Multiresolution approximation for volatility processes

Abstract

We present an application of wavelet techniques to non-stationary time series with the aim of detecting the dependence structure which is typically found to characterize intraday stock index financial returns. It is particularly important to identify what components truly belong to the underlying volatility process, compared with those features appearing instead as a result of the presence of disturbance processes. The latter may yield misleading inference results when standard financial time series models are adopted. There is no universal agreement on whether long memory really affects financial series, or instead whether it could be that non-stationarity, once detected and accounted for, may allow for more power in detecting the dependence structure and thus suggest more reliable models. Wavelets are still a novel tool in the domain of applications in finance; thus, one goal is to try to show their potential use for signal decomposition and approximation of time-frequency signals. This might suggest a better interpretation of multi-scaling and aggregation effects in high-frequency returns. We show, by using special dictionaries of functions and ad hoc algorithms, that a pre-processing procedure for stock index returns leads to a more accurate identification of dependent and non-stationary features, whose detection results are improved compared with those obtained by other traditional Fourier-based methods. This allows generalized autoregressive conditional heteroscedastic models to be more effective for statistical estimation purposes.     

Covariance and correlation stationarity: Experiences from seven Asian emerging markets

Because of the rising interest and the growing importance of the Asian emerging markets in international diversification, this paper examines the covariance and correlation stationarity in stock return relationships among seven Asian emerging markets. This paper also covers the issue of seasonality in stock return co-movements. Empirical results show that because the correlations among them and those with other developed markets are very small, huge gains from diversifying into the seven Asian emerging markets are possible. Results on stationarity indicate that correlation matrices of stock returns are much more stable then the corresponding variance-covariance matrices and that the length of the estimation period seems to have no impact on the stationarity of the correlation matrix. We also found that virtually no seasonality in the correlations exists among the seven Asian emerging markets. However, we did find that during our sample period covariance among stock returns is nonstationary in January. The author thanks an anonymous referee ofFinancial Engineering and the Japanese Markets for the valuable comments on the earlier version of this article.     

Reversal of Monday returns

This paper elaborates an interesting aspect of the Monday anomaly: Monday returns are relatively more likely to reverse over the subsequent days. We document that, although the Monday low-return anomaly disappeared, the subsequent reversal of Monday returns remains robust to date. The reversals, measured over a five-day horizon, are pervasive across international stock markets, reasonably stable over time, significant following both positive and negative Monday returns, and not confined to extreme Monday returns. Trading strategies designed to exploit these reversals earn economic profits. We examine potential explanations for the reversal of Monday returns using trading flows data of investor types from Korea. All predictions of the Foster and Viswanathan [J. Finance, 1993, 48, 187–211] model are confirmed: volatility is higher, trading volume is lower, market depth is lower and price impact costs are higher on Mondays. The model implies lower price quality on Mondays, but does not specifically predict reversal of Monday returns. We show that the trading intensity of international/institutional investors is lower on Mondays. This appears to make the market relatively more susceptible to individual investors’ trading, which is negatively correlated with international/institutional investors. Thus, Monday returns are relatively more likely to reverse during the subsequent days of the week when institutional investors trade more aggressively.     

Time-varying neural network for stock return prediction

We consider the problem of neural network training in a time-varying context. Machine learning algorithms have excelled in problems that do not change over time. However, problems encountered in financial markets are often time varying. We propose the online early stopping algorithm and show that a neural network trained using this algorithm can track a function changing with unknown dynamics. We compare the proposed algorithm to current approaches on predicting monthly US stock returns and show its superiority. We also show that prominent factors (such as the size and momentum effects) and industry indicators exhibit time-varying predictive power on stock returns. We find that during market distress, industry indicators experience an increase in importance at the expense of firm level features. This indicates that industries play a role in explaining stock returns during periods of heightened risk.     

An analysis of trading strategies in eleven European stock markets

Abstract

In recent years, the validity of the weak form efficient market hypothesis (EMH) has been called into question as several studies have uncovered evidence that technical trading rules have predictive ability with respect to both developed and emerging stock market indices. This study analyses the forecasting power of 2 of the most popular trading rules using index data for a selection of 11 European stock markets over the January 1991 to December 2000 period. The findings indicate that the emerging markets included in this paper are informationally inefficient; these markets displayed some degree of predictability in their share returns, although the developed markets did not. Furthermore, the results point to large differences in the performance of the rules examined; while small size filters consistently outperformed the buy-and-hold strategy in the emerging markets examined even after the consideration of transaction costs, the performance of the moving average rules was erratic and varied dramatically from market to market.     

