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This paper investigates five different Auto Regressive Moving Average (ARMA) and Generalized Auto Regressive Condition-al Heteroscedacity (GARCH models (GARCH, exponential GARCH or EGARCH, integrated GARCH or IGARCH, Component GARCH or CGARCH and the Glosten-Jagannathan-Runkle GARCH or GJR-GARCH) along with six distributions (normal, Student's t, GED and their skewed forms), which are used to estimate the price dynamics of the Bulgarian stock index SOFIX. We use the best model to predict how much time it will take, after the latest crisis, for the SOFIX index to reach its historical peak once again. The empirical data cover the period between the years 2000 and 2024, including the 2008 financial crisis and the COVID-19 pandemic. The purpose is to answer which of the five models is the best at analysing the SOFIX price and which distribution is most appropriate. The results, based on the BIC and AIC, show that the ARMA(1,1)-CGARCH(1,1) specification with the Student's t-distribution is preferred for modelling. From the results obtained, we can confirm that the CGARCH model specification supports a more appropriate description of SOFIX volatility than a simple GARCH model. We find that long-term shocks have a more persistent impact on volatility than the effect of short-term shocks. Furthermore, for the same magnitude, negative shocks to SOFIX prices have a more significant impact on volatility than positive shocks. According to the results, when predicting future values of SOFIX, it is necessary to include both a first-order autoregressive component and a first-order moving average in the mean equation. With the help of 5000 simulations, it is estimated that the chances of SOFIX reaching its historical peak value of 1976.73 (08.10.2007) are higher than 90% at 13.08.2087. [ABSTRACT FROM AUTHOR]

AbstractThis article evaluates the asymmetric impact of exchange rate volatility on the exports of nine ECOWAS countries to the Eurozone. By comparing Autoregressive Distributed Lag (ARDL) and Nonlinear ARDL (NARDL) models, the study concludes that the effect of volatility on ECOWAS-Eurozone exports (EEE) is asymmetric. The study also investigates the impact of foreign income and prices on the EEE and categorises the goods and services that make up the EEE for each country based on their coefficients. The results show that exchange rate volatility has an asymmetric effect on the EEE, which comprise both substitute and inferior goods. The study recommends that ECOWAS authorities avoid using proportional policies to address increased and decreased volatility, as their impact on trade is asymmetric. The long-run coefficients of income for Nigeria, Togo, and Benin are -1.29, -4.67, and -2.64 respectively, indicating that their exports are dominated by inferior goods. The long-run coefficients of foreign price for Nigeria, Niger, and Burkina Faso are 5.32, 7.87, and 1.91 respectively, suggesting that their exports are mainly substitute goods. The authors confirm long-run asymmetry for three out of nine countries and short-run asymmetry for five countries. Only three countries have an asymmetric trade-volatility relationship in both the short and long run. The study suggests that Nigeria, Togo, and Benin diversify their economies, as their exports to the Eurozone are dominated by inferior goods and services. Additionally, the study recommends that the governments of Nigeria, Niger, and Burkina Faso provide support, as their goods and services are substitutes.

This article evaluates the asymmetric impact of exchange rate volatility on the exports of nine ECOWAS countries to the Eurozone. By comparing Autoregressive Distributed Lag (ARDL) and Nonlinear ARDL (NARDL) models, the study concludes that the effect of volatility on ECOWAS-Eurozone exports (EEE) is asymmetric. The study also investigates the impact of foreign income and prices on the EEE and categorises the goods and services that make up the EEE for each country based on their coefficients. The results show that exchange rate volatility has an asymmetric effect on the EEE, which comprise both substitute and inferior goods. The study recommends that ECOWAS authorities avoid using proportional policies to address increased and decreased volatility, as their impact on trade is asymmetric. The long-run coefficients of income for Nigeria, Togo, and Benin are -1.29, -4.67, and -2.64 respectively, indicating that their exports are dominated by inferior goods. The long-run coefficients of foreign price for Nigeria, Niger, and Burkina Faso are 5.32, 7.87, and 1.91 respectively, suggesting that their exports are mainly substitute goods. The authors confirm long-run asymmetry for three out of nine countries and short-run asymmetry for five countries. Only three countries have an asymmetric trade-volatility relationship in both the short and long run. The study suggests that Nigeria, Togo, and Benin diversify their economies, as their exports to the Eurozone are dominated by inferior goods and services. Additionally, the study recommends that the governments of Nigeria, Niger, and Burkina Faso provide support, as their goods and services are substitutes. [ABSTRACT FROM AUTHOR]

