CROSS-COUNTRY EVIDENCE ON OUTPUT GROWTH VOLATILITY: NONSTATIONARY VARIANCE AND GARCH MODELS

This paper revisits the issue of conditional volatility in real gross domestic product (GDP) growth rates for Canada, Germany, Italy, Japan, the United Kingdom, and the United States. Previous studies find high persistence in the volatility. This paper shows that this finding largely reflects a nonstationary variance. Output growth in the six countries became noticeably less volatile over the past few decades. In this paper, we employ the modified iterated cumulative sum of squares (ICSS) algorithm to detect structural change in the variance of output growth. One structural break exists in each of the six countries after identifying outliers and mean shifts in the growth rates. We then use generalized autoregressive conditional heteroskedasticity (GARCH) specifications, modeling output growth and its volatility with and without the break in volatility. The evidence shows that the time-varying variance falls sharply in Canada and Japan, and disappears entirely in Germany, Italy, the United Kingdom and the United States, once we incorporate the break in the variance equation of output for the six countries. That is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH model demonstrates misspecification, if researchers neglect a nonstationary variance. Moreover, we also consider the possible effects of our more correct measure of output volatility on output growth as well as the reverse effect of output growth on its volatility. The conditional standard deviation possesses no statistical significance in all countries, except a significant negative effect in Japan. The lagged growth rate of output produces significant negative and positive effects on the conditional variances in Germany and Japan, respectively. No significant effects exist in Canada, Italy, the United Kingdom, and the United States.     

The Efficiency of the Realized Range Measure of Daily Volatility: Evidence from Greece

In this study we estimate and compare the realized range volatility, a novel efficient volatility estimator computed by summing high–low ranges for intra‐day intervals, to the recently popularized realized variance estimator obtained by summing squared intra‐day returns. Our results, derived from a Greek equity high‐frequency data set, show that realized range‐based measures improve upon the corresponding realized variance‐based ones in most cases, especially for the most actively traded stocks. The usefulness of high‐frequency data in measuring and forecasting financial volatility is apparent throughout the paper.     

Real or spurious long memory characteristics of volatility: Empirical evidence from an emerging market

We examine whether real or spurious long memory characteristics of volatility are present in stock market data. We empirically distinguish between true and spurious long memory characteristics by analysing different types and measurements of volatility, utilising different sampling frequencies and evaluating different financial markets. Because it is well known that long memory characteristics observed in data can be generated by either non-stationary structural breaks or slow regime-switching models, we additionally assess how the results of the analyses change during crisis periods by considering the effects of the US subprime mortgage crunch. The results support the presence of long memory characteristics that vary for diverse types and measurements of volatility, different financial markets, and distinct sampling periods, such as the pre-crisis and crisis periods. This result suggests that empirical investigations must be particularly careful in addressing long memory issues.     

Modelling the risk–return relation for the S&P 100: The role of VIX

A significantly positive risk–return relation for the S&P 100 market index is detected if the implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation. This result holds for 4 alternative GARCH specifications, irrespective of the conditional distribution, and regardless of whether the conditional mean equation includes a constant term. This finding is robust to sub-samples, and to using VIX innovations to control for dividend yield and trading volume effects. Monte Carlo evidence suggests that if VIX is not included, the risk–return relation is more likely to be negative or weak, in line with several previous studies. If VIX is included, the distribution of the risk–return parameter has more than 99% of its mass in the area of positive values. We conclude that VIX carries important forward-looking information which improves the precision of the conditional variance estimation and, subsequently, reveals a significantly positive relation.     

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.     

DISCRIMINATING SHORT AND LONG MEMORY IN FINITE SAMPLES USING SENSITIVITY ANALYSIS: AN APPLICATION TO GROWTH CONVERGENCE

The standard linear model where u_t is generated from an ARFIMA process, is considered. The sensitivity of the predictor and sensitivity of variance estimates of the linear model to long memory are investigated by constructing the statistical measures B_L/S and D_L/S , respectively. B_L/S and D_L/S is interpreted as a sensitivity measure for the long‐memory process without the short‐memory effects. As an application, the memory characteristics of per capita GDP of 30 countries are investigated from the Maddison GDP dataset. It is found that per‐capita GDP exhibits long memory characteristics, and the long‐run growth estimates are sensitive to the long memory characteristics.     

