Structural change and long-range dependence in volatility of exchange rates: either, neither or both?

In this paper, we test for the existence of long memory and structural breaks in the realized variance process for the DM/US$ and Yen/US$ exchange rates. While long memory is evident in the actual processes, a structural break analysis reveals that this feature is partially explained by unaccounted changes in regime. We then compare the forecasting performance of Markov switching models with that of an ARFIMA model. The results indicate that neglecting the break process is not important for very short term forecasting once it is allowed for a long memory component in the model, but that superior forecasts can be obtained at longer horizons by modelling both long memory and structural change.     

True or spurious long memory in European non-EMU currencies

We examine the Croatian Kuna, the Czech Koruna, the Hungarian Forint, the Polish Złoty, the Romanian Leu, and the Swedish Krona whether their Euro exchange rates volatility exhibits true or spurious long memory. Recent research reveals long memory in foreign exchange rate volatility and we confirm this finding for these currency pairs by examining the long memory behavior of squared residuals by means of the V/S test. However, by using the ICSS approach we also find structural breaks in the unconditional variance. Literature suggests that structural breaks might lead to spurious long memory behavior. In a refined test strategy, we distinguish true from spurious long memory for the six exchange rates. Our findings suggest that Czech Koruna and Hungarian Forint only feature spurious long memory, while the rest of the series have both structural breaks and true long memory. Lastly, we demonstrate how to extend existing models to jointly model both properties yielding superior fit and better Value-at-Risk forecasts. The results of our work help to avoid misspecification and provide a better understanding of the properties of the foreign exchange rate volatility.     

Long memory and level shifts in REITs returns and volatility

This paper provides an empirical investigation of the long memory in the returns and volatility of REITs markets of the USA, the UK, Hong Kong, Australia, and Japan. Initially, we subject the series to unit root tests proposed by Saikkonen and Lütkepohl (2002) and Lanne et al. (2002), which allow for a level shift in the data generating process. We confirm the stationarity of the REITs returns in the presence of structural breaks, with the breaks happening during the 2008 and 2009 periods. Second, by employing long memory tests and estimators, a weak long memory is demonstrated in the return series, but a strong evidence is provided in the volatility measures. Then using Smith (2005)'s modified GPH estimator, we find that a short-memory model with a level shift is a viable alternative to a long memory model for the USA, Hong Kong and Japan and not for the UK nor for Australia. Finally, we confirm that the long memory in volatility is real and not caused by shifts in variance for all markets. Our results should be useful to market participants in the REITs markets, whose success depends on the ability to forecast and model REITs price movements.     

The one-trading-day-ahead forecast errors of intra-day realized volatility

Two volatility forecasting evaluation measures are considered; the squared one-day-ahead forecast error and its standardized version. The mean squared forecast error is the widely accepted evaluation function for the realized volatility forecasting accuracy. Additionally, we explore the forecasting accuracy based on the squared distance of the forecast error standardized with its volatility. The statistical properties of the forecast errors point the standardized version as a more appropriate metric for evaluating volatility forecasts.We highlight the importance of standardizing the forecast errors with their volatility. The predictive accuracy of the models is investigated for the FTSE100, DAX30 and CAC40 European stock indices and the exchange rates of Euro to British Pound, US Dollar and Japanese Yen. Additionally, a trading strategy defined by the standardized forecast errors provides higher returns compared to the strategy based on the simple forecast errors. The exploration of forecast errors is paving the way for rethinking the evaluation of ultra-high frequency realized volatility models.     

Long memory and tail dependence in trading volume and volatility

We investigate the relationship between volatility, measured by realized volatility, and trading volume for 25 NYSE stocks. We show that volume and volatility are long memory but not fractionally cointegrated in most cases. We also find right tail dependence in the volatility and volume innovations. Tail dependence is informative on the behavior of the volatility and volume when large surprising news impact the market. We estimate a fractionally integrated VAR with shock distributions modeled with a mixture of copula functions. The model is able to capture the main characteristics of the series, say long memory, marginal non-normality and tail dependence. A simulation and forecasting exercise highlight the importance of modeling both long memory and tail dependence to capture extreme events.     

Long memory in log-range series: Do structural breaks matter?

This paper examines whether the observed long memory behavior of log-range series is to some extent spurious and whether it can be explained by the presence of structural breaks. Utilizing stock market data we show that the characterization of log-range series as long memory processes can be a strong assumption. Moreover, we find that all examined series experience a large number of significant breaks. Once the breaks are accounted for, the volatility persistence is eliminated. Overall, the findings suggest that volatility can be adequately represented, at least in-sample, through a multiple breaks process and a short run component.     

The response of the Dollar/Yen exchange rate to economic announcements

The paper examines the impact of major U.S. macroeconomic announcements on the Dollar/Yen exchange rate. We find that these announcements are responsible for most intraday and day-of-the-week volatility patterns in this market and we identify the most important announcements. The initial reaction to a major 8:30 announcement begins around 8:30:10 and lasts until about 8:30:50. A partial price correction is normally observed between 8:31 and 8:32. Price movements after 8:32 are basically independent of those observed earlier although volatility continues to be higher than normal until about 8:55.     

