Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution

In this paper we investigate the dependence structure for Ornstein-Uhlenbeck processes with totally skewed tempered stable structure. They are natural extension of Ornstein-Uhlenbeck processes with stable (and Gaussian) distribution. However for the stable models the covariance is not defined therefore in order to compare the structure of dependence of Ornstein-Uhlenbeck with tempered stable and stable structure we analyze another measures of dependence defined for infinitely divisible processes such as Levy correlation cascade and codifference. We show that for analyzed processes the Levy correlation cascade goes faster to zero as in the stable case, while the codifference of the stable Ornstein-Uhlenbeck process has the same form as in the tempered case.truncated Levy flight, tempered stable, Ornstein-Uhlenbeck process, structure of dependence

Asymptotic behavior of measures of dependence for ARMA(1,2) models with stable innovations. Stationary and non-stationary coefficients

We derive the asymptotic behavior of two measures of dependence (Codifference and Covariation) for ARMA(1,2) models with symmetric alpha-stable innovations and non-stationary coefficients.ARMA model; Stable distribution; Codifference; Covariation;

The impact of forward trading on the spot power price volatility with Cournot competition

In this paper, we analyze the influence of forward trading on the volatility of spot power prices, in models where forward contracts are strategic tools used by energy producers to obtain profit security. We define volatility as the variance of the percentage change in spot power prices over a given time interval. As shown in Sapio (2008), volatility is related to stochastic fluctuations in preference and technology fundamentals, and is tuned by the price-elasticity of demand and supply, evaluated at equilibrium. We study two cases. First, we analyze the volatility implications of a model wherein the amount of forward trading is fixed, and producers compete a la Cournot. Fixed forward trading increases spot volatility, because forwards lower the spot price level, corresponding to a less elastic region of a linear demand function. However, if the amount of forward trading is endogenous, as in the two-stage model of Allaz (1992), producers can anticipate the spot market impact of stochastic shocks on fundamentals and 'sterilize' them. As a result, spot price volatility is closer to the value implied by an efficient market. Our theoretical results are illustrated by means of a simple simulation study.Electricity market; Cournot model; forward contract; volatility of spot price; elasticity;

Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution

In this paper we investigate the dependence structure for Ornstein-Uhlenbeck processes with totally skewed tempered stable structure. They are natural extension of Ornstein-Uhlenbeck processes with stable (and Gaussian) distribution. However for the stable models the covariance is not defined therefore in order to compare the structure of dependence of Ornstein-Uhlenbeck with tempered stable and stable structure we analyze another measures of dependence defined for infinitely divisible processes such as Levy correlation cascade and codifference. We show that for analyzed processes the Levy correlation cascade goes faster to zero as in the stable case, while the codifference of the stable Ornstein-Uhlenbeck process has the same form as in the tempered case

Measures of dependence for Ornstein-Uhlenbeck processes with tempered stable distribution

In this paper we investigate the dependence structure for Ornstein-Uhlenbeck processes with totally skewed tempered stable structure. They are natural extension of Ornstein-Uhlenbeck processes with stable (and Gaussian) distribution. However for the stable models the covariance is not defined therefore in order to compare the structure of dependence of Ornstein-Uhlenbeck with tempered stable and stable structure we analyze another measures of dependence defined for infinitely divisible processes such as Levy correlation cascade and codifference. We show that for analyzed processes the Levy correlation cascade goes faster to zero as in the stable case, while the codifference of the stable Ornstein-Uhlenbeck process has the same form as in the tempered case

Periodic correlation vs. integration and cointegration (Okresowa korelacja a integracja i kointegracja)

In this paper we present a new approach to integration and cointegration. We show that a periodically correlated time series can be divided in a natural way into subseries that are integrated. Moreover, with high probability they are cointegrated. Therefore it is enough to show periodic correlation of the original series to conclude that the subseries are integrated. In the first part of the paper we present the main features of periodically correlated processes and a method of detecting periodic correlation. We illustrate it using a data set of spot electricity prices from the Nord Pool Power Exchange. In the next section we show that the subseries (one for each day of the week) exhibit integration as well as cointegration.Cointegration; Integration; PARMA model; Periodic correlation;

On detecting and modeling periodic correlation in financial data

For many economic problems standard statistical analysis, based on the notion of stationarity, is not adequate. These include modeling seasonal decisions of consumers, forecasting business cycles and - as we show in the present article - modeling wholesale power market prices. We apply standard methods and a novel spectral domain technique to conclude that electricity price returns exhibit periodic correlation with daily and weekly periods. As such they should be modeled with periodically correlated processes. We propose to apply periodic autoregression (PAR) models which are closely related to the standard instruments in econometric analysis - vector autoregression (VAR) models.periodic correlation, sample coherence, electricity price, periodic autoregression, vector autoregression

Identification of cyclic components in presence of non-Gaussian noise – application to crusher bearings damage detection

In this paper an issue of local damage detection in a rolling element bearing is discussed. The bearing operates in a hummer crusher, thus the vibration signal acquired on the housing contains a lot of impacts that originate in various sources. In the case of local damage detection it is crucial to find a set of cyclic impulses in the signal. These impulses are informative, in spite of impulses related to the crushing process, which are non-informative. In order to find the damage signature we provide feasibility study on a tool based on cyclostationary approach, namely cyclic spectral coherence. This comprehensive analysis includes study on four different signals from bearings in various condition and operating with or without load applied. This analysis is preceded by motivating preliminary analysis where we examine a few widely-used methods for local damage detection

Automatic calculation of thresholds for load dependent condition indicators by modelling of probability distribution functions – maintenance of gearboxes used in mining conveying system

Limit values for gearbox vibration-based condition indicators are key to determine in order to be able to estimate moment when object is in a need of maintenance. Further decision making process usually might utilize simple if-then-else rule using established threshold values. If diagnostic data takes the values from the Gaussian distribution, finding the decision boundaries is not difficult. Simplistically, that comes down to standard pattern recognition technique for “good condition” and “bad condition” based on probability density functions (PDFs) of diagnostic data. This situation is becoming more and more complicated when distribution is not Gaussian. Such cases require to develop much more advanced analytically solution. In this paper, we present the case of belt conveyor’s gearbox for which PDFs of diagnostic features overlap each other because of strong influence of time varying operating conditions on spectral features. New approach to automatic threshold recognition has been proposed based on modeling diagnostic features with Weibull distribution and using agglomerative clustering to distinguish classes of technical condition, which leads to determination of thresholds separating them