Top PDF Modeling and Forecasting Volatility of the Malaysian Stock Markets

Traditional regression tools have shown their limitation in the modeling of high-frequency (weekly, daily or intra-daily) data. Assuming that only the mean response could be changing with covariates while the variance remains constant over time often revealed to be an unrealistic assumption in practice. This fact is particularly obvious in series of financial data where clusters of volatility can be detected visually. During the last few decades we have seen a multitude of different suggestions for how to model the second moment, often referred to as volatility, of financial returns. Indeed, it is now widely accepted that high frequency financial returns are heteroskedastic. Among the models that have proven the most successful are the Auto-Regressive Conditional Heteroskedasticity (ARCH) family of models introduced by Engle [4] and the models of Stochastic Variance (SV) pioneered by Taylor [14] . One of the main purposes of modeling variance is forecasting, which is crucial in many areas of finance such as option pricing, value at risk applications and portfolio selection. Therefore, the out of-sample forecasting ability should be a natural model selection criterion for volatility models. The vast

Within the traditional approach we have considered the GARCH (1, 1), IGARCH (1, 1) and FIGARCH (1, d, 1) specifications, whose main results are listed in Table 1. The conclusions are similar to all the three indexes considered. Specif- ically, for the GARCH (1, 1) it was found evidence of heteroscedastic condi- tional variance. Also, the fact that α + β ≃ 1 could denounce the presence of nonlinear persistence in the log-returns of the stock market indexes led us to estimate the IGARCH (1, 1) model. However, evidence has shown that many coefficients were not statistically significant. Then, the next step was to adjust the FIGARCH specification (1, d, 1) with the restriction d 6= 1 whose main results corroborate the long memory hypothesis.

Lin(2018) performed the test of modelling and forecasting the stock market volatility of SSE Composite Index(daily closing prices over the period extending from July 26, 2013 to July 28, 2017) using GARCH models. To better describe the significant properties of SSE Composite Index as time-varying, clustering, leptokurtosis and significant ARCH and GARCH effects, he compared the fitting and forecast result of GARCH (1, 1) (symmetric), TARCH (1, 1) and EGARCH (1, 1) (asymmetric), and found the EGARCH (1, 1) outperforms the others. The advice he finally gave is to strengthen the country’s system construction, reduce excessive government intervention and advocate rational investment philosophy for Chinsese investors. The SSE50 Index also been tested by Li and Zhang (2017) performed the unit root test, serial correlation test and (G) ARCH model method to analyze the effectiveness of the stock index and futures market. The dataset they chose is the high-frequency data of every five minutes since the early days of CSI 500 and SSE50 on April 16, 2015 to June 16, 2015 and they found the weak-form efficiency appeared in the Chinses stock index and future market. They also suggested the financial reform and structural reform by supply-side to be taken by Chinese government.

This paper examines day of the week and month of the year effects in seventeen European stock market indexes in the period 1994-2007. We discuss the shortcomings of model specifications and tests used in previous work, and propose a simpler specification, usable for detecting all types of calendar effects. Recognizing that returns are non-normally distributed, autocorrelated and that the residuals of linear regressions are variant over time, we use statically robust estimation methodologies, including bootstrapping and GARCH modeling. Although returns tend to be lower in the months of August and September, we do not find strong evidence of across-the-board calendar effects, as the most favorable evidence is only country-specific. Additionally, using rolling windows regressions, we find that the stronger country-specific calendar effects are not stable over the whole sample period, casting additional doubt on the economic significance of calendar effects. We conclude that our results are not immune to the critique that calendar effects may only be a “chimera” delivered by intensive data mining.

Volatility is a prevailing characteristic of stock markets that has major consequences in financial activities such as risk management, investment decisions and portfolio valuation, to cite just a few. Thus, understanding its im- plications is crucial to accurately assess investment risk and develop trading strategies. One important feature that characterizes volatility is long memory. Originally dicovered by Hurst [1] in the domain of hydrology, this concept was rapidly extended to other domains of sci- ence such as geophysics, biology, etc. According to this author, who derived the so-called Hurst exponent, two different situations could occur while analyzing the de- gree of memory in a process: (a) for H = 1/2 we have the usual Brownian motion; but (b) for H 6= 1/2 there is evidence of long range correlations. For an overview of the various estimators of the Hurst exponents such as rescaled range analysis (R/S) and detrended fluctuation analysis (DFA) refer to Taqqu et al. [2].

