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Multifractal approaches in econometrics and fractal-inspired robust regression
Kalina, Jan
While the mainstream economic theory is based on the concept of general economic equilibrium, the economies throughout the world have recently been facing serious transformations and challenges. Thus, instead of a convergence to equilibrium, the economies can be regarded as unstable, turbulent or chaotic with properties characteristic for fractal or multifractal processes. This paper starts with a discussion of recent data analysis tools inspired by fractal or multifractal concepts. We pay special attention to available data analysis tools based on reciprocal weights assigned to individual observations - these are inspired by an assumed fractal structure of multivariate data. As an extension, we consider here a novel version of the least weighted squares estimator of parameters for the linear regression model, which exploits reciprocal weights. Finally, we perform a statistical analysis of 31 datasets with economic motivation and compare the performance of the least weighted squares estimator with various weights. It turns out that the reciprocal weights, inspired by the fractal theory, are not superior to other choices of weights. In fact, the best prediction results are obtained with trimmed linear weights.
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Wavelet portfolio optimization: Investment horizons, stability in time and rebalancing
Kvasnička, Tomáš ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of the thesis is to analyse impact of wavelet covariance estimation in the context of Markowitz mean-variance portfolio selection. We use a rolling window to apply maximum overlap discrete wavelet transform to daily returns of 28 companies from DJIA 30 index. In each step, we compute portfolio weights of global minimum variance portfolio and use those weights in the out-of- sample forecasts of portfolio returns. We let rebalancing period to vary in order to test influence of long-term and short-term traders. Moreover, we test impact of different wavelet filters including Haar, D4 and LA8. Results reveal that only portfolios based on the first scale wavelet covariance produce significantly higher returns than portfolios based on the whole sample covariance. The disadvantage of those portfolios is higher riskiness of returns represented by higher Value at Risk and Expected Shortfall, as well as higher instability of portfolio weights represented by shorter period that is required for portfolio weights to significantly differ. The impact of different wavelet filters is rather minor. The results suggest that all relevant information about the financial market is contained in the first wavelet scale and that the dynamics of this scale is more intense than the dynamics of the whole market.
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Capital Market Hypotheses and Their Statistical Implications: A Comparative Study
Petras, Petr ; Krištoufek, Ladislav (advisor) ; Křehlík, Tomáš (referee)
In this bachelor thesis we focus on different Market Hypotheses. Specifically on Efficient Market Hypothesis, Fractal Market Hypothesis and Coherent Market Hypothesis. In the first part of the work we provide description of researched hypotheses and methods used for testing. In the second part of the work we run test on time series of share markets, gold markets and currency markets and test if our hypotheses can provide explanation about price changes on those markets. For Efficient Market Hypothesis we wonder if prices are following random walk (via augmented Dickey-Fuller test), if residuals are normally distributed (via Shapiro-Wilk and Jarque-Bera tests) and if residuals are uncorrelated (via Box-Pierce test). For Fractal Market Hypothesis we are trying to find value of Hurst exponent via Rescaled Range analysis. This exponent describes if time series are persistent or not. And for Coherent Market Hypothesis we develop simple method for testing if some time periods can yield above-average revenues, thanks to increased mean and decreased standard deviation. After that we find out what are consequences of short time series and different frequencies for obtaining data points and we learn that some hypotheses describes different time periods or lengths better and are not so good for different ones. Powered...
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Modelování vkusu na finančních trzích
Vácha, Lukáš ; Vošvrda, Miloslav
Heterogeneous agents model with the stochastic forecasts formation is considered. Fundamentalists rely on their model employing fundamental information basis to forecast the next price period. Chartists determine whether current conditions call for the acquisition of fundamental information in a forward looking manner rather than relying on the past performance. This paper shows an influence of the mood change on the financial market structure. This feature is simulated by changing of the forecast structure trend.
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Fractal Market Hypothesis and R/S analysis of the Czech capital market
Barkhanskyy, Kostyantyn ; Korbel, Jiří (advisor)
This work is aimed at the modern theory of the capital market -- Fractal Market Hypothesis. The content of my work includes both basic theoretical assumptions of the hypothesis and aplication of R/S analysis on the Czech capital market. The goal of this bachelor's thesis is to confirm Czech capital market nonlinear structure with determination it's fractal features and set the memory period by R/S analysis output.
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