Modelling the persistence of conditional variances

In highly volatile market conditions it's always difficult to predict returns using heteroscedastic Garch models. This paper tries to investigate the impact of sample data inputs over forecast using nested conditional mean ARMAX(2,2,0) and conditional variance Garch(1,1), Gjr-garch(1,1) and Egarch(1,1) models. Research also tries to indentify relationship between outcome of formal hypothesis tests, the Ljung-Box-Pierce Q-test and Engle's ARCH test, sample input and forecast results. Study is conducted over two diversified stock markets index of America (NASDAQ Composite) and Asia (Nikkei 225). Returns are forecasted for the volatile month of aug-08 using sample inputs of last one month, two months up to seven months before aug-08 and a complete year before inputi.e from 1-aug-07 to 31-jul-08 of 246 trading days has also been taken. Graphical and correlative comparison of forecasted and observed returns is also done to identify any trend followed by Garch models in relation to size of sample inputs and forecast. Results show that forecast of mean of returns is far more accurate with Nikkei as compared to Nasdaq.

Autoregressive Conditional Skewness

To be utilized in the smart charging of plug-in electric vehicles, this paper proposes semiparametric conditional mean and variance models for the daily density forecasting of the electricity load. The mean is modeled by means of an autoregressive moving average model with exogenous inputs (ARMAX), whereas several options for the variance evolution are investigated, starting with modeling the variance as a power of the conditional mean, then as a piecewise constant function, and finally as a generalized autoregressive conditional heteroskedasticity (GARCH) model. Due to the possible non-Gaussianity of the distribution of the stochastic components, a quasi-maximum likelihood estimation (QMLE) with the Pearson type IV (P-IV) distribution is also considered, apart from the estimation with the Gaussianity assumption. Moreover, the daily density forecasts are generated in a non-parametric manner by propagating samples from the stochastic components iteratively through the available model. These strategies, involving different options for variance modeling and estimation, are compared in terms of their forecast performances on two representative phase currents from the low voltage cables of medium-to-low voltage transformers in the Netherlands. The results indicate that the QMLE with the Gaussianity assumption performs better due to the additional complexity of the P-IV distribution on estimation. Concerning the variance models, the piecewise constant and GARCH models are more preferable when processing phase currents exhibiting only daily seasonality, and the model as a power of the conditional mean outperforms the others if both daily and weekly seasonality and hence more complexity is present.

This paper introduces the new FITVGARCH model to describe both long memory and structural change behaviour in the volatility process by allowing for time varying dynamic structure in the conditional variance. The parameters of the conditional variance in the FIGARCH model are allowed to change smoothly over time. We derive an LM-type test for parameter constancy of the FIGARCH model against the alternative of time dependent parameters. Simulation analysis shows that both empirical size and power of the constancy test are quite good. An empirical application to the stock market volatility indicates that this new class of model seems to outperform the FIGARCH model in the description of the daily NASDAQ composite index returns.

PurposeThe purpose of this paper is to deal with the different phases of volatility behavior and the dependence of the variability of the time series on its own past, models allowing for heteroscedasticity like autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), or regime‐switching models have been suggested by reserachers. Both types of models are widely used in practice.Design/methodology/approachBoth regime‐switching models and GARCH are used in this paper to model and explain the behavior of crude oil prices in order to forecast their volatility. In regime‐switching models, the oil return volatility has a dynamic process whose mean is subject to shifts, which is governed by a two‐state first‐order Markov process.FindingsThe GARCH models are found to be very useful in modeling a unique stochastic process with conditional variance; regime‐switching models have the advantage of dividing the observed stochastic behavior of a time series into several separate phases with different underlying stochastic processes.Originality/valueThe regime‐switching models show similar goodness‐of‐fit result to GARCH modeling, while has the advantage of capturing major events affecting the oil market. Daily data of crude oil prices are used from NYMEX Crude Oil market for the period 13 February 2006 up to 21 July 2009.

Quasi score-driven models

This paper attempts to model and forecast the sugar prices volatility in the India using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Various types of GARCH models for instance; GARCH (1, 1), EGARCH(1, 1)were applied to sugar the period 1995–2015; to test the hypothesis of persistence, asymmetry and volatility of the spot and futuresprices. It is found that, the sum of ARCH and GARCH coefficients is not close to one, indicating that volatility shocks is not quite persistent, moreover volatility, in addition none of sugar spot and futures prices has an impact of bad news on the price volatility, while lastly leverage effect is not present on the conditional variance. Therefore (GARCH) models are appropriate in modeling and forecasting sugar prices volatility.