We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against the alternative that there is an 'abnormal' period with changed parameter values. During this period, the parameter-value change may lead to an integrated or mildly explosive behaviour of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double-supreme test for the existence of breaks, and then provide an algorithm to identify the periods of changes. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the quasi-maximum likelihood estimation in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian process. Simulations in the Appendix show that the test has good size and power for reasonably long time series. We apply the test to the conventional early-warning indicators of both the financial market and a representative of the emerging Fintech market, i.e., the Bitcoin returns. [ABSTRACT FROM AUTHOR]

In this study, the RiskMetrics method is used to estimate Value at Risk for two exchange rates: BitCoin/dollar and the South African Rand/dollar. Value at Risk is used to compare the riskiness of the two currencies. This is to help South Africans and investors understand the risk they are taking by converting their savings/investments to BitCoin instead of the South African currency, the Rand. The Maximum Likelihood Estimation method is used to estimate the parameters of the models. Seven statistical error distributions, namely Normal Distribution, skewed Normal Distribution, Student’s T-Distribution, skewed Student’s T-Distribution, Generalized Error Distribution, skewed Generalized Error Distribution, and the Generalized Hyperbolic Distributions, were considered when modelling and estimating model parameters. Value at Risk estimates suggest that the BitCoin/dollar return averaging 0.035 and 0.055 per dollar invested at 95% and 99%, respectively, is riskier than the Rand/dollar return averaging 0.012 and 0.019 per dollar invested at 95% and 99%, respectively. Using the Kupiec test, RiskMetrics with Generalized Error Distribution (p > 0.07) and skewed Generalized Error Distribution (p > 0.62) gave the best fitting model in the estimation of Value at Risk for BitCoin/dollar and Rand/dollar, respectively. The RiskMetrics approach seems to perform better at higher than lower confidence levels, as evidenced by higher p-values from backtesting using the Kupiec test at 99% than at 95% levels of significance. These findings are also helpful for risk managers in estimating adequate risk-based capital requirements for the two currencies.

In this work, we study the famous model of volatility; called model of conditional heteroscedastic autoregressive with mixed memory MMGARCH for modeling nonlinear time series. The MMGARCH model has two mixing components, one is a GARCH short memory and the other is GARCH long memory. the main objective of this search for finds the best model between mixtures of the models we made (long memory with long memory, short memory with short memory and short memory with long memory) Also, the existence of its stationary solution is discussed. The Monte Carlo experiments demonstrate we discovered theoretical. In addition, the empirical application of the MMGARCH model (1, 1) to the daily index DOW and NASDAQ illustrates its capabilities; we find that for the mixture between APARCH and EGARCH is superior to any other model tested because it produces the smallest errors. [ABSTRACT FROM AUTHOR]

The purpose of this study is to measure the food price volatility for sixteen food commodities [beef, chicken, pulse mash, pulse moong, pulse masoor, rice iri, wheat, tomato, potato, onion, ginger, garlic, milk, egg, sugar and tea] for fourteen main cities of Pakistan [Bahawalpur, Faisalabad, Hyderabad, Islamabad, Karachi, Khuzdar, Lahore, Multan, Peshawar, Quetta, Rawalpindi, Sargodha, Sialkot and Sukkur]. Furthermore, to provide comparative analyses of volatilities among different cities GARCH (1,1), I GARCH (1,1) and standard deviation techniques are employed on the monthly food price data for the period July 2002 to June 2016 collected from various issues of Pakistan Bureau of Statistics for fourteen cities. The results elaborate that volatility is exist in the series of food prices with strong heterogeneity among cities. It is suggested that the government should develop a mechanism to keep a check on the variation in prices and design separate policies for each city according to the volatility in the prices of food commodities in that city.

The purpose of this study is to measure the food price volatility for sixteen food commodities [beef, chicken, pulse mash, pulse moong, pulse masoor, rice iri, wheat, tomato, potato, onion, ginger, garlic, milk, egg, sugar and tea] for fourteen main cities of Pakistan [Bahawalpur, Faisalabad, Hyderabad, Islamabad, Karachi, Khuzdar, Lahore, Multan, Peshawar, Quetta, Rawalpindi, Sargodha, Sialkot and Sukkur]. Furthermore, to provide comparative analyses of volatilities among different cities GARCH (1,1), I GARCH (1,1) and standard deviation techniques are employed on the monthly food price data for the period July 2002 to June 2016 collected from various issues of Pakistan Bureau of Statistics for fourteen cities. The results elaborate that volatility is exist in the series of food prices with strong heterogeneity among cities. It is suggested that the government should develop a mechanism to keep a check on the variation in prices and design separate policies for each city according to the volatility in the prices of food commodities in that city. [ABSTRACT FROM AUTHOR]

