Time-varying Volatility Research Articles

A wavelet analysis of investing in cryptocurrencies in the Indian stock market

PurposeThis study is designed to examine the dynamic interrelationships between four cryptocurrencies (Bitcoin, Ethereum, Dogecoin and Cardano) and the Indian equity market. Additionally, the study seeks to investigate the potential safe haven, hedge and diversification uses of these digital currencies within the Indian equity market.Design/methodology/approachThis study employs the wavelet approach to examine the time-varying volatility of the studied assets and the lead-lag relationship between stocks and cryptocurrencies. The authors execute the entire analysis using daily data from 1st October 2017 to 30th September 2023.FindingsThe result of the study shows that financial distress due to the pandemic and the Russian invasion of Ukraine have a negative effect on the Indian equities and cryptocurrency markets, escalating their price volatility. Also, the connectedness between the returns of stock and digital currency exhibits a strong positive relationship during periods of financial distress. Additionally, cryptocurrencies serve as a tool of diversification or hedging in the Indian equities markets during normal financial circumstances, but they do not serve as a diversifier or safe haven during periods of financial turmoil.Originality/valueThis study contributes to understanding the relationship between the Indian equity market and four cryptocurrencies using wavelet techniques in the time and frequency domains, considering both normal and crisis times. This can offer valuable insights into the potential of cryptocurrencies inside the Indian equities markets, mainly with respect to varying financial conditions and investment horizons.

The estimations of drift parameters for the Gaussian Vasicek process with time-varying volatility

This article mainly considers the parameter estimation problem for the Gaussian Vasicek process defined as d X t = ( α − β X t ) d t + σ t d G t , t≥0 with unknown parameters α∈ℝ and β < 0, where G t is a continuous centered Gaussian process. The volatility parameter σ t is allowed to vary with time t. Based on the time-continuous observations and least squares method, the Least squares estimations of drift parameters for the non ergodic Gaussian Vasicek model with time-varying volatility are obtained. The strong consistency and asymptotic distributions of proposed estimations are verified under some sufficient conditions. Finally, we verify that the results are still valid under different forms of the volatility function when G t is fractional Brownian motion, sub-fractional Brownian motion, and bi-fractional Brownian motion, respectively. In some sense, our results extend the findings of El Machkouri, Es-Sebaiy, and Ouknine (2016) and Es-Sebaiy and Sebaiy (2021).

Exploring Volatility: Evolution, Advancements, Trends, and Applications

Volatility is a fundamental notion in financial markets, influencing investment decisions, risk management techniques, and market dynamics. This paper provides a thorough overview of the historical evolution and practical implications of volatility, focusing on important works and key advancements in the field. The overview begins with early conceptions of volatility and the necessity for measurement prompted by market collapses, then progresses to advanced quantitative models and computer tools. The study includes key innovations such as the Black-Scholes model, which revolutionized options pricing and pioneered the concept of implied volatility. The Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models introduced frameworks for modeling time-varying volatility, paving the way for greater forecasting accuracy. Advancements in computing techniques have made it easier to analyze high-frequency data and estimate realized volatility, providing timely insights into market trends. The review also investigates contemporary trends, such as the use of machine learning algorithms and the issues provided by cryptocurrency marketplaces. Furthermore, the article examines the various characteristics and metrics of volatility, emphasizing its multidimensional nature and diverse uses in risk management, portfolio optimization, derivative pricing, and market analysis. Practical examples show how investors, traders, and financial professionals may use volatility to navigate complex market settings and make sound judgments. Finally, the study highlights the enduring significance of volatility in financial markets and highlights the need for continuing research and analysis to improve our understanding of market behavior. Acknowledging the complexities of volatility prepares market participants with valuable understandings to manage risks effectively and capitalize on market opportunities, thus contributing to financial stability and optimal portfolio performance.