Forecasting stock market returns over multiple time horizons

In this paper, we seek to demonstrate the predictability of stock market returns and explain the nature of this return predictability. To this end, we introduce investors with different investment horizons into the news-driven, analytic, agent-based market model developed in Gusev et al. [Algo. Finance, 2015, 4, 5–51]. This heterogeneous framework enables us to capture dynamics at multiple timescales, expanding the model’s applications and improving precision. We study the heterogeneous model theoretically and empirically to highlight essential mechanisms underlying certain market behaviours, such as transitions between bull and bear markets and the self-similar behaviour of price changes. Most importantly, we apply this model to show that the stock market is nearly efficient on intraday timescales, adjusting quickly to incoming news, but becomes inefficient on longer timescales, where news may have a long-lasting nonlinear impact on dynamics, attributable to a feedback mechanism acting over these horizons. Then, using the model, we design algorithmic strategies that utilize news flow, quantified and measured, as the only input to trade on market return forecasts over multiple horizons, from days to months. The backtested results suggest that the return is predictable to the extent that successful trading strategies can be constructed to harness this predictability.     

Do emerging markets with consistent returns have better future performance?

Using monthly data for 25 emerging markets around the world, it is found that emerging markets with recently consistent stock returns tend to have future returns that continue in the same direction. The effects are long-lived for negative consistency, and imply that capital flows are much more sensitive to market downturns than market upturns. Additionally, the longer a market has had consistently negative (positive) stock returns, the more negative (positive) are future returns. These results serve as confirmation that the consistency effects of Grinblatt and Moskowitz [J. Finan. Econ., 2004 Grinblatt, M and Moskowitz, T. 2004. Predicting stock price movements from the pattern of past returns. J. Finan. Econ., 71: 541–579. [Crossref], [Web of Science ®] , [Google Scholar], forthcoming] and Watkins [J. Behav. Finan., 2003 Watkins, B. 2003. Riding the wave of investor sentiment: an analysis of consistency as a predictor of future stock returns. J. Behav. Finan., 4: 1–32.  [Google Scholar], 4, 1–32] exist in emerging markets around the world.     

Idiosyncratic volatility and cross‐sectional stock returns in Southeast Asian stock markets

We examine the role of idiosyncratic risk in five ASEAN markets of Malaysia, Singapore, Thailand, Indonesia, and the Philippines. Our research was motivated by the findings of Ang et al. (2006, 2009) of a ‘puzzling’ negative relation between idiosyncratic volatility and 1‐month ahead stock returns in developed markets and the suggestion of the ubiquity of these results in other markets. In contrast, we find no evidence of an idiosyncratic volatility puzzle in these Asian stock markets; instead, we document a positive relationship between idiosyncratic volatility and returns in Malaysia, Singapore, Thailand, and Indonesia and no relationship in the Philippines. The idiosyncratic volatility trading strategy could result in significant trading profits in Malaysia, Singapore, Thailand, and to some extent in Indonesia. Our study underscores the fact that generalizing empirical results obtained in developed stock markets to new and emerging markets could potentially be misleading.     

24-Hour realized volatilities and transatlantic volatility interdependence

This paper proposes an innovative econometric approach for the computation of 24-h realized volatilities across stock markets in Europe and the US. In particular, we deal with the problem of non-synchronous trading hours and intermittent high-frequency data during overnight non-trading periods. Using high-frequency data for the Euro Stoxx 50 and the S&P 500 Index between 2003 and 2011, we combine squared overnight returns and realized daytime variances to obtain synchronous 24-h realized volatilities for both markets. Specifically, we use a piece-wise weighting procedure for daytime and overnight information to take into account structural breaks in the relation between the two. To demonstrate the new possibilities that our approach opens up, we use the new 24-h volatilities to estimate a bivariate extension of Corsi et al.’s [Econom. Rev., 2008, 27(1–3), 46–78] HAR-GARCH model. The results suggest that the contemporaneous transatlantic volatility interdependence is remarkably stable over the sample period.     

The Comovement of US and UK Stock Markets

US and UK stock returns are highly positively correlated over the period 1918–99. Using VAR‐based variance decompositions, we investigate the nature of this comovement. Excess return innovations are decomposed into news about future dividends, real interest rates, and excess returns. We find that the latter news component is the most important in explaining stock return volatility in both the USA and the UK and that stock return news is highly correlated across countries. This is evidence against Beltratti and Shiller's (1993) finding that the comovement of US and UK stock markets can be explained in terms of a simple present value model. We interpret the comovement as indicating that equity premia in the two countries are hit by common real shocks.     

