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Modely finančních časových řad a jejich aplikace
Kladívko, Kamil ; Arlt, Josef (advisor) ; Witzany, Jiří (referee) ; Cipra, Tomáš (referee)
I study, develop and implement selected interest rate models. I begin with a simple categorization of interest rate models and with an explanation why interest rate models are useful. I explain and discuss the notion of arbitrage. I use Oldrich Vasicek's seminal model (Vasicek; 1977) to develop the idea of no-arbitrage term structure modeling. I introduce both the partial di erential equation and the risk-neutral approach to zero-coupon bond pricing. I briefly comment on affine term structure models, a general equilibrium term structure model, and HJM framework. I present the Czech Treasury yield curve estimates at a daily frequency from 1999 to the present. I use the parsimonious Nelson-Siegel model (Nelson and Siegel; 1987), for which I suggest a parameter restriction that avoids abrupt changes in parameter estimates and thus allows for the economic interpretation of the model to hold. The Nelson-Siegel model is shown to fit the Czech bond price data well without being over-parameterized. Thus, the model provides an accurate and consistent picture of the Czech Treasury yield curve evolution. The estimated parameters can be used to calculate spot rates and hence par rates, forward rates or discount function for practically any maturity. To my knowledge, consistent time series of spot rates are not available for the Czech economy. I introduce two estimation techniques of the short-rate process. I begin with the maximum likelihood estimator of a square root diff usion. A square root di usion serves as the short rate process in the famous CIR model (Cox, Ingersoll and Ross; 1985b). I develop and analyze two Matlab implementations of the estimation routine and test them on a three-month PRIBOR time series. A square root diff usion is a restricted version of, so called, CKLS di ffusion (Chan, Karolyi, Longsta and Sanders; 1992). I use the CKLS short-rate process to introduce the General Method of Moments as the second estimation technique. I discuss the numerical implementation of this method. I show the importance of the estimator of the GMM weighting matrix and question the famous empirical result about the volatility speci cation of the short-rate process. Finally, I develop a novel yield curve model, which is based on principal component analysis and nonlinear stochastic di erential equations. The model, which is not a no-arbitrage model, can be used in areas, where quantification of interest rate dynamics is needed. Examples, of such areas, are interest rate risk management, or the pro tability and risk evaluation of interest rate contingent claims, or di erent investment strategies. The model is validated by Monte Carlo simulations.
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Econometric Analysis of Microeconomic Processes. Application on Wages in the Czech Republic
Kalčevová, Jana ; Pánková, Václava (advisor) ; Arlt, Josef (referee) ; Cahlík, Tomáš (referee)
This thesis is focused on wages models on the czech labor market in 1996 and 2002. Wages models are built on non-trivial mathematical background and parameters of given models are estimated by methods based on sum of squared residuals and also not often used quantile regression. The quantile regression theory is described in the thesis together with test statistics. Properties of estimations, demonstration examples and proposal of practical application are also indroduced. The theory was applied to two large-size data-files, recieved results show the difference between years 1996 and 2002; a comparison with European Union countries is also given.
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Empirical Testing of the New Keynesian Phillips Curve in the Czech Republic
Plašil, Miroslav ; Arlt, Josef (advisor) ; Pánková, Václava (referee) ; Komárek, Luboš (referee)
New keynesian Phillips curve (NKPC) has become a central model to study the relation between inflation and real economic activity, notably in the framework of optimal monetary policy design. However, some recent evidence suggests that empirical data are usually at odds with the underlying theory. The model due to its inherent structure represents a statistical challenge in its own right. Since Galí and Gertler (1999) published their seminal paper introducing estimation via GMM techniques, they have triggered a heated debate on its empirical relevance. Their approach has been heavily criticised by later authors, mainly on the grounds of questionable behaviour of GMM estimator in the NKPC context and/or its small sample properties. The common criticism includes sensitivity to the choice of instrument set, weak identification and small sample bias. In this thesis I propose a new estimation strategy that provides a remedy to above mentioned shortcomings and allows to obtain reliable estimates. The procedure exploits recent advances in GMM theory as well as in other fields of statistics, in particular in the area of time series factor analysis and bootstrap. The proposed estimation strategy consists of several consecutive steps: first, to reduce a small sample bias resulting from excessive use of instruments I summarize all available information by employing factor analysis and include estimated factors into information set. In the second step I use statistical information criteria to select optimal instruments and eventually I obtain confidence intervals on parameters using bootstrap method. In NKPC context all these methods were used for the first time and can also be used independently. Their combination however provides synergistic effect that helps to improve the properties of estimates and to check the efficiency of given steps. Obtained results suggest that NKPC model can explain Czech inflation dynamics fairly well and provide some support for underlying theory. Among other things the results imply that the policy of disinflation may not be as costly with respect to a loss in aggregate product as earlier versions of Phillips curve would indicate. However, finding a good proxy for real economic activity has proved to be a difficult task. In particular we demonstrated that results are conditional on how the measure is calculated, some measures even showed countercyclical behaviour. This issue -- in the thesis discussed only in passing -- is a subject of future research. In addition to the proposed strategy and provided parameter estimates the thesis brings some partial simulation-based findings. Simulations elaborate on earlier literature on naive bootstrap in GMM context and study performance of bootstrap modifications of unit root and KPSS test.