Global impacts of US monetary policy uncertainty shocks

We build a new empirical model, which admits time-varying variances of local structural shocks, to estimate the global impact of an increase in the volatility of US monetary policy shocks. By allowing for rich dynamic interaction between the endogenous variables and time-varying volatility in the global setting, we find that US interest rate uncertainty not only drives local output and inflation volatility, but also causes declines in output, inflation, and the interest rate. Moreover, we document strong global impacts, making the world move in a very synchronous way. Crucially, spillback effects are found to be significant even for the US economy.

Fast estimation of a large TVP-VAR model with score-driven volatilities

This paper proposes a fast approach to estimating a large time-varying parameter vector autoregressive (TVP-VAR) model. Based on a score-driven modeling framework, we first assume that the time-varying variances of random errors in each equation of the TVP-VAR are score-driven, and then propose filtering and smoothing procedures to estimate time-varying parameters and time-varying volatilities. We show that under the forgetting factors, the filtering estimation of time-varying parameters is equivalent to an equation-by-equation estimator, significantly reducing the dimension of state space and thus delivering fast estimation. Moreover, a fast smoothing estimation can be derived, avoiding the inverse of the super-high dimensional state equation covariance matrix. We provide dynamic model averaging (selection) and maximum likelihood estimates for forecasting and inference. Our simulation study shows that the proposed method is more accurate than the popular methods and enjoys tremendous computational gain from the equation-by-equation estimator. Finally, we conduct an empirical study on the dynamic connectedness of global stock markets, demonstrating the merits of our methods in real-time and ex-post analysis.

The Fortune and crash of common risk factors in Chinese commodity markets

This paper investigates the performance of nine commonly discussed market anomalies in the Chinese commodity market. By studying a data sample from 2005 to 2020, we find the common risk factors associated with term structure and momentum anomalies effectively explain the cross-sectional excess returns and generate profitable sorting portfolios. Meanwhile, we empirically demonstrate that the term structure and momentum risk factors significantly crash during periods of high market stress, although they bring overall good outperformance in out-of-sample. We attribute these crashes to high time-varying volatility. Inspired by the augmented momentum crash strategy of Daniel and Moskowitz (2016), we construct augmented term structure and momentum risk factors to improve their performances in the Chinese commodity futures market. The out-of-sample Sharpe ratios of the term structure and momentum risk factors increase from 0.75 to 1.08 and from 0.66 to 0.77, respectively. In particular, both risk factors exhibit over 100% increments in out-of-sample Sharpe ratios during bear markets.

Time-Varying Uncertainty of the Federal Reserve's Output Gap Estimate

AbstractA factor stochastic volatility model estimates the common component to output gap estimates produced by the staff of the Federal Reserve, its time-varying volatility, and time-varying, horizon-specific forecast uncertainty. The output gap estimates are uncertain even well after the fact. Nevertheless, the common component is clearly procyclical, and positive innovations to the common component produce movements in macroeconomic variables consistent with an increase in aggregate demand. Heightened macroeconomic uncertainty, as measured by the common component's volatility, leads to persistently negative economic responses.

Time-varying coefficient DAR model and stability measures for stablecoin prices: An application to Tether

This paper examines the dynamics of Tether, the stablecoin with the largest market capitalization. We show that the distributional and dynamic properties of Tether/USD rates have been evolving between 2017 - 2021. We use local analysis methods to detect local trends and time-varying volatility and persistence. To accommodate these dynamic patterns, we introduce the time-varying parameter Double Autoregressive tvDAR(1) process under the assumption of local stationarity of Tether/USD rates. We also propose a set of simple plug-in measures of stability based on the Lyapunov exponent for assessing and comparing the stability of Tether and other stablecoins. We show the consistency of stability measure estimators and study their distributional properties. The tvDAR model is estimated on Tether prices and compared with other stablecoins. We find that it provides good fit to data with time-varying persistence and volatility and produces reliable out-of-sample forecasts at short horizons. In the application, the proposed stability measures provide reliable indicators of local explosive patterns for stablecoin monitoring.