Volatility spillovers between oil prices and the stock market under structural breaks

This paper employs univariate and bivariate GARCH models to examine the volatility of oil prices and US stock market prices incorporating structural breaks using daily data from July 1, 1996 to June 30, 2013. We endogenously detect structural breaks using an iterated algorithm and incorporate this information in GARCH models to correctly estimate the volatility dynamics. We find no volatility spillover between oil prices and US stock market when structural breaks in variance are ignored in the model. However, after accounting for structural breaks in the model, we find strong volatility spillover between the two markets. We compute optimal portfolio weights and dynamic risk minimizing hedge ratios to highlight the significance of our empirical results which underscores the serious consequences of ignoring these structural breaks. Our findings are consistent with the notion of cross-market hedging and sharing of common information by financial market participants in these markets.     

Accurate minimum capital risk requirements: A comparison of several approaches

In this paper we estimate, for several investment horizons, minimum capital risk requirements for short and long positions, using the unconditional distribution of three daily indexes futures returns and a set of short and long memory stochastic volatility and GARCH-type models. We consider the possibility that errors follow a t-Student distribution in order to capture the kurtosis of the returns’ series. The results suggest that accurate modelling of extreme observations obtained for long and short trading investment positions is possible with an autoregressive stochastic volatility model. Moreover, modelling futures returns with a long memory stochastic volatility model produces, in general, excessive volatility persistence, and consequently, leads to large minimum capital risk requirement estimates. Finally, the models’ predictive ability is assessed with the help of out-of-sample conditional tests.     

Security bid/ask dynamics with discreteness and clustering: Simple strategies for modeling and estimation

This paper proposes a dynamic model of bid and ask quotes that incorporates a stochastic cost of market-making, discreteness (restriction of quotes to a fixed grid) and clustering (the tendency of quotes to lie on `natural' multiples of the tick size). The Gibbs sampler provides a convenient vehicle for estimation. The model is estimated for daily and intradaily US Dollar/Deutschemark Reuters quotes.     

Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns

This paper shows that occasional breaks generate slowly decaying autocorrelations and other properties of I(d) processes, where d can be a fraction. Some theory and simulation results show that it is not easy to distinguish between the long memory property from the occasional-break process and the one from the I(d) process. We compare two time series models, an occasional-break model and an I(d) model to analyze S&P 500 absolute stock returns. An occasional-break model performs marginally better than an I(d) model in terms of in-sample fitting. In general, we found that an occasional-break model provides less competitive forecasts, but not significantly. However, the empirical results suggest a possibility such that, at least, part of the long memory may be caused by the presence of neglected breaks in the series. We show that the forecasts by an occasional break model incorporate incremental information regrading future volatility beyond that found in I(d) model. The findings enable improvements of volatility prediction by combining I(d) model and occasional-break model.     

MENA stock market volatility persistence: Evidence before and after the financial crisis of 2008

The global financial crisis began with a financial meltdown in the United States in early 2008 and then it had spread to the rest of the world. In this paper we test whether the MENA equity market volatility presents a different behavior before and after the financial crisis of 2008. Using long range dependence techniques we test for long memory in the returns, absolute and squared returns of the MENA equity markets. We subject the series to unit root tests that allow for structural breaks and use the Bai and Perron (1998, Econometrica, 66, 47; 2003a, J. Appl. Econometrics, 6, 72; 2003b, Econometrics J., 18, 1) to test for multiple breaks in the mean returns. The results indicate that the volatility measures represented by absolute and squared returns show evidence of long memory for the full and subsample periods, while the returns show a weak evidence of long memory. Considering the shift dates and corresponding to the 2008 financial crisis, the returns and volatility measures display less evidence of long memory in the after crisis period as opposed to the before crisis period. The change in the returns and volatility dynamics of these markets was due to financial and economic conditions that took place in the MENA region after the crisis.     

Forecasting implied volatility in foreign exchange markets: a functional time series approach

We utilise novel functional time series (FTS) techniques to characterise and forecast implied volatility in foreign exchange markets. In particular, we examine the daily implied volatility curves of FX options, namely; Euro/United States Dollar, Euro/British Pound, and Euro/Japanese Yen. The FTS model is shown to produce both realistic and plausible implied volatility shapes that closely match empirical data during the volatile 2006–2013 period. Furthermore, the FTS model significantly outperforms implied volatility forecasts produced by traditionally employed parametric models. The evaluation is performed under both in-sample and out-of-sample testing frameworks with our findings shown to be robust across various currencies, moneyness segments, contract maturities, forecasting horizons, and out-of-sample window lengths. The economic significance of the results is highlighted through the implementation of a simple trading strategy.     

