No description available.

Η μελέτη αυτή ασχολείται με την ανάλυση των χρονολογικών σειρών ως αντικείμενο κατανόησης του παρελθόντος και πρόβλεψης του μέλλοντος. Στα πρώτα κεφάλαια γίνεται μια εισαγωγή στις χρονολογικές σειρές, ποια η χρησιμότητα τους και τι μπορούν αυτές να περιγράψουν, καθώς αναλύονται ορισμένες βασικές έννοιες αυτών, όπως διάφορα μέτρα και στασιμότητα, και αναλύονται χαρακτηριστικά όπως η τάση, η περιοδικότητα κ.α. Έπειτα εξετάζονται συγκεκριμένες κατηγορίες χρονολογικών σειρών, όπως είναι οι στάσιμες και μη στάσιμες, και γίνεται εκτίμηση των παραμέτρων των παραπάνω σειρών με διαφορές μεθόδους. Τέλος, παρουσιάζονται διάφοροι μέθοδοι πρόβλεψης με την βοήθεια των χρονολογικών σειρών και γίνεται εφαρμογή αυτών των μεθόδων. / This work deals with time series analysis in a way to understand the past and predict the future. In the firsts chapters an introduction to time series was presented, in order to figure out their usage and what they can describe such as, main concerns’ analysis, (e.g. measures, stationary) and various other analysis characteristics as trend, variation, etc. In addition specific categories of time series were examined, like stationary and non stationary time series, and estimate same of their parameters with various methods. In the final chapters, various estimation methods were presented with the help of time series and who these methods are applied in practice.

Standard and Poor¡¦s (S & P), a global leading corporation in providing credit rating, published the sovereign rating outlook of Taiwan which was ¡§negative sign¡¨ at the end of 2007. The main reason was that the situation of public finance continued worsening. Based on traditional economic theory, the increased deficits or debts led to higher interest rates, and the increasing burden on enterprises for paying more loan cost, would have more adverse effects on the domestic investment activities. Therefore, this study is intended to explore the relationships among the long-term interest rates of public bonds, the outstanding debts, fiscal deficits, and government expenditure in Taiwan by analyzing 53 seasonal data from 1994:4 to 2007:4 as the samples. The findings indicate that no structure breaking points exist in every variable by using CUSUM test, and almost every variable is integrated of order one in unit root test. The results also reveal that there is no long-term relationship among the deficits, government expenditure, and interest rates using the cointegration analysis. There are probably two reasons for explanation: one is that people will increase saving automatically, and another is that the increased interest rates in the tax cut may be offset by the decreased interest rates in debts financing. Moreover, the outstanding debts and interest rates exist a significant negative relationship of long-term equivalence, and further variance decomposition shows that the effect of debts on interest rates is higher than the effect of interest rates on debts in the variable¡¦s explanatory ability. To explain the significant negative relationship, the possible main causes are liquidity factor, and the psychological anticipation of saving in public bond form directly or indirectly; the secondary cause is the fluctuation of interest rates affects the willingness of government financing.

The goal in this thesis is to develop a novel statistical approach to identity functional interactions between regions in a brain network. Wavelets are effective for capturing time varying properties of non-stationary signals because they have compact support that can be compressed or stretched according to the dynamic properties of the signal. Wavelets provide a multi-scale decomposition of signals and thus can be few for exploring potential cross-scale interactions between signals. To achieve this, we propose the scale-specific sub-processes of a multivariate locally stationary wavelet stochastic process. Under this proposed framework, a novel cross-scale dependence measurement is developed, which provides a measure for dependence structure of components at different scales of multivariate time series. Extensive simulation experiments are conducted to demonstrate that the theoretical properties hold in practice. The developed cross-scale analysis is performed on the electroencephalogram (EEG) data to study alterations in the functional connectivity structure in children diagnosed with attention deficit hyperactivity disorder (ADHD). Our approach identified novel interesting cross-scale interactions between channels in the brain network. The proposed framework can be extended to other signals, which can also capture the statistical association between the stocks at different time scales.

No description available.

This thesis is comprised of five papers that all relate to bootstrap methodology in analysis of non-stationary time series. The first paper starts with the fact that the Dickey-Fuller unit root test using asymptotic critical value has bad small sample performance. The small sample correction proposed by Johansen (2004) and bootstrap are two effective methods to improve the performance of the test. In this paper we compare these two methods as well as analyse the effect of bias-adjusting through a simulation study. We consider AR(1) and AR(2) models and both size and power properties are investigated. The second paper studies the asymptotic refinement of the bootstrap cointegration rank test. We expand the test statistic of a simplified VECM model and a Monte Carlo simulation was carried out to verify that the bootstrap test gives asymptotic refinement. The third paper focuses on the number of bootstrap replicates in bootstrap Dickey-Fuller unit root test. Through a simulation study, we find that a small number of bootstrap replicates are sufficient for a precise size, but, with too small number of replicates, we will lose power when the null hypothesis is not true. The fourth and last paper of the thesis concerns unit root test in panel setting focusing on the test proposed by Palm, Smeekes and Urbain (2011). In the fourth paper, we study the robustness of the PSU test with comparison with two representative tests from the second generation panel unit root tests. In the last paper, we generalise the PSU test to the model with deterministic terms. Two different methods are proposed to deal with the deterministic terms, and the asymptotic validity of the bootstrap procedure is theoretically checked. The small sample properties are studied by simulations and the paper is concluded by an empirical example. / <p>Ogiltigt ISBN: 978-91-554-9069-0</p>

The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1

<p>This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the&nbsp / Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots)&nbsp / and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South&nbsp / African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric&nbsp / Brownian motion time series should be characterised by the Hurst exponent of &frac12 / . A value of a Hurst exponent different from that would indicate the presence of long memory or&nbsp / fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by&nbsp / assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the&nbsp / rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.</p>

<p>This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the&nbsp / Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots)&nbsp / and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South&nbsp / African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric&nbsp / Brownian motion time series should be characterised by the Hurst exponent of &frac12 / . A value of a Hurst exponent different from that would indicate the presence of long memory or&nbsp / fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by&nbsp / assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the&nbsp / rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.</p>

Magister Scientiae - MSc / This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric Brownian motion time series should be characterised by the Hurst exponent of ½. A value of a Hurst exponent different from that would indicate the presence of long memory or fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added. / South Africa