Even though the Standard Model (SM) is weakly coupled at the Fermi scale, a new strong dynamics involving its degrees of freedom may conceivably lurk at slightly higher energies, in the multi TeV range. Approximate symmetries provide a structurally robust context where, within the low energy description, the dimensionless SM couplings are weak, while the new strong dynamics manifests itself exclusively through higher-derivative interactions. We present an exhaustive classification of such scenarios in the form of effective field theories, paying special attention to new classes of models where the strong dynamics involves, along with the Higgs boson, the SM gauge bosons and/or the fermions. The IR softness of the new dynamics suppresses its effects at LEP energies, but deviations are in principle detectable at the LHC, even at energies below the threshold for production of new states. Our construction provides the so far unique structurally robust context where to motivate several searches in Higgs physics, diboson production, or WW scattering, which were so far poorly justified. Perhaps surprisingly, the interplay between weak coupling, strong coupling and derivatives, which is controlled by symmetries, can override the naive expansion in operator dimension, providing instances where dimension-8 dominates dimension-6, well within the domain of validity of the low energy effective theory. This result reveals the limitations of an analysis that is both ambitiously general and restricted to dimension-6 operators.

We develop a Bayesian analysis based on two different Jeffreys priors for the Student-t regression model with unknown degrees of freedom. It is typically difficult to estimate the number of degrees of freedom: improper prior distributions may lead to improper posterior distributions, whereas proper prior distributions may dominate the analysis. We show that Bayesian analysis with either of the two considered Jeffreys priors provides a proper posterior distribution. Finally, we show that Bayesian estimators based on Jeffreys analysis compare favourably to other Bayesian estimators based on priors previously proposed in the literature.

Nonlinear GARCH Models for Highly Persistent Volatility

This study aims to determine whether daily television audience dynamics exhibit statistically significant conditional variance dependence that is systematically overlooked in conventional ARIMA-based broadcasting forecasts and to assess the incremental empirical value of integrating ARIMA with GARCH modeling. Using 1,096 consecutive daily observations (2022–2024) of viewers for a nationally broadcast program, we implement a diagnostic-first framework that jointly evaluates conditional mean and variance processes. Stationarity is confirmed through the Augmented Dickey–Fuller test (ADF = −3.4693, p = 0.0088), and an MA(1) specification is selected for the conditional mean (AIC = 1302.76). Residual diagnostics reveal pronounced ARCH effects (ARCH-LM = 78.4602, p < 0.001), justifying second-moment modeling. Among competing variance specifications, GARCH(2,2) yields the lowest information criterion (AIC = 1060.321) and indicates near-unit volatility persistence (Σα + Σβ = 0.9856), evidencing durable intertemporal uncertainty transmission. Out-of-sample forecast evaluation demonstrates low relative error (MAPE ≈ 1.0%), supporting empirical robustness. Unlike prior ARIMA-centered broadcasting studies that prioritize point accuracy under homoscedastic assumptions, this integration explicitly models volatility clustering as an object of inference, aligning media analytics with established volatility frameworks without overstating cross-domain novelty. The findings show that incorporating conditional variance dynamics provides measurable gains in risk-sensitive forecasting, offering a replicable approach for advertising allocation and scheduling decisions in competitive media environments.

Purpose- The primary purpose of this study is to model Bitcoin price volatility and forecast its future price returns using advanced econometric models such as ARCH and GARCH. The study aims to enhance risk management strategies and support informed investment decisions by addressing the time-varying nature of Bitcoin’s volatility. The research explores the persistence of volatility shocks and the clustering of price movements to provide insights into market dynamics. Methodology- This research examines daily Bitcoin closing prices over the period from January 2020 to October 2024. The data was preprocessed to ensure reliability, including applying logarithmic transformations to standardize the data and eliminate trends. Stationarity tests, such as the Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), and KPSS tests, were conducted to confirm the series' stationarity. The ARCH-LM test was utilized to detect volatility clustering which is essential for validating the use of ARCH and GARCH models. Following this, ARIMA models were employed to define mean equations and GARCH models were used to estimate conditional variance and capture volatility dynamics. The dataset was split into training and validation subsets with data from July to October 2024 reserved for validation. Findings- The findings demonstrate that Bitcoin’s price movements exhibit significant volatility clustering and persistence of shocks which are key characteristics effectively captured by ARCH and GARCH models. These models provide valuable insights into the volatility patterns of Bitcoin, supporting their application in cryptocurrency analysis. Despite their robustness, the models face limitations in precise return forecasting during highly volatile periods, suggesting the need for further refinement or integration with advanced approaches. Conclusion- The research concludes that ARCH and GARCH models are effective tools for understanding and forecasting Bitcoin’s volatility. The study underscores the importance of acknowledging volatility persistence and clustering effects when analyzing cryptocurrency price behavior. However, it also highlights areas for improvement in econometric modelling by including the exploration of hybrid models and the integration of macroeconomic factors to enhance forecasting accuracy. Keywords: Bitcoin, ARCH models, GARCH Models, forecasting, ARIMA models JEL Codes: C58, G10, G12

Is the volatility and non-stationarity of the Atlantic Multidecadal Oscillation (AMO) changing?

