This work presents results of studies on possibilities of finding periodicity related to solar activity changes in annual growth sequences of trees. The analyzed material were subfossil oak trunks (so-called black oaks) lifted from alluvial deposits of the Vistula river in the vicinity of Cracow, which had been felled and subsequently buried around 8000, 4600, 3500, 2000 and 1000 years ago. Treatment of the tree-ring data with methods of spectral analysis of time series revealed that most of the analyzed annual growth sequences contained distinct cyclic components, among them such ones of which periods might have corresponded to periods of solar activity cyclic changes. The obtained results suggest that lengths of the identified cycles were increasing between 8000 and 4600 years ago and decreasing in later millennia.
This paper presents results of investigations on possibilities of finding periodicity related to solar activity changes in annual growth sequences of trees. The research materials were six chronologies based on subfossil oak trunks (so-called black oaks) coming from alluvial deposits of the Vistula river in the vicinities of Cracow. The analyzed chronologies cover the period of the last 4000 years. Treatment of these data with the methods of spectral analysis of time series permitted to conclude that they all contained distinct cyclic components, of which periods could correspond to the periods of cyclic changes of solar activity. The results obtained confirm the earlier presented thesis that in the analyzed period of time the length of the basic, so-called 11-year (Schwabe) solar cycle declined to below 10 years.
During modeling of short-run exchange rate fluctuations, there is usually a need for taking into consideration some random-type conditions, i.e. it is necessary to abandon the fundamental exchange rate theories in favor of probabilistic modeling. Among stochastic models, of special interest are Markov models. The main advantages of Markov models include a relative simplicity of construction, easy inferences, well-known estimation methods and especially consistence of properties of these models with the observed properties of many real phenomena. Application of switching models is based on a general assumption that the examined time series can be presented as sequences of random variables of a known type of conditional distribution in all regimes. Known from literature propositions concerning the modeling of exchange rate with the use of switching models did not provide sufficiently good forecasts of the future exchange rate levels because of, among others, low frequency of data used for the construction of the model (quarterly or monthly data). The authors are going to continue the examination of the PLN exchange rate fluctuation with the use of Markov models that was started in this paper. The next stage of their work will be connected with conducting empirical research concerning the occurrence of calendar anomalies in the Polish currency market. For this purpose, a new method based on the Markov chains theory will be applied, which offers a new perspective to this problem. Testing o f the calendar time hypothesis has been considered so far mostly in the aspect of comparison of daily expected values and variances of exchange rate return rates. Then, on the basis of the da ta concerning exchange rates for high measurement frequency, a Ma rkov switching model will be constructed and used for description of the PLN depreciation and appreciation period.
PL
Prawidłowe oszacowanie kierunku zmian kursu wymiany może zmniejszyć ryzyko inwestycji w walutę lub może pozwolić na osiągnięcie większych dochodów z tej inwestycji. W opracowaniu tym autorzy przedstawiają propozycję zastosowania modeli Markowa do wykrycia i opisania prawidłowości rządzących procesem zmienności kursu walutowego. W pierwszej części została wykorzystana teoria łańcuchów Markowa do badania anomalii kalendarzowych występujących n a rynku walutowym związanych z efektem weekendowym lub efektem stycznia. W artykule przedstawiona została również metoda o parta na teorii łańcuchów Markowa, k tó ra może posłużyć d o zbadania wzajemnych powiązań pomiędzy zmiennością wolumenu obrotu oraz zmiennością cen dla terminowych kontraktów walutowych. W drugiej części zostaną przedstawione zagadnienia związane z budową i estymacją parametrów przełącznikowych modeli Markowa. W oparciu o modele przełącznikowe można prognozować zmiany kursu walutowego. Praca ma charakter teoretyczny. Badania empiryczne zostaną przeprowadzone w późniejszym terminie.
In the paper we present the examples of forecasts of time series with seasonal fluctuations. Based on the jackknife method we estimate variances of seasonal factors and the MSE of prediction. Jackknife method has been introduced by M. Quenouille (1949) and then it has been developed among others by J. Tukey (1958) and J. Shao, D. Tu (1995).