In this study the dynamic of the Brazilian stock market is explored from the point of view of the behavior of a group of stocks that were frequently present in the Sao Paulo Stock Exchange Index (Ibovespa) in the period between 1995 and 2003. Using the sample we study the possible factors that determine the behavior of securities. The predictability of the behavior of a stock is related to the volatility of the asset’s return. If the volatility of stock returns follows a logic that can be foreseen then it is possible to estimate the variation in the price of the security. Obviously the possibility of producing an estimate of the behavior of a stock reflects the fact that markets are not fully efficient. Various works have been developed with the idea of producing an explanation for the behavior of the volatility of stock returns. Among the approaches existing on volatility behavior three will be developed in this study: the gearing theory (Christie, 1982), the volatility feedback theory (Pindyck, 1984) and the divergence of opinion between economic agents model (Hong and Stein, 2003). According to Lo and Wang (2000), the price and traded volume of assets are fundamental building blocks when it comes to constructing any theory about the interaction of agents in the market.

In the overall, it appears that the use of entropy as a measure of uncertainty allows better insights over the identification of volatile markets, by distinguishing them more sharply, than simply using the standard deviation. This leads us to the conclusion that entropy is more general and better suited for describing stock market volatility with its generality arising directly from the fact that it can be computed from metric and non-metric data. Apart from that the major advantages of entropy when compared to the standard deviation can be summarized as follows [12]: (i) it incorporates much more information than the latter; (ii) it is not dependent upon any particular distribution; in other words, it is distribution free, thus avoiding the introduction of errors through the fitting of the distribution of returns to a normal-like distribution. This is especially true when dealing with non-symmetric distributions with generally non-normal additional moments, which seems to be the case in some phenomena in Finance; (iii) Since entropy is independent of the mean for all types of distributions, it satisfies the first order conditions and (iv) finally, due to its common understanding of mean uncertainty, it also serves as a measure of dispersion.

Abstract: This paper performs a thorough statistical examination of the time-series properties of the daily market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies not only on the widespread consensus that the VIX is a barometer of the overall market sentiment as to what concerns investors’ risk appetite, but also on the fact that there are many trading strategies that rely on the VIX index for hedging and speculative purposes. Prelimi- nary analysis suggests that the VIX index displays long-range dependence. This is well in line with the strong empirical evidence in the literature supporting long memory in both options-implied and realized variances. We thus resort to both parametric and semiparametric heterogeneous autore- gressive (HAR) processes for modeling and forecasting purposes. Our main findings are as follows. First, we confirm the evidence in the literature that there is a negative relationship between the VIX index and the S&P 500 index return as well as a positive contemporaneous link with the volume of the S&P 500 index. Second, the term spread has a slightly negative long-run impact in the VIX index, when possible multicollinearity and endogeneity are controlled for. Finally, we cannot reject the linearity of the above relationships, neither in sample nor out of sample. As for the latter, we actually show that it is pretty hard to beat the pure HAR process because of the very persistent nature of the VIX index.

There are several studies with different approaches that confirm the relationship between politics and stock market volatility. In the paper by (Bialkowski, Gottschalk, & Wisniewski, 2008) the authors proceed to show that, in OECD countries, stock markets can become very unsettled during periods of important political changes. In this paper it is demonstrated that National Elections affect the stock market volatility in the days that surround the Election Day. Apart from these results, the authors found that markets with short trading history exhibit stronger reaction.