Re-examining the impact of oil prices on stock returns in the presence of time-varying volatility

Re-examining the impact of oil prices on stock returns in the presence of time-varying volatility

Has the COVID-19 Pandemic Led to a Switch in the Volatility of Biopharmaceutical Companies?

Biopharmaceutical companies are critical in developing vaccines, treatments, and diagnostics for COVID-19. Thus, understanding the contagion effects of their stock market can have important economic implications, especially in the context of global financial markets. Due to the COVID-19 pandemic, biopharmaceutical companies’ stock markets may have experienced sudden volatility and risk changes, which may have had spillover effects on other sectors and markets. Policymakers can take pre-emptive measures to stabilize financial markets. Analyzing the contagion effects makes it even more relevant to analyze the stock market response of four leading pharmaceutical companies that either developed vaccines against COVID-19 or drugs that help to fight the virus, namely, Pfizer, AbbVie Inc., Sanofi, and Bristol Myers Squibb. The analysis considers two periods, before and during the COVID-19 crisis, and considers the influence of the market volatility and technological market index. In order to capture the contagion effects, DCC-GARCH models have been applied, which estimate time-varying correlation coefficients using a multivariate GARCH framework, allowing for the modeling of time-varying volatility and correlations in financial returns. The results reveal the impact of market volatility on the returns of all four pharmaceutical companies. Additionally, a contagion effect between all four companies, the technological market, and market volatility was observed during the COVID-19 period.

Robust Fixed-[formula omitted] Inference in the Presence of Time-Varying Volatility

Time-varying volatility arises in many macroeconomic and financial applications. While “fixed-b” arguments provide refinements in the use of estimators for the asymptotic variance of GMM estimators, the resulting fixed-b distributions of test statistics are not pivotal under time-varying volatility. Three approaches to robustify inference are investigated: (i) wild bootstrapping, (ii) time transformations and (iii) selection of test statistics and critical values according to the outcome of a pretest for heteroskedasticity. Simulations quantify the distortions from using the original fixed-b approach and compare the effectiveness of the proposed corrections. Overall, the wild bootstrap is to be recommended. An empirical application to the Fama & French five factor model illustrates the relevance of the procedures.

Financial and Macroeconomic Data Through the Lens of a Nonlinear Dynamic Factor Model

Through the lens of a nonlinear dynamic factor model, we study the role of exogenous shocks and internal propagation forces in driving the fluctuations of macroeconomic and financial data. The proposed model 1) allows for nonlinear dynamics in the state and measurement equations; 2) can generate asymmetric, state-dependent, and size-dependent responses of observables to shocks; and 3) can produce time-varying volatility and asymmetric tail risks in predictive distributions. We find evidence in favor of nonlinear dynamics in two important U.S. applications. The first uses interest rate data to extract a factor allowing for an effective lower bound and nonlinear dynamics. Our estimated factor coheres well with the historical narrative of monetary policy. We find that allowing for an effective lower bound constraint is crucial. The second recovers a credit cycle. The nonlinear component of the factor boosts credit growth in boom times while hinders its recovery post-crisis. Shocks in a credit crunch period are more amplified and persist for longer compared with shocks during a credit boom.

Analytical Perspective of Trade Volatility Spillover Analysis During COVID Pandemic Times

No one in the world, particularly the economic community, could have predicted the manner in which the 2019 COVID pandemic erupted or shook the economies. Developing countries, particularly South Asian economies and the lower middle income (LMI) countries (India, Pakistan, Sri Lanka, Bangladesh, Bhutan, and Nepal), had also experienced similar turmoil. The COVID outbreak and trade-related risks were closely associated with exports, imports, international liquidity, and SDR exchange rates, posing time-varying risks. In this sphere, an analytical approach to generate meaningful trade-related time-varying volatility predictions with respect to India’s position is critical while considering the above-listed variables. The Markov-switching (endogenous switching) VAR model using the exponential moving average volatility model (EWMA) of the four macroeconomic variables was used. The author tried to use the EWMA volatility model to witness the impact of spillovers and shock persistence. The present study earmarked the behaviour of time-varying trade-related risks (for Regime 1, i.e., the Early COVID period versus Regime-2 during the COVID period) in terms of the top six economies (as per December 2021 data) when endogenous factors like international liquidity and exchange rate shocks are implemented.

