We analyze a 19-year time series of North American electric power transmission system blackouts. ... more We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter-occurrence times and evidence of seasonal dependence in the number of events. Our findings question the use of self-organized criticality, and in particular the sandpile model, as a paradigm of blackout dynamics in power transmission systems. Hopefully, though, they will provide guidelines to more accurate models for evaluation of blackout risk.
2009 6th International Conference on the European Energy Market, 2009
We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. ... more We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. Our empirical study shows that (i) models with shifted spike regime distributions lead to more realistic models of electricity spot prices and that (ii) introducing heteroskedasticity in the base regime leads to better spike identification and goodness-of-fit than in MRS models with the standard mean-reverting, constant volatility dynamics.
This paper is intended as a guide to building insurance risk (loss) models. A typical model for i... more This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.
Physica A: Statistical Mechanics and its Applications, 2004
For many economic problems standard statistical analysis, based on the notion of stationarity, is... more 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 models which are closely related to the standard instruments in econometric analysis-vector autoregression models.
MRS2IR_SIM(P,PARAM,MODEL,STARTVALUE,KSI_0,T,N) generates N trajectories of a Markov regime-switch... more MRS2IR_SIM(P,PARAM,MODEL,STARTVALUE,KSI_0,T,N) generates N trajectories of a Markov regime-switching (MRS) model with 2 independent regimes: (i) an AR(1) process in the base regime X(t+1)=phi_1*X(t)+c_1+sigma_1*|X(t)|^g_1*N(0,1), (ii) and a Gaussian (MODEL='G'), lognormal ('LN'), Pareto ('P'), Weibull ('W') or exponential ('E') distributed spike regime. P, PARAM and KSI_0 are the transition matrix, model parameters and probabilities classifying the first observation to one of the
We develop a simple test for deviations from power law tails, which is based on the asymptotic pr... more We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans.
In this paper we address the issue of modeling spot electricity prices. After analyzing factors l... more In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price's main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.
In this paper, we present a procedure for consistent estimation of the severity and frequency dis... more In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a nonhomogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodnessof-fit procedures and forecasting, using classical and robust methodologies.
[KSI_TT,PARAM,P]=PS2R_EST(DATA) returns smoothed inferences KSI_TT, estimated parameters PARAM an... more [KSI_TT,PARAM,P]=PS2R_EST(DATA) returns smoothed inferences KSI_TT, estimated parameters PARAM and transition matrix P of a 2-regime parameter switching (PS) model, i.e. a 2-regime Markov regime-switching (MRS) model with both regimes driven by AR(1) processes of the form: X(t+1)=phi_i*X(t)+c_i+sigma_i*|X(t)|^g_i*N(0,1). The first column (KSI_TT) or row (PARAM, P) contains results for the base regime and the second column/row for the spike regime.
We analyze a 19-year time series of North American electric power transmission system blackouts. ... more We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter-occurrence times and evidence of seasonal dependence in the number of events. Our findings question the use of self-organized criticality, and in particular the sandpile model, as a paradigm of blackout dynamics in power transmission systems. Hopefully, though, they will provide guidelines to more accurate models for evaluation of blackout risk.
2009 6th International Conference on the European Energy Market, 2009
We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. ... more We calibrate Markov regime-switching (MRS) models to mean daily spot prices from the EEX market. Our empirical study shows that (i) models with shifted spike regime distributions lead to more realistic models of electricity spot prices and that (ii) introducing heteroskedasticity in the base regime leads to better spike identification and goodness-of-fit than in MRS models with the standard mean-reverting, constant volatility dynamics.
This paper is intended as a guide to building insurance risk (loss) models. A typical model for i... more This paper is intended as a guide to building insurance risk (loss) models. A typical model for insurance risk, the so-called collective risk model, treats the aggregate loss as having a compound distribution with two main components: one characterizing the arrival of claims and another describing the severity (or size) of loss resulting from the occurrence of a claim. In this paper we first present efficient simulation algorithms for several classes of claim arrival processes. Then we review a collection of loss distributions and present methods that can be used to assess the goodness-of-fit of the claim size distribution. The collective risk model is often used in health insurance and in general insurance, whenever the main risk components are the number of insurance claims and the amount of the claims. It can also be used for modeling other non-insurance product risks, such as credit and operational risk.
Physica A: Statistical Mechanics and its Applications, 2004
For many economic problems standard statistical analysis, based on the notion of stationarity, is... more 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 models which are closely related to the standard instruments in econometric analysis-vector autoregression models.
MRS2IR_SIM(P,PARAM,MODEL,STARTVALUE,KSI_0,T,N) generates N trajectories of a Markov regime-switch... more MRS2IR_SIM(P,PARAM,MODEL,STARTVALUE,KSI_0,T,N) generates N trajectories of a Markov regime-switching (MRS) model with 2 independent regimes: (i) an AR(1) process in the base regime X(t+1)=phi_1*X(t)+c_1+sigma_1*|X(t)|^g_1*N(0,1), (ii) and a Gaussian (MODEL='G'), lognormal ('LN'), Pareto ('P'), Weibull ('W') or exponential ('E') distributed spike regime. P, PARAM and KSI_0 are the transition matrix, model parameters and probabilities classifying the first observation to one of the
We develop a simple test for deviations from power law tails, which is based on the asymptotic pr... more We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans.
In this paper we address the issue of modeling spot electricity prices. After analyzing factors l... more In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price's main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.
In this paper, we present a procedure for consistent estimation of the severity and frequency dis... more In this paper, we present a procedure for consistent estimation of the severity and frequency distributions based on incomplete insurance data and demonstrate that ignoring the thresholds leads to a serious underestimation of the ruin probabilities. The event frequency is modelled with a nonhomogeneous Poisson process with a sinusoidal intensity rate function. The choice of an adequate loss distribution is conducted via the in-sample goodnessof-fit procedures and forecasting, using classical and robust methodologies.
[KSI_TT,PARAM,P]=PS2R_EST(DATA) returns smoothed inferences KSI_TT, estimated parameters PARAM an... more [KSI_TT,PARAM,P]=PS2R_EST(DATA) returns smoothed inferences KSI_TT, estimated parameters PARAM and transition matrix P of a 2-regime parameter switching (PS) model, i.e. a 2-regime Markov regime-switching (MRS) model with both regimes driven by AR(1) processes of the form: X(t+1)=phi_i*X(t)+c_i+sigma_i*|X(t)|^g_i*N(0,1). The first column (KSI_TT) or row (PARAM, P) contains results for the base regime and the second column/row for the spike regime.
Uploads
Papers by R. Weron