As economies become increasingly interconnected, individual economies are at risk of shocks from external uncertainties ranging from fluctuations in climate regulations to geopolitical conflicts and international economic policies.The purpose of the study is to investigate the time-varying correlation between global uncertainties (e. g., global economic policy uncertainty, climate policy uncertainty and geopolitical risk) and economic activity in a developing economy using a dynamic conditional correlation generalized autoregressive conditional heteroskedasticity (GARCH) model.The relevance of the research lies in the increasing interconnectedness of global economies and the subsequent exposure of individual economies to external shocks.The scientific novelty is hinged on the study being among the first to study the relationship in Ghana. Using monthly data for the 2002–2022 period for Ghana, we estimate a multivariate GARCH model.The results of the study indicate that climate policy uncertainty and global economic policy uncertainty are mean reverting, implying that the volatility of the variables decay slowly and persists for a longer time such that the conditional variance will eventually return to its long-term average level after being disturbed by shocks. Global uncertainties over time are strongly negatively correlated with economic activity and produce significant spikes, especially during periods of major world events.The study recommends that policymakers need to consider the prolonged impact of global uncertainties on economic performance when designing economic policies and interventions. The significant spikes during major global events highlight the importance of crisis management and preparedness in maintaining economic stability during periods of heightened uncertainty.

This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which implies that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the UK foreign exchange market experienced a similar pattern of volatility shifts and suffered smaller but longer volatility than the Korean one. The volatility shifts are estimated using a Markov switching GARCH model and a Bayesian method is suggested.Keywords: Bayesian Inference, Markov Switching GARCH Models, Exchange Rate Volatility, Credit CrisisJEL classification: C11, C22, F31(ProQuest: ... denotes formulae omitted.)1. INTRODUCTIONThe Korean foreign exchange market has experienced two crises during the last two decades, as shown in Figure 1. The exchange rate was managed by the government before the Asian financial crisis in 1997-8. The Korean currency, or the won, depreciated sharply during the crisis and showed a trend of appreciating during the next decade. The foreign exchange market suffered from another foreign capital flight during the global credit crisis in 2008-9. Contrary to the case of the 1997-8 crisis, the 2008-9 credit crisis stemmed from the developed economies. However, the credit crisis led many developing countries, including South Korea, to an economic or financial crisis. Many policies were implemented to stabilize the financial and foreign exchange markets in Korea. The Bank of Korea has swiftly lowered the policy rate from 5.25% to 2% for 4 months since October 2008. The government announced the Financial Market Stabilization Measures, which included government warrants of the foreign currency debt of the commercial banks and provision of dollar liquidity to them, on October 19, 2008. The Bank of Korea has also made a 30-billion US dollar swap arrangement with the Federal Reserve on October 30, 2008 and other deals with the People's Bank of China and the Bank of Japan on December 12, 2008. From October 2008 to February 2009, it provided around 30-billion dollar liquidity to financial institutions which had difficulties in overseas fund raising.This paper estimates the volatility of the won-dollar exchange rate during the 2008-9 crisis and investigates what determined the volatility. We find that the volatility increased in September 2008 and decreased in May 2009. The volatility rose gradually for one month and subdued in a similar manner, which suggests that the volatility was not governed by any specific event or government policy. The overall changes in the volatility are similar to the movements of the CDS premium. We also find that the dollar-pound exchange rate experienced a similar pattern of volatility shifts to that of the won-dollar exchange rate. But, the UK foreign exchange market suffered smaller but longer volatility than the Korean one.Since the Autoregressive Conditional Heteroskedastic (ARCH) model was suggested by Engle (1982), the conditional heteroskedastic models have been updated and developed to analyze the volatility of the financial markets. Researchers, including Bollerslev (1986), generalized the ARCH model to GARCH (generalized ARCH) and its variants, such as IGARCH, GARCH-M, and EGARCH. The models are known to describe well the many features of volatility, such as volatility clustering and the leverage effect.1 However, as Schwert (1990) and Engle and Mustaffa (1992) show, the GARCH models imply too much persistence in the conditional variance. To overcome this shortcoming, Cai (1994) and Hamilton and Susmel (1994) incorporate the Markov switching component into the ARCH model. Gray (1996) and Dueker (1997) generalize their model to Markov switching GARCH (hereafter, MS-GARCH) models. …