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In Linear Systems with Spatio-Temporal Dynamics

Abstract

The asymmetric short – and long-run relationships between BRICS stock markets are examined using monthly stock price data from January 2001 through December 2014. The asymmetric co-integration analysis confirms the presence of a long-run association between the BRICS stock markets; where, the speed of adjustment to the negative shocks is higher and statistically significant for the Brazil-India and China-India pairs, which indicates quick adjustment of stock prices to bad news compared to good news. Conversely, the speed of adjustment for Indian and South African stock markets is higher for positive shocks, while the relationship between the stock markets pair of Russia and South Africa is linear. The results of asymmetric error correction model (AECM) reveal evidence of bidirectional causality between China-India, India-South Africa and South Africa-Russia, while unidirectional causality runs from the Indian to Brazilian stock market. Thus, we can safely conclude that the Indian stock market has long-run and short-run relationships with most of the other stock markets. This suggests that investors should pay attention to the Indian stock market when investing in BRICS stock markets.

Abstract

The NoVaS methodology for prediction of stationary financial returns is reviewed, and the applicability of the NoVaS transformation for volatility estimation is illustrated using realized volatility as a proxy. The realm of applicability of the NoVaS methodology is then extended to non-stationary data (involving local stationarity and/or structural breaks) for one-step ahead point prediction of squared returns. In addition, a NoVaS-based algorithm is proposed for the construction of bootstrap prediction intervals for one-step ahead squared returns for both stationary and non-stationary data. It is shown that the “Time-varying” NoVaS is robust against possible nonstationarities in the data; this is true in terms of locally (but not globally) financial returns but also in change point problems where the NoVaS methodology adapts fast to the new regime that occurs after an unknown/undetected change point. Extensive empirical work shows that the NoVaS methodology generally outperforms the GARCH benchmark for (i) point prediction of squared returns, (ii) interval prediction of squared returns, and (iii) volatility estimation. With regard to target (i), earlier work had shown little advantage of using a nonzero α in the NoVaS transformation. However, in terms or targets (ii) and (iii), it appears that using the Generalized version of NoVaS—either Simple or Exponential—can be quite beneficial and well-worth the associated computational cost.

Abstract

The relationship between hormonal contraceptive method use and sexually transmitted infections is not well understood. Studies that implement routine screening for STIs among different contraceptive users, such as the ASPIRE HIV-1 prevention trial, can be useful for identifying potential risk factors of STIs. However, the complex nature of non-random data can lead to challenges in estimation of associations for potential risk factors. In particular, if screening for the disease is not random (i. e. it is driven by symptoms or other clinical indicators), estimates of association can suffer from bias, often referred to as informative sampling bias. Time-varying predictors and potential stratification variables can further contribute to difficulty in obtaining unbiased estimates. In this paper, we estimate the association between time- varying contraceptive use and Sexually transmitted infections acquisition, in the presence of informative sampling, by extending the work Buzkova (2010). We use a two-step procedure to jointly model the non-random screening process and sexually transmitted infection risk. In the first step, inverse intensity rate ratios (IIRR) weights are estimated. In the second step, a weighted proportional rate model is fit to estimate the IIRR weighted hazard ratio. We apply the method to evaluate the relationship between hormonal contraception and risk of sexually transmitted infections among women participating in a biomedical HIV-1 prevention trial. We compare our results using the proposed weighted method to those generated using conventional approaches that do not account for potential informative sampling bias or do not use the full potential of the data. Using the IIRR weighted approach we found depot medroxyprogesterone acetate users have a significantly decreased hazard of Trichomonas vaginalis acquisition compared to IUD users (hazard ratio: 0.44, 95% CI: (0.25, 0.83)), which is consistent with the literature. We did not find significant increased or decreased hazard of other STIs for hormonal contraceptive users compared to non-hormonal IUD users.

Abstract

This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.