In recent years, the innovation and improvement of forecasting techniques have caught more and more attention. Especially, in the fields of financial economics, management planning and control, forecasting provides indispensable information in decision-making process. If we merely use the time series with the closing price array to build a forecasting model, a question that arises is: Can the model exhibit the real case honestly? Since, the daily closing price of a stock index is uncertain and indistinct. A decision for biased future trend may result in the danger of huge lost. Moreover, there are many factors that influence daily closing price, such as trading volume and exchange rate, and so on. In this research, we propose a new approach for a bivariate fuzzy time series analysis and forecasting through fuzzy relation equations. An empirical study on closing price and trading volume of a bivariate fuzzy time series model for Taiwan Weighted Stock Index is constructed. The performance of linguistic forecasting and the comparison with the bivariate ARMA model are also illustrated.

Left truncatrion, Right censorship, Product-limit, Quantile process, Strong Gaussian approximations, Lorenz process, Gini index, Law of the iterated logarithm,

Left truncation, right censorship, product-limit, quantile process, Gaussian approximations,

No abstract

COVID-19 research has relied heavily on convenience-based samples, which—though often necessary—are susceptible to important sampling biases. We begin with a theoretical overview and introduction to the dynamics that underlie sampling bias. We then empirically examine sampling bias in online COVID-19 surveys and evaluate the degree to which common statistical adjustments for demographic covariates successfully attenuate such bias. This registered study analysed responses to identical questions from three convenience and three largely representative samples (total N = 13,731) collected online in Canada within the International COVID-19 Awareness and Responses Evaluation Study ( www.icarestudy.com ). We compared samples on 11 behavioural and psychological outcomes (e.g., adherence to COVID-19 prevention measures, vaccine intentions) across three time points and employed multiverse-style analyses to examine how 512 combinations of demographic covariates (e.g., sex, age, education, income, ethnicity) impacted sampling discrepancies on these outcomes. Significant discrepancies emerged between samples on 73% of outcomes. Participants in the convenience samples held more positive thoughts towards and engaged in more COVID-19 prevention behaviours. Covariates attenuated sampling differences in only 55% of cases and increased differences in 45%. No covariate performed reliably well. Our results suggest that online convenience samples may display more positive dispositions towards COVID-19 prevention behaviours being studied than would samples drawn using more representative means. Adjusting results for demographic covariates frequently increased rather than decreased bias, suggesting that researchers should be cautious when interpreting adjusted findings. Using multiverse-style analyses as extended sensitivity analyses is recommended. Supplementary Information The online version contains supplementary material available at 10.1007/s10654-022-00932-y.