A MULTIFACTOR ANALYSIS OF COUNTRY FUND RETURNS

Previous closed‐end country fund research concludes that returns behave more like the U.S. market than like their target markets. We argue this finding may be biased by model misspecification and inappropriate estimation techniques. We propose a single‐equation model containing five hypothesized factors of fund returns. We estimate this model for nineteen pooled seasoned funds using a time‐series cross‐section regression that corrects for two types of autocorrelation. We show that returns are strongly related to target markets. Returns are also related to changes in discounts, exchange rates, and other countries' markets, but are only weakly related to the U.S. market. JEL classification: G10, G12     

Have European Stocks become More Volatile? An Empirical Investigation of Idiosyncratic and Market Risk in the Euro Area

We examine the dynamics of idiosyncratic risk, market risk and return correlations in European equity markets using weekly observations from 3515 stocks listed in the 12 euro area stock markets over the period 1974–2004. Similarly to Campbell et al. (2001) , we find a rise in idiosyncratic volatility, implying that it now takes more stocks to diversify away idiosyncratic risk. Contrary to the US, however, market risk is trended upwards in Europe and correlations are not trended downwards. Both the volatility and correlation measures are pro‐cyclical, and they rise during times of low market returns. Market and average idiosyncratic volatility jointly predict market wide returns, and the latter impact upon both market and idiosyncratic volatility. This has asset pricing and risk management implications.     

MEAN AND VOLATILITY SPILLOVERS ACROSS MAJOR NATIONAL STOCK MARKETS: FURTHER EMPIRICAL EVIDENCE

This paper provides additional insight into the nature and degree of interdependence of stock markets of the United States, Japan, the United Kingdom, Canada, and Germany, and it reports the extent to which volatility in these markets influences expected returns. The analysis uses the multivariate GARCH-M model. Although they are considered weak, statistically significant mean spillovers radiate from stock markets of the U.S. to the U.K., Canada, and Germany, and then from the stock markets of Japan to Germany. No relation is found between conditional market volatility and expected returns. Strong time-varying conditional volatility exists in the return series of all markets. The own-volatility spillovers in the U.K. and Canadian markets are insignificant, supporting the view that conditional volatility of returns in these markets is “imported” from abroad, specifically from the U.S. Significant volatility spillovers radiate from the U.S. stock market to all four stock markets, from the U.K. stock market to the Canadian stock market, and from the German stock market to the Japanese stock market. The results are robust and no changes occur in the correlation structure of returns over time.     

The Halloween Effect and Japanese Equity Prices: Myth or Exploitable Anomaly

Bouman and Jacobsen (American Economic Review 92(5), 1618–1635, 2002) examine monthly stock returns for major world stock markets and conclude that returns are significantly lower during the May–October periods versus the November–April periods in 36 of 37 markets examined. They argue that, in general, the Halloween strategy outperforms the buy and hold strategy thereby casting doubt on the validity of the efficient market paradigm. More recently, Maberly and Pierce (Econ Journal Watch 1(1), 29–46, 2004) re-examine the evidence for U.S. equity prices and conclude that Bouman and Jacobsen’s results are not robust to alternative model specifications. Extending prior research, this paper examines the robustness of the Halloween strategy to alternative model specifications for Japanese equity prices. The Halloween effect is concentrated in the period prior to the introduction of Nikkei 225 index futures in September 1986. After the internationalization of Japanese financial markets in the mid-1980s, the Halloween effect disappears.JEL classification: G14, G15     

The changing and relative efficiency of European emerging stock markets

The martingale hypothesis is tested for 15 European emerging stock markets located in Croatia, the Czech Republic, Estonia, Hungary, Iceland, Latvia, Lithuania, Malta, Poland, Romania, Russia, the Slovak Republic, Slovenia, Turkey and the Ukraine. For comparative purposes, the developed stock markets in Greece, Portugal and the UK are also included. Rolling window variance ratio tests based on returns and signs and with wild bootstrapped p-values are used with daily data over the period beginning in February 2000 and ending in December 2009. The fixed-length rolling sub-period window captures changes in efficiency and is used to identify events which coincide with departures from weak-form efficiency and to rank markets by relative efficiency. Overall, return predictability varies widely. The most efficient are the Turkish, UK, Hungarian and Polish markets; the least efficient are the Ukrainian, Maltese and Estonian stock markets. The global financial market crisis of 2007–2008 coincides with return predictability in the Croatian, Hungarian, Polish, Portuguese, Slovakian and UK stock markets. However, not all markets were affected: the crisis had little effect on weak-form efficiency in stock markets located in Greece, Latvia, Romania, Russia and Turkey.     