PL
W pracy zaproponowano wykorzystanie metody jackknife do prognozowania szeregów czasowych. Oprócz problemu prognozowania tą metodą, podjęto także problem oceny średniego błędu tak wyznaczanych prognoz. W oparciu o rzeczywiste dane zaprezentowane zostały przykłady prognozowania szeregów czasowych z wahaniami sezonowymi przy wykorzystaniu wersji jackknife metody wskaźników sezonowości. Oprócz wyznaczenia wartości prognozowanej w rozważanym przypadku będzie możliwa ocena wariancji błędu predykcji. Metodę jackknife wprowadził M. Quenouille (1949), a była rozwijana m. in. przez J. Tukey’a (1958) oraz J. Shao i D. Tu (1995).
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The short-term effects of ambient black smoke concentrations on total non-accidental, cardiovascular and respiratory mortalities in Nis, during the 2000-2003 period, were investigated. Daily measurements for black smoke (BS), as well as the daily number of deaths have been collected. Generalised linear models extending Poisson regression were applied. The e.ects of time trend, seasonal variations, days of the week, temperature, humidity and air pressure were adjusted. The per cent increase in the daily number of total deaths associated with a 10 μg/m3 increase in BS was 1.13% (0.08–2.20%). The e.ect size was slightly higher for cardiovascular mortality (1.25%, 95% CI: 0.53–1.97%). There was no signi.cant association between air pollution and respiratory mortality. These results indicate that current levels of ambient BS have signi.cant e.ects on total and cardiovascular mortalities in Nis.
In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.
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Monitoring data on water pH are presented for the period between 1972 and 2009 from the sampling stations Längden and Storgadden, at the entrance to the Gulf of Finland, Baltic Sea. The overall pH in the area ranged from 9.2 to 7.4, on average 8.1, and showed a significant decreasing trend during the winter period corresponding to a median annual decrease of 0.006. The data corroborate previous findings about a seasonal effect, where pH is higher during summer than winter.
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Higuchi's method is a procedure that, if applied appropriately, can determine in a reliable way the fractal dimension D of time series; this fractal dimension permits to characterize the degree of correlation of the series. However, when analyzing some time series with Higuchi's method, there are oscillations at the right-hand side of the graph, which can cause a mistaken determination of the fractal dimension. In this work, an appropriate explanation is given to this type of behaviour. Using the seismogram as a time series and the properties of the P and S waves, it is possible to use the properties of Higuchi's method to previously detect the arrival of the earthquake shacking stage, some seconds in advance, approximately 30-35 s in the case of Mexico City. Thus, we propose the Higuchi's method to characterize and detect the P waves in order to estimate the strength of the forthcoming S waves.
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Tectonism in the Himalayan fold-thrust belt had generated great earthquakes in the past and will spawn more in the future. Sequential cumulative moment release data of macroearthquakes (Mb ≥ 4.5) over the years 1964–2006 in four zones of the Himalaya was analysed by nonparametric RUD method. The Z values of RUD analysis had neither rejected nor supported the null hypothesis of randomness. However, the Hurst analysis and plot, a statistical procedure to identify clustering of low and high values in a time series, brought out a pattern for earthquake prognostication. The pattern was a negative sloping segment representing a sluggish moment release over years, followed by a positive sloping segment indicating a sudden high moment release with occurrence of medium/large size earthquake(s). In recent past, such a negative sloping has been found in Zones B (1992–2006) and D (1998–2006), indicating an impending moderate/mega earthquake event in near future.
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The SEM microfractographies of Zircaloy-4 are studied by the time-series method. We first develop a computer application which associates a time series to each SEM micrograph. Furthermore, we will apply the phase space embedding technique to reconstruct the attractor and to compute the autocorrelation dimension. Using the fractal analysis technique, the SEM microfractographies of the fracture surface of the Zircaloy-4 samples have been analyzed.
Control charts are the most commonly used quality control tools. These tools are dedicated to monitoring processes characteristic over time. Control charts may be successfully applied in other statistical areas. The non-classical use of control charts for time series prediction has been presented by Z. Pawłowski in the paper Predykcja za pomocą kart kontrolnych (Control Chart Based Prediction, 1969). The forecasts obtained by this method are quantitative or qualitative. The modification of this method is presented in the paper. It leads to quantitative predictions in all cases. The proposal was compared to some well-known classical prediction methods in the Monte Carlo study.