Modeling long memory volatility using realized measures of volatility: A realized HAR GARCH model

Long memory is an important feature of the volatility of financial returns. We document that the recently developed Realized GARCH model (Hansen et al., 2012) is insufficient for capturing the long memory of underlying volatility. We develop a parsimonious variant of the Realized GARCH model by introducing the HAR specification of Corsi (2009) into the volatility dynamics. A comparison of the theoretical and sample autocorrelation functions shows that the new model specification better captures the long memory dynamics of volatility. We calculate the multi-period out-of-sample volatility forecasts for several return series and find that the new model is a significant improvement over the classic Realized GARCH model.     

PERSISTENCE IN CONVERGENCE AND CLUB FORMATION

In this paper, we examine the convergence hypothesis using a long memory framework that allows for structural breaks and does not rely on a benchmark country using both univariate and multivariate estimates of the long memory parameter d. Using per capita GDP gaps, we confirm the findings of non‐stationarity and long memory behavior that have been found previously in the literature using univariate tests. However, the support for these findings is much weaker when using a multivariate framework, in which case we find more evidence of stationary behavior. Based on these results, we also investigate club formation, something that would suggest the presence of conditional convergence. We describe a club formation methodology using the sequential testing criteria that we have employed in our analysis as the basis for forming clusters or clubs of countries with similar convergence characteristics.     

Modelling exchange rate volatility with random level shifts

Recent literature has shown that the volatility of exchange rate returns displays long memory features. It has also been shown that if a short memory process is contaminated by level shifts, the estimate of the long memory parameter tends to be upward biased. In this article, we directly estimate a random level shift model to the logarithm of the absolute returns of five exchange rates series, in order to assess whether random level shifts (RLSs) can explain this long memory property. Our results show that there are few level shifts for the five series, but once they are taken into account the long memory property of the series disappears. We also provide out-of-sample forecasting comparisons, which show that, in most cases, the RLS model outperforms popular models in forecasting volatility. We further support our results using a variety of robustness checks.     

Effects of volatility shocks on the dynamic linkages between exchange rate,interest rate and the stock market: The case of Turkey

This study analyzes the dynamic relationship between exchange rate (against US dollar), interest rate and the stock market (both in local currency) of Turkey from January 2003 to September 2013. In particular, the paper tries to answer if the correlations between these important variables change abruptly in high volatile periods and if they do, is this change temporary or permanent? In that manner, we first estimate the dynamic correlations between these variables using the VAR(p)–FIAPARCH(1,d,1)–cDCC(1,1) approach. Then, we endogenously detect the volatility shift dates by a novel method of penalized contrast functions and investigate the relation between the dynamic correlations and the high volatile periods. Results reveal that volatility shocks create abrupt changes in the dynamic correlations, however this effect is only short term and do not sustain between consecutive high volatility regimes. Thus, policymakers and investors do not need to be concerned about long run contagion effects.     

Panel LM unit root tests with level and trend shifts

This paper considers a Lagrange multiplier (LM) based panel unit root test that allows for heterogeneous structural breaks in both the intercepts and slopes of a series. We note that many popular time series variables are likely to exhibit changing means and/or trends over time. Given that the usual tests will depend on the nuisance parameters indicating the locations of the trend breaks, we adopt a transformation procedure that makes our new panel unit root tests invariant to the nuisance parameters. To illustrate the importance of the power gain provided by our test, we examine the convergence hypothesis using relative ratios of per capita health care expenditures in 20 OECD countries. Our results provide evidence that the convergence hypothesis is supported.     