The Cross-Section of Stock Returns on The Shanghai Stock Exchange

This study explores the cross-sectional stock return behavior on the A-share market of the Shanghai Stock Exchange (SSE), which is segmented from world's other equity markets. We estimate the effects of beta, firm size, book-to-market equity ratio and a variable unique to the Chinese stock markets, the proportion of firm's floating (tradable) equity over total equity on SSE stocks over the period 1993–2002. We find that smaller firms and value stocks perform better. Systematic risk is negatively significant in down markets. The proportion of floating equity has no direct effect on stock returns. JEL Classification: G14, G15     

Asia-Pacific Stock Market Integration: New Evidence by Incorporating Regime Changes

ABSTRACT

This work provides new evidence of Asia-Pacific stock market integration by incorporating the regime changes of each stock market through the smooth transition autoregressive (STAR) model. According to empirical results, most Asia-Pacific stock market returns follow STAR dynamics to a significant degree with more rapid and frequent regime changes of a shorter nature compared with G7 markets. A series of STAR-based Granger causality tests reveal evidence of stronger equity market integration compared with linear Granger causality tests. We also find that Asia-Pacific stock markets are integrated in different levels. Finally, we provide evidence that in the early twenty-first century the influence of China and the United States on Asia-Pacific stock markets has been maintained while that of Japan has been weakened.     

Short-term Dynamics in the Cyprus Stock Exchange

Abstract

This paper investigates the short-term dynamics of stock returns in an emerging stock market namely, the Cyprus Stock Exchange (CYSE). Stock returns are modelled as conditionally heteroscedastic processes with time-dependent serial correlation. The conditional variance follows an EGARCH process, while for the conditional mean three nonlinear specifications are tested, namely: (a) the LeBaron exponential autoregressive model; (b) the Sentana and Wadhwani positive feedback trading model; and finally (c) a model that nests both (a) and (b). There is an inverse relationship between volatility and autocorrelation consistent with the findings from several other stock markets, including the US. This pattern could be the manifestation of a certain form of noise trading namely positive feedback trading or, momentum trading strategies. There is little evidence that market declines are followed with higher volatility than market advances, the so-called ‘leverage effect’, that has been observed in almost all developed stock markets. In out of sample forecasts, the nonlinear specifications provide better results in terms of forecasting both first and second moments of the distribution of returns.     

Testing for persistence in stock returns with GARCH-stable shocks

We investigate persistence in CRSP monthly excess stock returns, using a state space model with stable disturbances. The non-Gaussian state space model with volatility persistence is estimated by maximum likelihood, using the optimal filtering algorithm given by Sorenson and Alspach (1971 Automatica 7 465–79). The conditional distribution has a stable α of 1.89, and normality is strongly rejected even after accounting for GARCH. However, stock returns do not contain a significant mean-reverting component. The optimal predictor is the unconditional expectation of the series, which we estimate to be 9.8% per annum.     

Economic determinants of evolution in international stock market integration

This study investigates how and why different pairs of national equity markets display differing degrees of co-movement over time. We interpret a greater degree of co-movement to reflect greater stock market integration. We hypothesize the extent of stock market integration may depend upon certain macroeconomic variables that characterize and influence the degree of economic integration between two countries. As the degree of economic integration varies over time for a given pair of countries, we may expect the extent of equity market integration to vary systematically. We empirically investigate this hypothesis by employing a two-step procedure to explore first, how the degree of co-movement for a given pair of markets varies over time and second, why this interdependence varies over time. First, we employ daily data for nine national equity markets over 22 yearly samples to estimate annual Geweke [J. Am. Statist. Assoc. 77 (1982) 304–313] measures of feedback for different pairs of markets. For each pair of markets, the time series of 22 annual Geweke measures reveals the evolution in how co-movement in daily returns varies over time. Second, we specify a set of macroeconomic variables that characterize and influence the degree of economic integration for each pair of countries. Finally, we incorporate these variables in a pooled time series regression model across all possible pairs of these nine markets to estimate the influence of macroeconomic determinants on evolution in stock market integration.