A Bootstrapped Vector Autoregressive Model for Tourist Arrivals in Zimbabwe: A Case Study of Great Zimbabwe Monuments (2009-2012)
Abstract: The time series monthly data for local and international tourist arrivals at Great Zimbabwe Monuments from January 2009 to December 2012 were analyzed and modeled using bootstrapped vector autoregressive method. The first difference of the monthly bootstrapped data suggested stationarity. A vector autoregressive (VAR) model was estimated since there was no cointegration among the variables as suggested by the Johansen’s cointegration test. Consumer Price Index (CPI), exchange rate and tourist arrivals were all accommodated in the model. Zimbabwean tourist visits are seasonal as evidenced by high numbers in August and December every year.
Pages: 47 – 58 | Full PDF Paper
Abstract: A control charts Reexpression Vector Variance (RVV) can be used to monitoring the dispersion of multivariate process as an alternative to the control charts Generalized Variance (GV) is commonly used. The synthetic control chart RVV is built in a combination the standard control charts RVV (Shewhart class control chart) with the control chart of conforming run length (CRL). Average run length of the synthetic control charts VV be compared with the standard control charts VV, the standard control charts GV and the synthetic control charts GV. The result, the synthetic control chart RVV superior than standard GV chart, synthetic GV chart, and standard RVV chart to all of the condition change of the covariance matrix.
Keywords: Multivariate dispersion, vector variance, conforming run length, average run length.
Pages: 59 – 74 | Full PDF Paper
Estimations in Step-Partially Accelerated Life Tests for an Exponential Lifetime Model Under Progressive Type-I Censoring and General Entropy Loss Function
Alaa H. Abdel-Hamid
Abstract: Based on progressively type-I censored samples, this paper discusses some estimation methods in step-partially accelerated life tests when the lifetimes of items under use condition follow the exponential distribution. Maximum likelihood estimations for the considered parameters are obtained in closed forms. The observed Fisher information matrix is derived to calculate confidence intervals for the considered parameters. Bayesian estimations for the parameters are carried out based on (a) informative prior for the scale parameter and discrete prior for the acceleration factor, (b) both the symmetric loss (squared error loss) function and asymmetric loss (general entropy loss) function. The resulting Bayes estimates are obtained in closed forms. The precision of the estimates and a comparison among them are investigated through a Monte Carlo simulation study.
Keywords: Partially accelerated life tests, Progressive type-I censoring, Exponential distribution, Maximum likelihood and Bayesian estimations, general entropy loss, Simulation.
Pages: 75 – 93 | Full PDF Paper
Frank Ranganai Matenda
Abstract: Portfolio insurance techniques have been in existence for a long period of time. Cont and Tankov (2007) propose that portfolio insurance refers to investment strategies that limit the downside risk of a portfolio whilst maintaining its upside potential at the same time. Constant proportion portfolio insurance (CPPI) is a fundamental and prominent example of portfolio insurance strategies. Several authors have analysed CPPI based on probability theory (for example, Neftci, 2008 and Cont and Tankov, 2007) and uncertainty theory (such as, Matenda, Chikodza and Gumbo, 2015). Probability theory and uncertainty theory recognise randomness and uncertainty, respectively, as the only legitimate forms of indeterminacy. However, there are other forms of material indeterminacy in financial markets, such as fuzziness, which cannot be modelled by probability theory and uncertainty theory. In order to deal with fuzziness, credibility theory was founded. The main aim of this research work is to analyse the mechanics of CPPI strategies in fuzzy financial markets. Assuming continuous time diffusion models, CPPI techniques always work. However, in practice, CPPI strategies are exposed to gap risk which originates from sudden significant downward asset price jumps. In this research paper a direct relationship between the participation rate, and the CPPI-insured portfolio value, has been established. The risk of loss in a CPPI strategy increases with the participation rate. Gap risk for CPPI strategies is not insignificant. Therefore, it has to be quantified. This research paper develops a strong foundation for the analytical computation of gap risk for CPPI strategies when asset price processes evolve as fuzzy differential equations with jumps. This study is the first peace of work to apply credibility theory to CPPI.
Pages: 94 – 109 | Full PDF Paper