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Wavelet Transform and its Application in the Analysis of Economic and Financial Time Series
Bašta, Milan ; Arlt, Josef (advisor) ; Málek, Jiří (referee) ; Mareš, Milan (referee)
The thesis deals with a brief compilation of the theory of Fourier transform, linear filtration and a triad of wavelet transforms -- the maximal overlap discrete wavelet transform (MODWT), the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT). These transforms are among others applied to the analysis of the time-varying character of variability in the time series, to the detection of events of significant changes of variability, to the removal of noise in the time series (denoising) and to the time-scale analysis of the relationship of two time series. The analyzed time series used in this thesis are the logarithm of the Garman-Klass estimate of the historical volatility, the time series of stock returns and the logarithm of the monthly inflation rate. In some cases artificial time series are analyzed. The procedures and methods introduced in the thesis might be well implemented in the analysis of other economic and financial time series. The contribution of the thesis is a brief and easy-to-use compilation of the wavelet theory and the application of the wavelet transform to such financial and economic time series, where such an analysis tool has never been applied before. New insights into the properties of time series are thus obtained, insights, which might be hardly recovered by traditional means and methods.
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Perceived Inflation - The New Phenomenon After The Euro Changeover
Smrčková, Gabriela ; Šaroch, Stanislav (advisor) ; Arlt, Josef (referee) ; Lacina, Lubor (referee) ; Čech, Zdeněk (referee)
The thesis focuses on theoretical and empirical analysis of the deterioration of price perception among European consumers after the introduction of the euro banknotes and coins. The aim of the thesis is to find out the major factors which provoked a rapid increase of the indicator of perceived inflation after 2002, while inflation in euro zone continued developing moderately, and to derive some conclusions for economic policy of candidate countries to euro introduction. There are at least four reasons why it matters to analyse the distortion of the indicator of perceived inflation from the HICP index which measures the inflation in the euro zone. Firstly, from the political and economical perspective there is a risk of weak support for the European monetary integration. Secondly, the distortion of price perception can deteriorate the belief in the official statistics. Thirdly, the inaccurate price perception can lead to wrong consumer decisions having an impact on a volume or a structure of national consumption. Last but not least, there is a risk of a negative impact on price expectations. In order to meet its goals, the thesis stases several hypotheses which analyse the problem from two perspectives. Firstly, from a mere review of detailed prices in the period of the introduction of the euro banknotes and coins (Hypotheses: (i) the consumers are more sensitive towards some price movements, therefore the deterioration of the indicator of perceived inflation can be explained by the abnormal evolution of some prices in the critical period of the euro introduction, (ii) convergence of the new euro prices towards round prices lead to frequent price movements having an impact on price perception) Secondly, from the point of view of limited perception of prices by consumers (Hypothesis: (iii) consumers does not behave rationally when deciding about prices therefore they are not able to perceive all price movements). The thesis is organized in three chapters. The first chapter is mainly theoretical and introduces the problem of perceived inflation. It is followed by two chapters which combine empirical and theoretical analysis of the drivers of perceived inflation after the euro introduction. Within its conclusions, the thesis identifies a combination of several factors that caused a rapid increase of the indicator of perceived inflation after the changeover which have their origins in a changed monetary environment. The effects coming from using rounded conversion rates instead of the official ones in mental conversions of the new euro prices to the old prices in national currencies, limited the possibility for consumers to perceive correctly the price movements. Moreover, higher sensitivity towards price increases in comparison to price decreases and a higher inflation in some areas led to blaming the new currency for high inflation. The irrational behaviour of consumers in relation to prices was strengthened by the effects of the new currency. The thesis also states that while the increase of the indicator of perceived inflation had no negative impact on inflation expectations, the deterioration of inflation perception might negatively influence consumption.