These methodologies allowed us to gather some of the following results. Focusing first in the return co-movements, time-varying correlations are fitter to represent reality. Thus, Greece and United States stand out as the two most independent countries of our sample, whilst France and the Netherlands are the most correlated ones. Regarding the volatility spillovers, the methodology from Diebold and Yilmaz (2012) overcomes the problem regarding the ordering of variables and provides a spillover index that appears to coincide with major economic events/crisis, namely the dotcom, the subprime, the sovereign debt and the Russian financial crises. In the 11 stock markets considered, the level of volatility spillovers is substantially high (79,2%), emphasizing the importance of economic integration of euro area countries in the transmission of volatility. Furthermore, much like in the return co-movements, France and the Netherlands are, on average, transmitters of volatility, as both countries registered the highest levels of net spillovers. On the contrary, Greece stands out as the main receiver of volatility, followed by Ireland and Portugal. In fact, these countries are amongst the most affected economies by recent crises. Although we did not utilize the exact same database to compute both the daily and the weekly standard deviations, the overall findings point that both approaches are in tune and in consistency with financial and economic environments. In addition, this dissertation has the particularity of analyzing the connection among two measures of systemic stress and the volatility spillover index. A positive correlation concerning the CISS and the volatility spillover index is illustrated, transpiring signs of co-movement. However, the same does not apply over the spillover ratio and the FFSI.

Providing operational oceanographic data on biological and chemical variables has become an issue of concern over the last years. The demand for this kind of information arises from a range of fields and applications such as scientific research on marine ecosystems, monitoring of seawater quality and decision-making support for marine and coastal management. A recent question- naire conducted by ICES-WGOOFE (International Council for the Exploration of the Sea, Working Group on Operational Oceanographic Products for Fisheries and Environment) showed that temperature, currents, salinity, chlorophyll standing stock and primary production were the most requested products among ocean sciences scientific community, who scored several biological parameters in the top 10 rankings of products on demand [1]. There is a well known increasing interest in combined physical, chemical and biological operational products, including near-real time and forecast, which are currently possible due to facilitated access to computational resources, development of numerical solutions and improvement of modelling algorithms and perfor- mance.

For example, there are good reasons to believe that speculative financial asset changes have in general an asymmetric behaviour. As mentioned above, the leverage effect was found in many empirical studies that analyse the behaviour of stock returns. This circumstance highlights the need for using asymmetric models when one is analysing data on stock market behaviour. Asymmetric behaviour in financial data can be detected with relatively ease, since volatil- ity raises more for negative shocks than for positive shock with the same amplitude. In order to account for this phenomenon, two extensions of the basic GARCH model can be used, among other possibilities: the Threshold Autoregressive Conditional Heteroskedasticity (TARCH) and the Exponential Generalised Autoregressive Conditional Heteroskedasticity (EGARCH) mod- els (see Nelson [10], Zakoian [25], and Glosten et al. [26]).

Predicting stock market prices is far from being a trivial task. The uncertainty and volatility that characterize stock markets makes very hard and sometimes even impossible to predict what will happen. Understanding what can and will happen in financial markets is extremely important nowadays to everyone who needs to plan investments, management of risks or allocate efficiently their resources. In order to address this extremely hard problem, computational intelligence techniques have been proposed and applied with some degree of success. This computational intelligence techniques are often referred as Machine Learning and Predictive Models. In this work project we studied the application of evolutionary algorithms, namely Genetic Programming, in order to address this problem. A comparison between the standard approach of GP and some recent developments on GP systems, which incorporates the concept of semantics in the evolution process trough the definition of new genetic operators.

In a 1993 letter to the Shareholders of Berkshire Hathaway Inc., Warren Buffet quoted the American economist Ben Graham as "In the short-run, the market is a voting machine — reflecting a voter-registration test that requires only money, not intelligence or emotional stability — but in the long-run, the market is a weighing machine" (Buffett, 1993). What he means is that emotions control the short-run while a company’s assets and profits control the long-run. We can see one example of this when Twitter mood can be used to predict up and down movements in the closing values of the Dow Jones Industrial Average (DJIA) with an accuracy of 86.7% (Bollen, Mao, & Zeng, 2011). Even though the short-run is very volatile, the long-run follows a more stable path and, at least in comparison, more predictable.