Los procesos α-estables y su relación con el exponente de autosimilitud: paridades de los tipos de cambio dólar estadounidense,dólar canadiense,euro y yen

In this research we analyze the performance of the exchange rates of USA Dollar, Canadian Dollar, Euro and Yen; we estimate the basic statistics, α-stable parameters, we performed tests of goodness fit Kolmogorov-Smirnov, Anderson-Darling and Lilliefors; we estimate self-similarity exponents and we performed t y F tests, ruling that the series of the exchange rates are multi-fractal; we estimate confidence intervals of the exchange rates and we conclude that the estimated α-stable distributions are more efficient than the gaussian distribution to quantify market risks and the series are self-similar; by the ? index we infer the risk of events and we indicate that exchange rates are anti-persistent, have mean reversión, short-term memory, negative correlation and high risk in the short and medium term; the estimation and validation of α-stable distributions and the exponent of self-similarity are important for pricing and the creation of innovative investment instruments by financial engineering, risk management and derivatives pricing.     

Long memory in volatility and trading volume

We use fractionally-integrated time-series models to investigate the joint dynamics of equity trading volume and volatility. Bollerslev and Jubinski (1999) show that volume and volatility have a similar degree of fractional integration, and they argue that this evidence supports a long-run view of the mixture-of-distributions hypothesis. We examine this issue using more precise volatility estimates obtained using high-frequency returns (i.e., realized volatilities). Our results indicate that volume and volatility both display long memory, but we can reject the hypothesis that the two series share a common order of fractional integration for a fifth of the firms in our sample. Moreover, we find a strong correlation between the innovations to volume and volatility, which suggests that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.     

Gold and the Dollar (and the Euro, Pound, and Yen)

Usually, gold and the Dollar are negatively related; when the Dollar price of gold increases, the Dollar depreciates against other currencies. This is intuitively puzzling because it seems to suggest that gold prices are associated with appreciation in other currencies. Why should the Dollar be different? We show here that there is actually no puzzle. The price of gold can be associated with currency depreciation in every country. The Dollar price of gold can be related to Dollar depreciation and the Euro (Pound, Yen) price of gold can be related to Euro (Pound, Yen) depreciation. Indeed, this is usually the case empirically.     

Volume and Volatility in Foreign Currency Futures Markets

In this paper we propose and test several hypotheses concerning time series properties of trading volume, price, short and long-term relationships between price and volume and the determinants of trading volume in forcign currency futures. The nearby contracts for British Pound, Canadian Dollar, Japanese Yen, German Mark and Swiss Franc are analyzed in three frequencies i.e. daily, weekly and monthly.We find supportive evidence for all the five currencies that the price volatility is a determinant of the trading volume changes. Furthermore, the volatility of the price process is a determinant of the unexpected component of the changes in trading volume. Also, there is a significant relationship between the volatility of price and the volatility of trading volume changes for three of the five currencies in the daily frequency and for one currency in the monthly frequency.     

Structural breaks in volatility spillovers between international financial markets: Contagion or mere interdependence?

This paper conducts an investigation of volatility transmission between stock markets in Hong Kong, Europe and the United States covering the time period from 2000 up to 2011. Using intra-daily data we compute realized volatility time series for the three markets and employ a Heterogeneous Autoregressive Distributed Lag Model as our baseline econometric specification. Motivated by the presence of various crisis events contained in our sample, we detect time-variation and structural breaks in volatility spillovers. Particularly during the financial crisis of 2007, we find effects consistent with the notion of contagion, suggesting strong and sudden increases in the cross-market synchronization of chronologically succeeding volatilities. Investigating the role of mean breaks and conditional heteroskedasticity in the realized volatilities, however, we find the latter to be the main driver of breaks in volatility spillovers. Taking the volatility of realized volatilities into account, we find no evidence of contagion anymore.     

Testing for Serial Correlation in the Presence of Stochastic Volatility

This paper develops a regression-based testing procedure for serial correlation in the presence of stochastic volatility. The asymptotic distribution of the test is derived, and the finite sample properties are investigated. Monte Carlo results shows that the test is reliable in terms of both size and power performances, when the underlying process is a log-linear stochastic volatility. Moreover, the test is superior to Woolridge's (1991) robust LM tests in terms of size in finite sample. Serial correlation tests were conducted for nominal returns of ten exchange rates, and indicated that there is a strong evidence of serial correlation for Yen/Dollar exchange rates.     

Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models

We compare forecasts of the realized volatility of the pound, mark and yen exchange rates against the dollar, calculated from intraday rates, over horizons ranging from one day to three months. Our forecasts are obtained from a short memory ARMA model, a long memory ARFIMA model, a GARCH model and option implied volatilities. We find intraday rates provide the most accurate forecasts for the one-day and one-week forecast horizons while implied volatilities are at least as accurate as the historical forecasts for the one-month and three-month horizons. The superior accuracy of the historical forecasts, relative to implied volatilities, comes from the use of high frequency returns, and not from a long memory specification. We find significant incremental information in historical forecasts, beyond the implied volatility information, for forecast horizons up to one week.