Does the day-of-the-week effect exist in other asset classes? Investigation of the globally listed private equity markets

PurposeThis study aims to investigate the day-of-the-week (DoW) effect in globally listed private equity (LPE) markets using daily data covering the period 2004–2021.Design/methodology/approachTo investigate the existence of the DoW effect in globally LPE markets, ordinary least squares regression, generalised autoregressive conditional heteroscedasticity (GARCH) regression and robust regressions are used. In addition, robustness audits are conducted by subdividing the sampling period into two sub-periods: pre-financial and post-financial crisis.FindingsLimited statistically significant evidence is found for the DoW effect. By taking time-varying volatility into account, a statistically significant DoW effect can be observed, indicating that the DoW effect is driven by time-varying volatility. Economic significance is captured through visual inspection of average daily returns, which illustrate that Monday returns are lower than the other weekdays.Practical implicationsThe results have important implications on whether to adopt a DoW strategy for investors in LPE. The findings show that higher returns on selected days of the week for certain indices are possible.Originality/valueTo the best of the author’s knowledge, this paper provides the first study to examine the DoW effect for globally LPE markets by using LPX indices and contributes valuable insights on this growing asset class.

The Usage of Markov Chain Monte Carlo (MCMC) Methods in Time-varying Volatility Models

Abstract Markov Chain Monte Carlo (MCMC) techniques, in the context of Bayesian inference, constitute a practical and effective tool to produce samples from an arbitrary distribution. These algorithms are applied to calculate parameter values of predictive models of the phenomenon of varying volatility in data time series. For this purpose, 3 such research models of time-varying volatility are simulated in STAN a probabilistic programming language for statistical inference. The accuracy of these models’ predictive function is confirmed by applying in data time series with known prior values. Moreover, Stan models’ performance is illustrated by the real stock prices of two shares in the stock market of New York. Finally, an Information Criterion of the results is applied to each model as well, to evaluate their predictive ability, comparing and selecting the most effective one. Keywords: MCMC, Time-series, Time-varying volatility models, STAN.

Herding behavior in integrated financial markets: the case of MILA

PurposeIt has been argued in the literature that structural changes in the financial markets, such as integration, have the potential to cause herding behavior or correlated behavioral patterns in traders. The purpose of this study is to investigate whether there is any financial herding behavior in the Latin American Integrated Market (MILA), a transnational stock market composed of Chile, Peru, Colombia and Mexico stock exchanges and whether there is any ARCH or GARCH effect in the herding behavior models.Design/methodology/approachThis study uses the modified return dispersion approach on daily index return data. The sample period is from January 03, 2002 to May 07, 2019. The data are obtained from the MILA database. To count time-varying volatilities in herding models, the authors run ARCH family regression with GARCH (1,1) settings. Hwang and Salmon (2004) model is used as a robustness test.FindingsThe authors found strong herding behavior under the general market conditions and moderate and partial herding behavior under some specified markets circumstances, such as bull and bear markets and high-low volatility states. Moreover, the pre-MILA period exhibits more herding behavior than the post-MILA period. The empirical results show that most of the ARCH and GARCH effects are statistically significant, implying that the past information of stock returns and market volatility significantly affect the volatility of following periods, which can also explain the formation of herding tendency among investors. Finally, the results of the robustness tests (Hwang and Salmon, 2004) confirm herding in all periods, except full sample period for Mexico and post-MILA period for Mexico and Colombia.Research limitations/implicationsThis study investigates the herding behavior in the MILA market in terms of market return, volatility and timing. A limitation of the paper is that the authors have not included other factors on the formation of herding behavior, such as macroeconomic factors, effects of regional or international markets and policy influences. The authors will explore the issue in the extension of the paper.Practical implicationsAs MILA is the first virtual integration of stock exchanges without merging, the study provides useful findings and draws good inferences of herding behavior in the MILA market in terms of market return, volatility and timing which are useful for academics, investors and policymakers in their investment and decision makings.Social implicationsThe paper provides useful findings and draws good inferences of herding behavior in the MILA market in terms of market return, volatility and timing which are not only useful in practical implications, but also in social implications.Originality/valueThis study contributes to the herding literature by examining four different hypotheses in respect of the unique case of transnational stock exchange without fusions or corporate mergers, where each market maintains its independence and regulatory autonomy. The authors also contribute to the literature by including both ARCH and GARCH effects in the herding behavioral models along the Hwang and Salmon (2004) approach.

