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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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]).

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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.

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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.

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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.

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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.

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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.

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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.

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