There are four kinds of Cedar: Cedrus libani naturally occurring in Lebanon, Syria and Turkey, Cedrus atlantica in Morocco and Algeria, Cedrus brevefolia in Cyprus Island and Cedrus deodara which is distributed in Himalayan Mountains. Wood essential oils obtained from C. libani, C. atlantica and C. deodara were tested for the inhibition of K562 cell proliferation and for the induction of erythroid differentiation. The wood essential oils of C. libani, C. atlantica and C. deodara inhibited the proliferation of the K562 cell line exhibiting IC(50) values 23.38 ± 1.7, 59.37 ± 2.6 and 37.09 ± 1.4 µg mL(-1), respectively. Meanwhile, C. libani wood oils induced a percentage of erythroid differentiation of 15 ± 2% at concentration 5 µg mL(-1). Cedrus deodara wood oil indicated a percentage of erythroid differentiation of 20 ± 2% at concentration 25 µg mL(-1) and C. atlantica wood oils showed a percentage of erythroid differentiation of 12 ± 1.8% at concentration 10 µg mL(-1).

The portmanteau statistic for testing the adequacy of an autoregressive moving average (ARMA) model is based on the first m autocorrelations of the residuals from the fitted model. We consider some of portmanteau tests for univariate linear time series such as Box and Pierce [2], Ljung and Box [9], Monti [12], Peña and Rodríguez [13 and 14], Generalized Variance Test (Gvtest) by Mahdi and McLeod [11] and Fisher [4]. We conduct an extensive computer simulation time series data, to make comparison among these tests. We consider different model parameters for small, moderate and large samples to examine the effect of lag m on the power of the selected tests, and determine the most powerful test for ARMA models. The similar portmanteau tests models was evaluated for the real data set on electricity consumption in Khan Younis, Palestine (April 2009-May 2013). We found that, portmanteau tests have the highest values of power for large sample data (N = 500) comparing to small and moderate samples (N = 50 and 200). We found that the portmanteau tests are sensitive to the chosen for m value. Indeed there are loss of the power values for lags m ranging from m = 5 to 20, where Box-Pierce, Ljung-Box and Monti tests have more power loss than the other selected tests. The power loss reaches its minimum values for large sample data comparing to small and moderate samples. In addition, the results of the simulation study and real data analysis showed that the most powerful tests varies between Gvtest and Fisher tests.

The Auto Regressive Integrated Moving Average (ARIMA) model seems not to easily capture the nonlinear patterns exhibited by the 2019 novel coronavirus (COVID-19) in terms of daily confirmed cases. As a result, Artificial Neural Network (ANN) and Error, Trend, and Seasonality (ETS) modeling have been successfully applied to resolve problems with nonlinear estimation. Our research suggests that it would be ideal to use a single model of ETS or ARIMA for COVID-19 time series forecasting rather than a complicated Hybrid model that combines several models. We compare the forecasting performance of these models using real, worldwide, daily COVID-19 data for the period between January 22, 2020 till June 19, and June 20 till January 2, 2021 which marks two stages, each stage indicating the first and the second wave respectively. We discuss various forecasting approaches and the criteria for choosing the best forecasting technique. The best forecasting model selected was compared using the forecasting assessment criterion known as Mean Absolute Error (MAE). The empirical results show that the ETS and ARIMA models outperform the ANN and Hybrid models. The main finding from the ETS and ARIMA models analysis indicate that the magnitude of the increase in total confirmed cases over time is declining and the percentage change in the death rate is also on the decline. Our results shows that the chosen forecaste models are consistent during the first and second wave of of the pandemic. These forecasts are encouraging as the world struggles to contain the spread of COVID-19. This may be the result of the social distancing measures mandated by governments worldwide.

The ordinary least squares (OLS) estimates in the regression model are efficient when the disturbances have mean zero, constant variance, and are uncorrelated. In problems concerning time series, it is often the case that the disturbances are correlated. Using computer simulations, the robustness of various estimators are considered, including estimated generalized least squares. It was found that if the disturbance structure is autoregressive and the dependent variable is nonstochastic and linear or quadratic, the OLS performs nearly as well as its competitors. For other forms of the dependent variable, rules of thumb are presented to guide practitioners in the choice of estimators.

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