As pointed out previously in section 2.2.4 simple GARCH models also present some other problems. Black (1976) found evidence that stock returns are negatively correlated with changes in returns volatility. This means that volatility tends to increase in response to bad news and decrease in response to good news. GARCH models do not account for that since they only assume that the magnitude and not the positive or negative sign of excess returns influences the conditional volatility. Another limitation is that non-negativity constraints may be violated due to the fact that volatility is not constant over time and they can create difficulties in estimating GARCH models. Engle and Bollerslev (1986) focused on studying the persistence of shocks and their impact on conditional variance. If they persist indefinitely, there is the risk that they have significant impact in long lived capital goods (Poterba and Summers, 1986). These are the three main drawbacks of simple GARCH models according to Nelson (1991), thus in order to address to the drawbacks he adopted an exponential GARCH model.

This paper analyses the behaviour of volatility for several international stock market indexes, namely the SP 500 (USA), the Nikkei (Japan), the PSI 20 (Portugal), the CAC 40 (France), the DAX 30 (Germany), the FTSE 100 (UK), the IBEX 35 (Spain) and the MIB 30 (Italy), in the context of non-stationarity. Our empirical results point to the evidence of the existence of integrated behaviour among several of those stock market indexes of different dimensions. It seems, therefore, that the behaviour of these markets tends to some uniformity, which can be interpreted as the existence of a similar behaviour facing to shocks that may affect the worldwide economy. Whether this is a cause or a consequence of market globalization is an issue that may be stressed in future work.

This is the peer reviewed version of the following article: Curto, J., Pinto, J. C. & Tavares, G. N. (2009). Modeling stock markets' volatility using GARCH models with normal, Student's t and stable Paretian distributions. Statistical Papers. 50 (2), 311-321, which has been published in final form at https://dx.doi.org/10.1007/s00362-007-0080-5. This article may be used for non-commercial purposes in accordance with the Publisher's Terms and Conditions for self-archiving.

the results achieved. Finally, the purely local volatility effects are larger for Austria, Ireland and Portugal (means of 81.75%, 81.91% and 88%, respectively) than for the other countries (the means range between 27% and 78%). To all purposes of our study all the Non-EMU countries and the Non-EU country behave like EMU-member countries, which give an idea of how integrated the euro countries are. Figures 4 to 7 show the time series evolution of the variance ratios for Germany, UK (representing the non-EMU countries), Portugal and Spain. We chose these countries because Germany and the UK are a wide representation of the European stock markets, and the most liquid ones; and Portugal and Spain because of the interest that those two indexes bring to our study once we are in their financial space. The European variance ratio generally increases over the sample period for all countries except (again) Sweden and the UK, for which it appears to be stable.

Of note, results from the empirical study show that browsers prefer the site that is efficient, excellent, and present to them an economic value than the one with a good visual appeal and entertaining aspect. These findings lend us to conclude that the asked sample is purely calculator who looks for the good price-quality report. Besides, the analysis regression demonstrates that the entertainment value, economic value and excellence were found to be significantly related to future site patronage intent. Consistent with findings of Mathwick, Malhotra and Rigdon (2001), the site preference appeared as an important predictor to the future site patronage intent. Finally, and not surprising, all the dimensions of the site perceived value strongly influence the e-loyalty intention.

One of the most powerful effects manifested on the stock markets is the tendency exhibited by stocks issued by small companies (measured by their market value) to record returns higher than companies with a bigger capitalization. On the Romanian market, [Todea, 2008] has analyzed the manifestation of the size effect between 13.10.1999 and 31.03.2003 starting from a sample of 49 issuers grouped in three categories after their market capitalization. With this data the author then formed equally weighted portfolios and portfolios weighted after their size studying the resulted returns. As a conclusion of the study, the author stated that, regardless of the way in which returns were computed, on the Romanian Market a size effect is manifested which means that small caps tend to record a higher return compared with the medium and big caps. Using ANOVA-F decomposition, the author rejected the hypothesis of equality for the observed means of the equally weighted portfolios with a probability of 99% and 89% in the case of the portfolios weighted according to their size.