The Role of Wages in Trend Inflation: Back to the 1980s?

This paper examines whether the measurement of trend inflation can be improved by using wage data in a dynamic factor model of disaggregated prices and wages for the United States. The model features time-varying coefficients and stochastic volatility. An estimate of trend inflation is a time-varying distributed lag of prices and wages, where the weight on a series depends on its time-varying volatility, persistence, and comovement with other series. The results show that wages inform estimates of trend inflation. The weight on wages was highest around 1980, drifted down through the 2000s, and returned to its 1980s value by 2022. In addition, inflation in the 2020s appears to have unmoored moderately from the 2 percent range that prevailed for decades, as the role of the persistent component of inflation increased in recent year. However, accounting for wages lowers the model's view of the increase in the volatility of trend inflation.

Time-varying volatility and the housing market

AbstractThis paper studies the role of stochastic volatility in a setting where housing serves as an important propagation mechanism. After showing time-varying volatility in US house prices, we estimate a dynamic stochastic general equilibrium model with housing, financial frictions, and stochastic volatility using a nonlinear approximation and Bayesian econometric techniques. Incorporating stochastic volatility into the model greatly improves model fit and accounts for approximately half of the increased volatility in house prices observed during the Great Recession. Increased stochastic volatility escalates uncertainty which has significant effects on macroeconomic variables. While uncertainty in most sectors has negative effects on the economy, uncertainty on collateral constraints has the largest role. Unlike other uncertainty shocks, the housing demand uncertainty creates positive spillovers in the economy. Credit conditions, adjustment costs of capital and housing, and monetary policy are important transmission mechanisms for the stochastic volatility shocks.

An ARCH volatility analysis of real GDP, real gross capital formation, and foreign direct investment in Bangladesh

This paper aims to investigate the volatility of the growth rates of Bangladesh's real GDP, real gross capital formation, and net inflows of foreign direct investment. The study used data on these indicators from the World Bank for the period between 1972 and 2020. Autoregressive integrated moving average (ARIMA) and the autoregressive conditional heteroscedastic (ARCH) methods were applied to model the conditional mean and conditional variance components for each growth rate. The validity of the selected volatility models was evaluated using a variety of diagnostic techniques, such as the time series graph of estimated residuals, cumulative periodogram, and the portmanteau test for white noise. The overall performance of the selected models is evaluated using the mean squared error (MSE) and the root mean squared error (RMSE). For all three indicators, the conditional means depend on the growth rates of the previous year or two years, whereas conditional variances depend on the previous year’s rates. The outcomes of the study also indicate the existence of time-varying volatility in Bangladesh's economy. This study may be helpful in understanding the potential risks related to the volatile nature of macroeconomic growth rates.

Testing for explosive bubbles: a review

Abstract This review discusses methods of testing for explosive bubbles in time series. A large number of recently developed testing methods under various assumptions about innovation of errors are covered. The review also considers the methods for dating explosive (bubble) regimes. Special attention is devoted to time-varying volatility in the errors. Moreover, the modelling of possible relationships between time series with explosive regimes is discussed.