Structural breaks and GARCH models of stock return volatility: The case of South Africa

This paper investigates the empirical relevance of structural breaks in forecasting stock return volatility using both in-sample and out-of-sample tests applied to daily returns of the Johannesburg Stock Exchange (JSE) All Share Index from 07/02/1995 to 08/25/2010. We find evidence of structural breaks in the unconditional variance of the stock returns series over the period, with high levels of persistence and variability in the parameter estimates of the GARCH(1,1) model across the sub-samples defined by the structural breaks. This indicates that structural breaks are empirically relevant to stock return volatility in South Africa. However, based on the out-of-sample forecasting exercise, we find that even though there structural breaks in the volatility, there are no statistical gains from using competing models that explicitly accounts for structural breaks, relative to a GARCH(1,1) model with expanding window. This could be because of the fact that the two identified structural breaks occurred in our out-of-sample, and recursive estimation of the GARCH(1,1) model is perhaps sufficient to account for the effect of the breaks on the parameter estimates. Finally, we highlight that, given the point of the breaks, perhaps what seems more important in South Africa, is accounting for leverage effects, especially in terms of long-horizon forecasting of stock return volatility.     

我国短期利率序列均值过程和波动率过程的长期记忆性测度与检验

我们使用我国1996年1月至2008年6月期间的银行同业拆借利率,对我国利率均值过程及其波动过程的长期记忆性进行测度和检验。利用ARFIMA模型和FIGARCH模型的检验结果说明,我国利率序列的一阶矩中不存在长期记忆性,而二阶矩中存在显著的长期记忆性;进一步运用ARFIMA-FIGARCH模型对利率均值过程及其波动过程的双长期记忆性进行检验时发现,我国利率序列均值过程中不存在明显的长期记忆性,但波动率序列中存在非常显著且较强的长期记忆性特征;通过考虑Student-t分布进一步说明,我国利率序列中明显存在"尖峰厚尾"分布特征。     

Can GARCH-class models capture long memory in WTI crude oil markets?

This paper investigates the issue whether GARCH-type models can well capture the long memory widely existed in the volatility of WTI crude oil returns. In this frame, we model the volatility of spot and futures returns employing several GARCH-class models. Then, using two non-parametric methods, detrended fluctuation analysis (DFA) and rescaled range analysis (R/S), we compare the long memory properties of conditional volatility series obtained from GARCH-class models to that of actual volatility series. Our results show that GARCH-class models can well capture the long memory properties for the time scale larger than a year. However, for the time scale smaller than a year, the GARCH-class models are misspecified.     

Adaptive ARFIMA models with applications to inflation

Many previous analyses of inflation have used either long memory or nonlinear time series models. This paper suggests a simple adaptive modification of the basic ARFIMA model, which uses a flexible Fourier form to allow for a time varying intercept. Simulation evidence suggests that the model provides a good representation of various forms of structural breaks and also that the new model can be efficiently estimated by a QMLE approach. We investigate monthly CPI inflation series for the G7 countries and find evidence of stable long memory parameters across regimes and also of significant nonlinear effects. The estimated adaptive ARFIMA models generally have less persistent long memory parameters than previous studies, with the estimated time dependent intercept being an important component. The model is also supplemented with an adaptive FIGARCH component, yielding a double nonlinear long memory model.     

汇率收益率及其收益波动率存在长记忆性吗?——基于人民币汇率和欧元汇率的经验分析

长记忆性研究一直是金融实证研究的一个热点,但过去多数研究主要集中于资本市场。汇率收益率的长记忆性将影响外汇市场的有效性,汇率收益波动率的长记忆性则可能对汇率风险及汇率未来变化产生作用。基于此,本文选择人民币兑美元汇率、欧元兑美元汇率作为研究对象,运用经典重标极差分析法、重标方差分析法及小波方差分析法分别考察它们的收益率和收益波动率序列的长记忆性。研究结果表明:人民币汇率收益率存在长记忆性,而欧元汇率收益率不存在长记忆性;两种汇率收益波动率都存在显著的长记忆性特征,但人民币汇率收益波动率的非周期循环天数长于欧元汇率收益波动率。结论说明了欧元汇率发展的成熟以及人民币汇率形成机制的相对低效,并为追踪汇市行为特征及制定外汇政策提供了新的视角。     