El precio de la energía en bolsa es uno de los commodities con más volatilidad en mercados mundiales, lo que convierte su estimación en un reto, debido a los diferentes factores intervinientes: composición del parque generador, clima, precios del petróleo, correlación entre demanda de energía y el pib, entre otros, lo que provoca una volatilidad del precio en bolsa. El objetivo de este artículo es mostrar el modelo arima con igarch que mejor pronostique el precio de la energía en Colombia. Se concluye que si las variables estudiadas presentan estas características: comportamientos bruscos en periodos cortos, asimetría en distribución y no cumple con supuestos de estacionariedad, es preferible aplicar los modelos arch, garch y sus diferentes derivaciones por cubrir mejor la heterocedasticidad.

This paper uses an unobserved component model with heteroskedastic disturbances based on Harvey et al. (1992) to measure the time-varying importance of permanent and transitory components in the U.S. house prices. Our findings show that the cyclical component in the U.S. housing market is highly persistent and house prices were more than 20% above the trend at the peak of the housing boom in 2006. Our results also suggest that there was a big increase in the relative importance of the transitory shock variance at the peak of the housing crisis. [ABSTRACT FROM AUTHOR]

Abstract: This paper examines the long memory property in the conditional variance of the G7’s major stock market indices, using the FIGARCH model. The GARCH and IGARCH frameworks are also estimated for comparative purposes. To this end, a dataset encompassing the daily returns of the S&P/TSX 60, CAC 40, DAX 30, MIB 30, NIKKEI 225, FTSE 100 and S&P 500 indices from January 4th 1999 to January 21st 2009 is employed. Our results show evidence of long memory in the conditional variance, which is more pronounced for DAX 30, MIB 30 and CAC 40. However, NIKKEI 225 is found to be the less persistent. This may be explained by the fact that smaller markets, like DAX 30, are less liquid, less efficient, and more prone to experiencing correlated fluctuations and, therefore, more susceptible to being influenced by aggressive investors. On the other hand, bigger markets tend to exhibit lower correlations, thus favoring lower persistence levels. Finally, we use the log likelihood, Schwarz and Akaike Information Criteria to discriminate between models and found that FIGARCH is the most suitable model to capture the persistence. [Copyright &y& Elsevier]

Existen diferentes métodos para la medición del agrupamiento de la volatilidad en las series financieras, en las cuales el supuesto sobre la distribución del error determina la estructura de la función de log verosimilitud. En este documento se explota la flexibilidad de los modelos ARCH para capturar los agrupamientos de la volatilidad de la Tasa Representativa del Mercado TRM colombiana. Los resultados indican que el modelo MA (1) en media y el modelo GARCH (1, 1) en varianza superan otro tipo de especificación, que trate de medir el agrupamiento de la volatilidad de la TRM colombiana.

This article analyzes the relationship between co-persistence and hedging, which indicates that the co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persistence with dynamic hedging which can enhance the hedging effectiveness and reduce the persistence of the hedged portfolio. Finally, our strategy is illustrated to study the hedge of JIASHI300 index and HS300 stock index future. [ABSTRACT FROM AUTHOR]

This article investigates the problem of testing for a unit root in the case that the error, { u t}, of the model is a strictly stationary, mixing process with just barely infinite variance. Such errors have the property that for every δ such that 0 ≤ δ < 2, the moments E| u t| δ are finite. Under some additional restrictions on the rate of decay of the mixing rates, these errors belong to the domain of the non-normal attraction of the normal law and obey the invariance principle. This in turn implies that there might be conditions under which the usual Phillips-type test statistics for unit roots may still converge to the corresponding Dickey–Fuller distributions. In such a case, the unit-root hypothesis can be tested within an infinite-variance framework without any modifications to either the tests themselves or the critical values employed. This article derives a necessary and sufficient condition for convergence of the standard test statistics to the Dickey–Fuller distributions. By means of Monte Carlo simulations, the article also shows that this condition is likely to hold in the case that { u t} is a serially correlated, integrated generalized autoregressive conditionally heteroskedastic (IGARCH) process and the standard unit-root tests work well. [ABSTRACT FROM AUTHOR]