkey. The data cover the period from 2008 through 2013 in which gold prices hit an all-time high. ARFIMA–FIGARCH model provides evidence of dual long memory in spot series and a lack of long-memory property in futures returns. Anti-persistence in spot returns is indicative of an overreaction of gold prices to new information, thus disconfirming the weak form of market efficiency. The findings further provide evidence of one structural break, which is associated with correction in the gold prices during the post-global financial crisis. The analyses suggest that the long memory is true, not spurious. This implies that long memory is a feature of the data instead of an outcome of structural changes.

Long Memory and Structural Breaks in the Returns and Volatility of Gold: Evidence from Turkey

This paper examines the long memory properties and structural breaks in spot and futures gold returns and volatility in Turkey. The data covers the period from 2008 through 2013 in which gold prices hit an all-time high. ARFIMA-FIGARCH model provides evidence of anti-persistence in spot returns and a lack of long memory property in futures returns. Anti-persistence is indicative of an overreaction of gold prices to new information, thus, disconfirming the weak form of market efficiency. The findings further provide evidence of one structural break, which is associated with correction in the gold prices during the post-global financial crisis. The analysis suggests that the long memory is true, not spurious. This implies that long memory is a feature of the data instead of an outcome of structural changes.

Modelling and forecasting value at risk and expected shortfall for GCC stock markets: Do long memory, structural breaks, asymmetry, and fat-tails matter?

This paper addresses the question whether dual long memory (LM), asymmetry and structural breaks in stock market returns matter when forecasting the value at risk (VaR) and expected shortfall (ES) for short and long trading positions. We answer this question for the Gulf Cooperation Council (GCC) stock markets. Empirically, we test the occurrence of structural breaks in the GCC return data using the Inclan and Tiao (1994)’s algorithm and we check the relevance of LM using Shimotsu (2006) procedure before estimating the ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with different innovations’ distributions and computing VaR and ES. Our results show that all the GCC market's volatilities exhibit significant structural breaks matching mainly with the 2008–2009 global financial crises and the Arab spring. Also, they are governed by LM process either in the mean or in the conditional variance which cannot be due to the occurrence of structural breaks. Furthermore, the forecasting ability analysis shows that the FIAPARCH model under skewed Student-t distribution turn out to improve substantially the VaR and the ES forecasts.

Value-at-risk and expected shortfall: a dual long memory framework

In this article, we use the dual long memory properties to assess the value-at-risk and expected shortfall for the Argentinean stock market under both short and long daily trading positions. We attempt to show whether considering for long memory properties in both, the returns and volatility, volatility asymmetry and fat-tails could provide more accurate value-at-risk’s and expected shortfall’s estimations. For this purpose, the joint ARFIMA-FIGARCH, ARFIMA-HYGARCH and ARFIMA-FIAPARCH models are applied to the MERVAL stock price index under normal, student-t and skewed student-t distributed innovations. We show that the skewed student-t-ARFIMA-FIAPARCH model performs better in predicting the in-sample and out-of-sample one-step ahead value-at-risk and expected shortfall for both short and long trading positions.

Structural breaks and long memory in modeling and forecasting volatility of foreign exchange markets of oil exporters: The importance of scheduled and unscheduled news announcements

This paper analyzes the dual long memory properties of four major foreign exchange markets of the world oil exporter Saudi Arabia, using the ARFIMA–FIGARCH model under several global events. It discerns the impacts of both scheduled and unscheduled news announcements and structural changes on changing persistence. The results show little evidence of long memory in the conditional mean but provide strong support for long memory in conditional volatility for the four Saudi exchange rates versus major currencies. Moreover, scheduled news announcements have no significant impact on both expectations and volatility, while unscheduled news announcements demonstrate significant effects on the conditional volatility for all exchange rates. Furthermore, we detect at least five structural changes for the exchange rate with the yen and four for the rest of the exchange rates. The structural breaks seem to have greater impacts on changing persistence, and that the ARFIMA–FIGARCH model coupled with the dummy variables of the unscheduled news announcements and the structural changes is the most suitable for examining the long memory processes of these foreign exchange markets in in-sample. Finally, the out-of-sample forecasts provide mixed results and indicate that none of the specifications of the volatility model is appropriate for analyzing the LM dynamics in the Saudi Arabian exchange market. Overall, our results have implications for portfolio managers and policy makers in oil-producing countries.

Dual Long Memory Properties with Skewed and Fat-Tail Distribution

This paper examines the long memory properties in both the returns and volatility of Korean stock prices. For this purpose, the ARFIMA-FIGARCH model was applied to the daily KOSPI and KOSDAQ return series. In the data analysis, the ARFIMA-FIGARCH model establishes the robustness of long memory results, although the presence of long memory is questionable in the returns of two daily indices. In addition, the assumption of non-normality is appropriate for capturing the asymmetry and tail fatness of estimated residuals. These findings suggest that the model based on the Gaussian normality assumption may be inappropriate for modeling the long memory property. Finally, the presence of long memory in the Korean stock market is not spurious as a result of market structural changes.