PL
Metody statystyczne opracowane na potrzeby kontroli jakości produktów z powodzeniem mogą być stosowane w analizie innych zagadnień. Do najczęściej wykorzystywanych narzędzi kontroli jakości należy zaliczyć karty kontrolne. Nieklasyczne zastosowanie kart kontrolnych związane z wykorzystaniem ich do prognozowania przedstawił Z. Pawłowski w artykule Predykcja za pomocą kart kontrolnych (1969). Prognozy otrzymywane tą metodą mają charakter ilościowy lub jakościowy. W artykule przedstawiono propozycję modyfikacji tej metody w celu uzyskania wszystkich prognoz o charakterze ilościowym. Proponowaną metodę porównano symulacyjnie z wybranymi metodami predykcji.
It has been found that discontinuity plays a crucial role in natural evolutions (Lin 1998). In this presentation, we will generalize the idea of integration and differentiation, we developed in calculus, to the study of time series in the hope that the problem of outliers and discontinuities can be resolved more successfully than simply deleting the outliers and avoiding discontinuities from the overall data analysis. In general, appearances of outliers tend to mean existence of discontinuities, explosive growth or decline in the evolution. At the same time, our approach can be employed to partially overcome the problem of not having enough data values in any available time series. At the end, we will look at some real-life problems of prediction in order to see the power of this new approach.
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We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.
Time series analysis deals with records that are collected over time. The objectives of time series analysis depend on the applications, but one of the main goals is to predict future values of the series. These values depend, usually in a stochastic manner, on the observations available at present. Such dependence has to be considered when predicting the future from its past, taking into account trend, seasonality and other features of the data. Some of the most successful forecasting methods are based on the concept of exponential smoothing. There are a variety of methods that fall into the exponential smoothing family, each having the property that forecasts are weighted combinations of past observations. But time series analysis needs proper statistical modeling. The model that better describes the behavior of the series in study can be crucial in obtaining 'good' forecasts. Departures from the true underlying distribution can adversely affect those forecasts. Resampling techniques have been considered in many situations to overcome that difficulty. For time series, several authors have proposed bootstrap methodologies. Here we will present an automatic procedure built in R language that first selects the best exponential smoothing model (among a set of possibilities) for fitting the data, followed by a bootstrap approach for obtaining forecasts. A real data set has been used to illustrate the performance of the proposed procedure.
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Ito equations are derived for simple stochastic cellular automaton with parameters describing efficiencies for avalanche triggering and cell occupation. Analytical results are compared with the numerical one obtained from the histogram method. Good agreement for various parameters supports the wide applicability of the Ito equation as a macroscopic model of some cellular automata and complex natural phenomena which manifest random energy release. Also, the paper is an example of effectiveness of histogram procedure as an adequate method of nonlinear modeling of time series.
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Modigliani & Miller (1958) show the impact of debt-equity ratio on firm value in their capital structure theory. Economist and financial researchers have spent time to develop new thoughts around this theory. Despite their effort the Modigliani & Miller (MM) model is still in vague. In this paper attempt has been made to empirically support the argument of MM. The paper tests the influence of debt-equity structure on the value of shares given different sizes, industries and growth opportunities with the companies incorporated in Dhaka Stock Exchange (DSE) and Chittagong Stock Exchange (CSE) of Bangladesh. For the robustness of the analysis samples are drawn from the four most dominant sectors of industry i.e. engineering, food & allied, fuel & power, and chemical & pharmaceutical to provide a comparative analysis. A strong positively correlated association is evident from the empirical findings when stratified by industry
The problem of biased time series mathematical model parameter estimates is well known to be insurmountable. When used to predict future values by extrapolation, even a de minimis bias will even-tually grow into a large bias, with misleading results. This paper elucidates how combining antithetic time series’ solves this baffling problem of bias in the fitted and forecast values by dynamic bias can-cellation. Instead of growing to infinity, the average error can converge to a constant.
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