Assessment of regional best‐fit probability density function of annual maximum rainfall using CFSR precipitation data

The upper Cross River basin (UCRB) fits a true description of a data scarce watershed in respect of climatic data. This paper seeks to determine the best‐fit probability density function (PDF) of annual maximum rainfall for the UCRB using the Climate Forecast System Reanalysis (CFSR) precipitation data. Also, to evaluate the performance of the Intergovernmental Panel on Climate Change (IPCC) Coupled Model Inter‐comparison Project (CMIP3) Fourth Assessment Report (AR4) Global Circulation Models (GCMs) in simulating the monthly precipitation in the UCRB considering 1979–2014 data. For the determination of the best‐fit PDF, the models under review included the generalized extreme value (GEV), normal, gamma, Weibull and log‐normal (LN) distributions. Twenty‐four weather station datasets were obtained and subjected to frequency distribution analysis on per station basis, and subsequently fitted to the respective PDFs. Also, simulated monthly precipitation data obtained from 16 AR4 GCMs, for weather station p6191, were subjected to frequency distribution analysis. The results showed the percentages of best‐fit to worst‐fit PDFs, considering the total number of stations, as follows: 54.17%, 45.83%, 37.50%, 45.83%, and 50%/50%. These percentages corresponded to GEV, Weibull, gamma, gamma, and LN/normal, respectively. The comparison of the predicted and observed values using the Chi‐square goodness‐of‐fit test revealed that the GEV PDF is the best‐fit model for the UCRB. The correlation coefficient values further corroborated the correctness of the test. The PDF of the observed data (weather station p6191) and the simulations of the 16 GCMs computed using monthly rainfall datasets were compared using a mean square error (MSE) dependent skill score. The result from this study suggested that the CGCM3.1 (T47) and MRI‐CGCM2.3.2 provide the best representations of precipitation, considering about 36 years trend for station p6191. The results have no influence on how well the models perform in other geographical locations

Models for Heavy-tailed Asset Returns

Many of the concepts in theoretical and empirical finance developed over the past decades – including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR – rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model – the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which – like tempered stable distributions – can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples

Change Point Analysis based on Empirical Characteristic Functions

62G20, 62E20, 60F17, Empirical characteristic function, Change point analysis,

A homogeneity test for bivariate random variables

Homogeneity, Bivariate populations, Empirical characteristic function, Quadratic Powell–Sabin splines, Quadratic Taylor approximation, Bootstrap,

Estimating the codifference function of linear time series models with infinite variance

ARMA, Infinite variance, Codifference, Empirical characteristic function,