Modeling and forecasting the volatility of petroleum futures prices

We investigate volatility models and their forecasting abilities for three types of petroleum futures contracts traded on the New York Mercantile Exchange (West Texas Intermediate crude oil, heating oil #2, and unleaded gasoline) and suggest some stylized facts about the volatility of these futures markets, particularly in regard to volatility persistence (or long-memory properties). In this context, we examine the persistence of market returns and volatility simultaneously using the following ARFIMA–GARCH-class models: ARIMA–GARCH, ARFIMA–GARCH, ARFIMA–IGARCH, and ARFIMA–FIGARCH. Although the ARFIMA–FIGARCH model better captures long-memory properties of returns and volatility, the out-of-sample analysis indicates no unique model for all three types of petroleum futures contracts, suggesting that investors should be careful when measuring and forecasting the volatility (risk) of petroleum futures markets.

Long memory and structural breaks in modeling the return and volatility dynamics of precious metals

Abstract We investigate the potential of structural changes and long memory (LM) properties in returns and volatility of the four major precious metal commodities traded on the COMEX markets (gold, silver, platinum and palladium). Broadly speaking, a random variable is said to exhibit long memory behavior if its autocorrelation function is not integrable, while structural changes can induce sudden and significant shifts in the time-series behavior of that variable. The results from implementing several parametric and semiparametric methods indicate strong evidence of long range dependence in the daily conditional return and volatility processes for the precious metals. Moreover, for most of the precious metals considered, this dual long memory is found to be adequately captured by an ARFIMA–FIGARCH model, which also provides better out-of-sample forecast accuracy than several popular volatility models. Finally, evidence shows that conditional volatility of precious metals is better explained by long memory than by structural breaks.

Modelling heavy tails and double long memory in North African stock market returns

Modelling heavy tails and double long memory in stock returns is very important for financial asset pricing, asset allocation and risk management. In this paper, we demonstrate that an α-stable distribution is better fitted to the North African stock return data in TUNINDEX (Tunisia), MASI (Morocco) and EGX30 (Egypt) than the normal distribution. The empirical results show that the asymmetric leptokurtic features presented in these markets can be captured by an α-stable distribution. Moreover, estimation of the tail index allows us to determine the long-memory behaviour of stock returns. Additionally, this study examines the long-memory property in mean returns and volatility of these markets. The results indicate that long-memory dynamics in the returns and volatility might be modelled by the joint ARFIMA–FIGARCH model. The results of the joint ARFIMA–FIGARCH model show strong evidence of long memory in both returns and volatility. The long memory in returns implies that stock prices follow a predictable behaviour, which is inconsistent with the efficient market hypothesis. The evidence of long memory in volatility, however, shows that uncertainty or risk is an important determinant of the behaviour of daily stock data in North African stock markets. The implication of the present work is that the assumption of non-normality provides better specifications regarding the long-memory property.

Long Memory in Eastern European Financial Markets Returns

The paper examines the long memory property of stock returns and its implications using daily index returns for eight CEE emerging markets: Romania, Hungary, Czech Republic, Poland, Slovenia, Bulgaria, Slovakia, and Croatia. Several nonparametric methods for testing for long memory are employed, as well as parametric long memory models. The ARFIMA-FIGARCH model seems the most appropriate specification since the nonlinearity tests can not reject the null of independent and identically distributed residuals, implying that this specification accounts for the nonlinearity in the data. The estimated fractional differencing parameter is statistically significant in seven of the eight emerging economies employed in the study, suggesting the presence of long memory in the returns in these financial markets.

Analyzing the Volatility Transmission on the Eoniaswap Market

Globally, the interest rate swaps have became the most traded financial derivatives on the OTC markets in the last decade. In the Eurozone banking system swap contracts with the Eonia overnight interbank interest rate as underlying asset form the most liquid interbank market. But, the liquidity problems registered on the international markets have increased the volatility of Eoniaswap rates especially after September 2008 and also their spread form the European Central Bank policy rate. Applying long memory tests we have identified a persistent behavior of the Eoniaswap rates at different maturities. Using the Johansen and the Gregory-Hansen cointegration tests we found the existence of long run equilibrium relationships between Eonia and the Eoniaswap rates, that maintain in the presence of structural breaks in the cointegration relationship. Finally, we have estimated ARFIMA-FIGARCH models in order to capture the volatility transmission between Eoniaswap rates at different maturities.