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Kvantitativní analýza interakcí fiskální politiky a reálné ekonomiky v České republice
Valenta, Vilém ; Hronová, Stanislava (advisor) ; Arlt, Josef (referee) ; Slačálek, Jiří (referee)
After many decades, macroeconomic effects of fiscal policy have returned to the centre of the economic policy debate. Both automatic fiscal stabilizers and discretionary fiscal stimuli have been used to support aggregate demand during the recent global economic crisis with a subsequent need for large-scale fiscal consolidations. In this context, a proper assessment of the size of automatic fiscal stabilizers and fiscal multipliers represents a key input for fiscal policymaking. This dissertation provides a quantitative analysis of the interactions between fiscal policy and real economy in the Czech Republic. The impact of real economy developments on public finances is assessed based on the methods of the OECD, the European Commission and the ESCB for the identification of general government structural balances, i.e. balances adjusted for effects of the economic cycle and net of one-off and other temporary transactions. I find that the underlying fiscal position, as approximated by the government structural balance, was mostly below the level stabilising the debt-to-GDP ratio since mid-1990s. An indistinct improvement in the structural balance can be identified in the period 2004--2007, which was subsequently reversed by the adverse structural impact of the world economic crisis. At the same time, dynamics of unadjusted fiscal balance was largely determined by one-off transactions in the past. The effects of fiscal policy on real economy are analysed using the structural VAR approach. I find that an increase in government spending has a temporary positive effect on output that peaks after one to two years with a multiplier of around 0.6. Tax multiplier appears to be small and, in contrast to standard Keynesian assumptions, positive. Government spending is supportive to private consumption, contradicting the hypothesis of Ricardian equivalence, but it crowds out private investment in the short run. The results should be interpreted with caution, as the analysis is complicated by rapidly changing economic environment in the period of the economic transition, relatively short available time series and a large number of one-off fiscal transactions.
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Platnost Hyptézy očekávání v ČR. Analýza krátkého konce termínové struktury PRIBOR.
Binter, Roman ; Kodera, Jan (advisor) ; Arlt, Josef (referee) ; Vošvrda, Miloslav (referee)
Hypotéza očekávání (HO) termínové struktury úrokových sazeb je jednou z nejdéle používaných ekonomických teorií. Ji? od svého vzniku byla předmětem výzkumu mnoha ekonomických a ekonometrických studií. I p°es intenzivní výzkum trvající déle ne? 100 let jsou d?kazy o její platnosti sporné. Důležitými výjimkami v tomto ohledu jsou práce B. Hansena, J. Campbella a R. Shillera, kteří dokládají platnost HO pro případ dlouhodobých "US Treasury bonds", dále A. Longstaffa jehož studie se zaměřuje na krátkodobé instrumenty na amerických trzích a K. Cuthbertsona, který studuje londýnský trh mezibankovních depozit. Tato práce zkoumá platnost HO pro krátkodobé úrokové sazby Pražského mezibankovního trhu. Vzhledem k nejednoznačnosti výsledků v této oblasti aplikuji řadu statistických metod s cílem podrobného zmapování dynamiky sazeb PRIBOR.
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Testing for the weak form of the efficient market hypothesis on the Czech stock market by linear and nonlinear methods
Tran, Van Quang ; Musílek, Petr (advisor) ; Arlt, Josef (referee) ; Vošvrda, Miloslav (referee)
Hypotéza efektivního trhu postuluje, že ceny akcií na efektivním trhu reflektují všechny informace a jsou dobrými odhady jejich hodnot. Platnost této hypotézy byla testována na řadách denních a hodinových výnosností indexu PX a dalších 3 nejlikvidnějších titulů na českém akciovém trhu lineárními a nelineárními metodami. Ověřovaly se také přítomnost deterministického chaosu v těchto řadách a možnost predikovat výnosnosti různými ekonometrickými modely. Bylo zjištěno, že výnosnosti nejsou nezávislé a lze je predikovat zvolenými modely přesněji než modelem náhodné procházky. Přítomnost chaosu nelze jednoznačně prokázat. Přes tato zjištění se však český akciový trh nechová neefektivně.
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Slabá forma efektivnosti středoevropských akciových trhů
Hájek, Jan ; Musílek, Petr (advisor) ; Arlt, Josef (referee) ; Mejstřík, Michal (referee)
Disertační práce komplexně zkoumá efektivnost akciových trhů v ČR, Polsku, Maďarsku a Slovinsku v období 1995-2005, a to ve smyslu slabé formy hypotézy efektivních trhů. Ačkoli hypotéza je již delší dobu významnou součástí ekonomické teorie, která se zabývá chováním finančních trhů, na středoevropských trzích nebyla vzhledem k jejich krátké historii empiricky zmapována v takové míře a detailu, jako na vyspělých kapitálových trzích. Hlavním cílem práce je zanalyzovat, zda je možné na základě veřejně dostupných informací o historickém vývoji cen akciových titulů nebo indexů dlouhodobě dosahovat ekonomicky významných abnormálních výnosů, zda jednotlivé národní trhy vykazují obdobnou míru efektivnosti a zda mohlo dojít v čase ke změnám v jejich chování. Závěry jsou formulovány na základě relativní míry jejich efektivnosti vzhledem k vyspělým kapitálovým trhům, které jsou považovány za maximálně efektivní. Vedle časových řad denních, týdenních i měsíčních výnosů hlavních regionálních indexů jsou analyzovány také výnosy jednotlivých titulů, ze kterých se indexy skládají. Diskutován je i vliv nesynchronního obchodování na velikost vykazovaných lineárních závislostí. V případě ČR je vedle testu slabé formy efektivnosti analyzována reakce kurzů na nové fundamentální informace o nabídkách převzetí, tj. středně silná forma efektivnosti. Na základě sledování chování cen před zveřejněním informací lze také zkoumat, zda dochází k obchodování na základě vnitřních informací.
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