Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis

In the present work we propose the rescaled range analysis (R/S), modified R/S method and detrended fluctuation analysis (DFA) to investigate the long memory property of Chinese stock markets based on the conditional and actual volatility series, and show that the stock markets in China display moderate positive degree of long memory. For the robustness, we implement the multiscale analysis on dynamic changes of time-varying Hurst exponents by applying the rolling window method based on DFA. Our results reveal that APGARCH model with the superior forecasting ability captures the long memory property better than other GARCH-class models for different time scale interval. Interestingly, the time-varying Hurst exponents of the sudden “jumps” for the conditional volatility calculated by the DFA method using the APGARCH model are smaller than that of the actual volatility series, which indicates that APGARCH model may underestimate the long memory property in the Chinese stock market. Our evidences provide new perspectives for the financial market forecasting.     

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.     

The Exchange Rate and its Fundamentals in a Complex World

We develop a nonlinear exchange rate model with heterogeneous agents. Some agents adopt a “fundamentalist” forecasting rule, while others use a “chartist” forecasting rule. We show that the model is capable of explaining the empirical puzzles relating to exchange rate movements. In particular, the model explains the “exchange rate determination” and PPP puzzles, the excess volatility, and fat tails in exchange rate returns.     

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.     

股市收益率与波动性长期记忆效应的实证研究

股票市场长期记忆效应问题是近来金融实证研究的一个热点.多数的研究集中在收益率长期相关性的考察上,较少有对波动率序列的研究.然而,波动率的长期记忆性不仅会导致金融市场上的波动持久性特征,而且将对波动率的预测与衍生证券定价产生重要的影响.基于此,本文通过修正的R/S分析与ARFIMA模型对我国股市收益率及其波动性的长期相关性进行了实证研究.结果表明:中国股市具有显著的非线性特征,虽然收益率序列的自相关性较弱,但波动性序列却表现出显著的长期记忆效应.这一结论将为研究股票价格行为特征与金融经济学理论提供新的方向.     

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.     

Forecasting volatility of futures market: the S&P 500 and FTSE 100 futures using high frequency returns and implied volatility

We show that historical volatility from high frequency returns outperforms implied volatility when standardized returns by historical volatility tends to be normally distributed. For the FTSE 100 futures, we find that historical volatility using high frequency returns outperforms implied volatility in forecasting future volatility. However, we find that implied volatility outperforms historical volatility in forecasting future volatility for the S&P 500 futures. The results also indicate that historical volatility using high frequency returns could be an unbiased forecast for the FTSE 100 futures.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

基于FIGARCH模型的中国房地产指数的实证分析

在T分布和正态分布假设下采用GARCH模型和FIGARCH模型对上证地产股指数日收益率序列进行建模分析,结果表明,上证地产股指数日收益率序列的波动具有显著的长记忆性,表明外部冲击对波动有着长期的影响。因此,采用FIGARCH模型建模的效果优于采用GARCH模型建模的效果,并且在T分布假设下拟合模型,其效果优于在正态分布假设下拟合的模型。     

Why is it so difficult to outperform the random walk in exchange rate forecasting?

A simulation exercise is used to demonstrate the difficulty to outperform the random walk in exchange rate forecasting if forecasting accuracy is judged by the Root Mean Square Error (RMSE) or similar criteria that depend on the magnitude of the forecasting error. It is shown that, as the exchange rate volatility rises, the RMSE of the model rises faster than that of the random walk. While the literature considers this finding to be a puzzle that casts a big shadow of doubt on the soundness of international monetary economics, the results show that failure to outperform the random walk, in both in-sample and out-of-sample forecasting, should be the rule rather than the exception. However, the results do not imply that the random walk is unbeatable, because it can be easily outperformed if forecasting accuracy is judged according to criteria such as direction accuracy and profitability.     

Standard and seasonal long memory in volatility: an application to Spanish inflation

The historical series of many economic variables, such as inflation, are characterized by a strong persistent behaviour in the form of long memory, not only in the long run or at zero frequency but often also at seasonal frequencies. In financial series, long memory is not apparent in levels but strong persistence in higher order moments such as volatility has been proven to be a stylized fact in stock returns. Interest in economic time series has, however, focused on the persistence of levels and little attention has been paid to higher order dependence, which can be important for assessing the stability of the series. We propose a semiparametric analysis of the standard and seasonal persistence of the volatility of a monthly Spanish inflation series. The conclusions can be summarized in three main results. First volatility shows strong persistence implying an unstable trend in prices, but its structure depends on the proxy used, the absolute values, the squares or the logarithms of squares. Second, the structure of the persistence of volatility changed with the first oil crisis in 1973, with a persistent trend in both periods, in contrast with levels. Third, the Taylor effect, which is well documented in financial series, does not apply in this series.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

Modeling volatility with time-varying FIGARCH models

This paper puts the light on a new class of time-varying FIGARCH or TV-FIGARCH processes to model the volatility. This new model has the feature to account for the long memory and the structural change in the conditional variance process. The structural change is modeled by a logistic function allowing the intercept to vary over time. We also implement a modeling strategy for our TV-FIGARCH specification whose performance is examined by a Monte Carlo study. An empirical application to the crude oil price and the S&P 500 index is carried out to illustrate the usefulness of our techniques. The main result of this paper is that the long memory behavior of the absolute returns is not only explained by the existence of the long memory in the volatility but also by deterministic changes in the unconditional variance.     

