The probabilities of type I and II error of null of cointegration tests: A Monte Carlo comparison

This paper evaluates the performance of eight tests with null hypothesis of cointegration on basis of probabilities of type I and II errors using Monte Carlo simulations. This study uses a variety of 132 different data generations covering three cases of deterministic part and four sample sizes. The three cases of deterministic part considered are: absence of both intercept and linear time trend, presence of only the intercept and presence of both the intercept and linear time trend. It is found that all of tests have either larger or smaller probabilities of type I error and concluded that tests face either problems of over rejection or under rejection, when asymptotic critical values are used. It is also concluded that use of simulated critical values leads to controlled probability of type I error. So, the use of asymptotic critical values may be avoided, and the use of simulated critical values is highly recommended. It is found and concluded that the simple LM test based on KPSS statistic performs better than rest for all specifications of deterministic part and sample sizes.

Study the Trend Pattern in COVID-19 using Spline-Based Time Series Model: A Bayesian Paradigm

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

Bayesian Unit Root Test for AR(1) Model with Trend Approximated

The objective of present study is to develop a time series model for handling the non-linear trend process using a spline function. Spline function is a piecewise polynomial segment concerning the time component. The main advantage of spline function is the approximation, non linear time trend, but linear time trend between the consecutive join points. A unit root hypothesis is projected to test the non stationarity due to presence of unit root in the proposed model. In the autoregressive model with linear trend, the time trend vanishes under the unit root case. However, when non-linear trend is present and approximated by the linear spline function, through the trend component is absent under the unit root case, but the intercept term makes a shift with r knots. For decision making under the Bayesian perspective, the posterior odds ratio is used for hypothesis testing problems. We have derived the posterior probability for the assumed hypotheses under appropriate prior information. A simulation study and an empirical application are presented to examine the performance of theoretical outcomes.

Energy Consumption in the GCC Countries: Evidence on Persistence

This paper examines the statistical properties of energy consumption in the GCC countries applying fractional integration methods to annual data from 1980 to 2014. The results indicate that both the raw and the logged series exhibit a (statistically significant) linear time trend in the case of Bahrain, Oman and Qatar, and the raw series only in the case of Saudi Arabia. Mean reversion (and thus only transitory effects of shocks) is found in the case of Bahrain for both the raw and logged data, and in Qatar for the logged series. In the remaining cases, the unit root hypothesis (implying permanent effects of shocks) cannot be rejected except for the logged data in Saudi Arabia, since the order of integration of the series is found to be statistically higher than 1 in that country. The implication of these findings is that in the case of Bahrain and Qatar exogenous shocks to energy consumption have transitory effects, which disappear in the long run without the need for policy action, whilst the permanent nature of the effects of shocks elsewhere means that appropriate policies have to be designed to restore equilibrium.

Trends in cigarette consumption and time to first cigarette on awakening from 2002 to 2015 in the USA: new insights into the ongoing tobacco epidemic

ObjectiveThe current study estimates trends in the number of cigarettes smoked per day (CPD) and percentage of smokers having their first CPD within 30 min of waking (time to first cigarette (TTFC)<30 min) among smokers from 2002 to 2015 in the USA overall, and adjusting for demographics. Trends in TTFC<30 min were also estimated by varying levels of cigarette consumption.MethodsData were drawn from the National Household Survey on Drug Use, an annual nationally representative cross-sectional study of the US population aged 12 and older (n=54 079–58 397 per year). Linear time trend analyses of CPD and TTFC<30 min were conducted adjusting for age, gender and income; linear time trend analyses of TTFC among those at varying levels of CPD were then performed.ResultsEstimates suggest that CPD declined overall from 2002 to 2015, and that the prevalence of TTFC<30 min declined overall among smokers (p<0.0001). The proportion of smokers consuming fewer (ie, 1–5, 6–15) CPD has increased while the number consuming 16+ CPD has decreased overall. Among those smoking 1–5 (p=0.0006) and 6–15 (p<0.0001) CPD, TTFC<30 min has increased significantly, but TTFC<30 min has remained unchanged among those smoking 16 or more CPD (p=0.5838).ConclusionsFindings suggest that smokers today are consuming fewer CPD, yet are increasingly likely to have their first cigarette earlier on awakening than they were a decade ago. Intervention and outreach efforts aimed at moving the prevalence lower may benefit from evaluating and addressing nicotine dependence even among lighter smokers.