Volatility and Market Risk of Rubber Price in Malaysia: Pre- and Post-Global Financial Crisis

The volatility in rubber price is a significant risk to producers, traders, consumers and others who are involved in the production and marketing of natural rubber. Such being the case, forecasting the rubber price volatility is desired to assist in decision-making in this uncertain situation. The 2008 Global Financial Crisis caused some disruptions and uncertainties in the future supply or demand for natural rubber and thus leading to higher rubber price volatility. Using ARCH-type models, this paper intends to model the dynamics of the price volatility of Standard Malaysia Rubber Grade 20 (SMR 20) in the Malaysian market before and after the Global Financial Crisis. Additionally, Value-at-Risk (VaR) approach is implemented to evaluate the market risk of SMR 20. Our empirical result denotes the existence of volatility clustering and long memory volatility in the SMR 20 market for both crisis periods. Leverage effect is also detected in the SMR 20 market where negative innovations (bad news) have a larger impact on the volatility than positive innovations (good news) for post-crisis period. When tested with Superior Predictive Ability (SPA) test, FIGARCH model is the best model across five loss functions for short- and long-term forecasts for pre-crisis period. Meanwhile, over post-crisis period, FIGARCH and GJR GARCH indicate the superior out-of-sample-forecast results and better forecasting accuracy over short- and long-term horizons, respectively. In terms of market risk, the short trading position encounters higher risk or greater losses than the long trading position at both 1 and 5 % VaR quantile for pre-crisis period. In contrast, over post-crisis period, long traders of rubber SMR 20 tend to face limited gains but unlimited losses.

     

House price dynamics,conditional higher-order moments,and density forecasts

Most studies on housing price dynamics are only concerned with the conditional mean and variance, but overlook other higher-order conditional moments and the structural change characteristics inherent in housing prices. In order to take into account these two important issues, this study utilizes the generalized Markov switching GARCH model to explore house price dynamics and conditional distribution for US market over 1975Q1–2007Q4. The housing return follows two distinct dynamics: the bust regime and the boom regime. The volatility pattern is different in the bust and boom regimes. In addition, the conditional densities derived by the regime-switching model change dramatically over time and are significantly different from normal distribution. More importantly, the regime-switching model can detect in advance a weak US housing market such as the one that occurred in the middle of 2007. The in-sample fitting ability of regime-switching model, which incorporates higher-order moments, has significant improvements compared to the single-regime AR and AR-GARCH models. For the out-of-sample Value-at-Risk forecasting performance, the ability of regime-switching AR-GARCH model to forecast one-step-ahead density is better compared to the single-regime AR-GARCH model.     

中国宏观经济波动的结构性转变与启示

本文研究改革开放以来30年间中国主要宏观经济指标的季度时序波动性特征。笔者将时变参数随机波动模型应用于离散型时序分析,并运用存在干扰系数情况下的内生断点检验方法来正确识别不同经济指标波动性特征发生结构性变化的准确时间。研究结果表明,经济增长、通货膨胀、货币供给以及有效汇率等主要宏观经济指标的波动特征在20世纪90年代中期均发生显著结构性转变,宏观政策的系统性改进是这些变化的主要动因。     

Intraday return and volatility relationships between the Ibex 35 spot and futures markets

This paper analyses the intraday lead-lag relationships between returns and volatilities in the Ibex 35 spot and futures markets. Using hourly data, we jointly analyze the interactions between markets, estimating a bivariate error correction model with GARCH perturbations which captures stochastically the presence of an intraday U-shaped curve for both spot and futures market volatility. Our findings show a bidirectional causal relationship between market volatilities, with a positive feedback. This two-way transmission of volatility is consistent with market prices evolving according to a long-run equilibrium relationship, and shocks affecting both markets in the same direction. Our empirical results also support a unidirectional cross interaction from futures to spot market returns. This pattern suggests that the futures market leads the spot market in order to incorporate the arrival of new information.