Out‐of‐Sample Exchange Rate Forecasting and Macroeconomic Fundamentals: The Case of Japan

This study explores the respective out‐of‐sample exchange rate forecasting abilities of five macroeconomic fundamental models in comparison to a naïve random walk model for Japan during the post‐Bretton Woods era. To assess the influence of major economic changes, we estimate both linear and nonlinear models for all the macroeconomic fundamentals. Overall, most structural exchange rate models outperform a naïve random walk model in terms of forecasting accuracy in the short horizon. When the fundamentals are only linearly modelled, the forecasting ability of the Taylor rule is generally superior to other fundamental models. When the fundamentals are nonlinearly specified, the predictability of some other models rises dramatically to match that of the Taylor rule models in short and/or long horizons. Of importance, we determine that the yen/dollar exchange rate forecasting performance effectively improves in several fundamental models when influential economic changes are incorporated.     

Predictive ability of asymmetric volatility models at medium-term horizons

Using realized volatility to estimate conditional variance of financial returns, we compare forecasts of volatility from linear GARCH models with asymmetric ones. We consider horizons extending to 30 days. Forecasts are compared using three different evaluation tests. With data from an equity index and two foreign exchange returns, we show that asymmetric models provide statistically significant forecast improvements upon the GARCH model for two of the datasets and improve forecasts for all datasets by means of forecasts combinations. These results extend to about 10 days in the future, beyond which the forecasts are statistically inseparable from each other.     

Long memory in the volatility of China stock returns

In this paper, we empirically examine the volatility process of China's stock market returns using daily and weekly Shanghai and Shenzhen stock indices during January 1990 to August 2008. To investigate the property of the process, we used the FIGARCH (fractionally integrated GARCH) model including GARCH and IGARCH processes as special cases. Since the FIGARCH model allows fractional integration order, it can detect hyperbolically decaying volatility processes which cannot be explained by previous models with integer integration order. Our results show that the Shanghai and Shenzhen stock indices exhibit long-term dependencies. The long memory properties of the Shanghai and Shenzhen stock markets do not seem to be spuriously induced without exception.     

The Effects of US Macroeconomic Surprises on the Intraday Movements of Foreign Exchange Rates: Cases of USD-EUR and USD-JPY Exchange Rates

This paper characterizes the intraday dynamics of the high frequency US Dollar (USD)–Euro (EUR) and US Dollar (USD)–Japanese Yen (JPY) foreign exchange rates that have been subject to macroeconomic fundamentals. Even though the FIGARCH model with a normality assumption is found to be a good starting point, it appears to be inappropriate to represent the underlying movements of the high frequency returns due to the occurrences of jumps. Hence, this paper relies on the FIGARCH model with the mixture distribution that allows for the time-varying jumps that are determined by the US macroeconomic surprises. This paper generally finds that the US macroeconomic surprises are closely related to the intraday movements in the volatility process of the high frequency returns process through the jumps. In particular, the US macroeconomic surprises appear to affect the movements in the volatility process of the foreign exchange rates asymmetrically depending on the signs of the surprises and spuriously increasing the long memory persistence in the volatility process due to the jumps.     

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。     

Volatility forecasting: combinations of realized volatility measures and forecasting models

This article examines financial time series volatility forecasting performance. Different from other studies which either focus on combining individual realized measures or combining forecasting models, we consider both. Specifically, we construct nine important individual realized measures and consider combinations including the mean, the median and the geometric means as well as an optimal combination. We also apply a simple AR(1) model, an SV model with contemporaneous dependence, an HAR model and three linear combinations of these models. Using the robust forecasting evaluation measures including RMSE and QLIKE, our empirical evidence from both equity market indices and exchange rates suggests that combinations of both volatility measures and forecasting models improve the forecast performance significantly.     

Exchange rate volatility and export performance: a cointegrated VAR approach

During the last decades Norwegian exporters have–despite various forms of exchange rate targeting–faced a rather volatile exchange rate which may have influenced their behaviour. Recently, the shift to inflation targeting and a freely floating exchange rate has brought about an even more volatile exchange rate. We examine the causal link between export performance and exchange rate volatility across different monetary policy regimes within the cointegrated Vector Autoregression (VAR) framework using the implied conditional variance from a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model as a measure of volatility. Although treating the volatility measure as either a stationary or a nonstationary variable in the VAR, we are not able to find any evidence suggesting that export performance has been significantly affected by exchange rate uncertainty. We find, however, that volatility changes proxied by blip dummies related to the monetary policy change from a fixed to a managed floating exchange rate and the Asian financial crises during the 1990s enter significantly in a dynamic model for export growth–in which the level of relative prices and world market demand together with the level of exports constitute a significant cointegration relationship. A forecasting exercise on the dynamic model rejects the hypothesis that increased exchange rate volatility in the wake of inflation targeting in the monetary policy has had a significant impact on export performance.