The data on physical capital were constructed

The data on physical capital were constructed by accumulating real gross fixed capital formation (obtained from the WDI) assuming a constant depreciation rate using the perpetual inventory method [4] and a depreciation rate of 4%. The data on human capital (H) were constructed as follows:where L=total labour force (millions of people, obtained from the WDI)where s=average years of schooling (obtained from [5]) r=return to education, set at 10% following [6]. All the data were converted into logarithms for the purposes of the analysis [1].
Data
Experimental design, materials and methods The datasets, daily closing price time series of asset , are obtained from the Wind Finance Database (http://www.wind.com.cn/Default.aspx) in China. In order to explore the asset return distribution describing performance of jump diffusion models, the datasets are converted into daily percentage return values by using the following equation:where is the natural logarithm of the closing price at . All the datasets are listed in Table 1. The daily closing prices and daily percentage return values are shown in Supplementary materials (data.xlsx). Finally, on the performance of volatility forecasts, several GARCH family models with some URB597 return distributions are presented. The datasets are split into two samples, the in-sample data and out-of-sample data (see Fig. 1). In order to compare the performance of volatility forecasts of relevant models, we use the rolling-window approach (One step forward). The initial time period of in-of-sample data is from January 3, 1995 to 26 April, 2013. For each data series, these relevant models are first estimated using the in-of-sample data (before the time t), and a volatility value is obtained as a forecast volatility at the next time t+1 (see Fig. 1). Subsequently, the estimation period was rolled forward by adding one new day. By repeating this procedure, the out-of-sample volatility forecasts were calculated for the rest days.
Data The data set includes a balanced daily (Monday, Tuesday and Wednesday) for oil and natural gas volatility and the oil rich economies’ stock markets for Saudi Arabia, Qatar, Kuwait, Abu Dhabi, Dubai, Bahrain and Oman, using daily data over the period spanning Oct. 18, 2006–July 30, 2015 (a total of 3055 observations). The GCC indices under consideration are the Saudi Arabian Tadawul All Share Index (Saudi Arabia-TASI, hereafter), the Kuwait Stock Exchange Index, (Kuwait-SE), the Dubai General Index (Dubai-DFM), the Abu Dhabi General Index (Abu Dhabi-ADX), the Qatar Doha Securities Market (Qatar-QD), the Oman MSM30 Index (Oman-MSM30), Bahrain stock index (Bahrain-BE), the oil price (WTI-Oil) and the natural gas price (NG). a summary of the selected series is in Appendix A, Table 1. Additionally, we have included unique GAUSS codes for estimating the SAMEM. The data, the model and the codes have many applications in business and social science. The formula used to estimate volatility, Parkinson [6], is (ln(Max)−ln(Min))*(1/4*ln(2))^0.5. The choice of the sample period is motivated by the desire to capture the interactions among the markets over the years that are mostly characterized by several crisis and number of disruptions in the selected markets. With respect to the GAUSS codes, they are written and are tested to overcome the shortage in estimating the SAMEM model, for more information about the basic model of MEM, see Engle and Gallo [2]. Selected results of the estimated model is included in Appendix A (Table 2).
Experimental design, materials and methods With respect to the code of the SAMEM model, see Otranto [1,3–5], it is written based on the In the basic MEM model, the volatility of a certain financial time series is modeled as the product of a time varying scale factor , which represents the conditional mean of , which follows a GARCH-type dynamic, and a positive valued error :