In time series modeling, the residuals are often checked for white noise and normality. In practice, the useful tests are Ljung Box test. Mcleod Li test and Lin Mudholkar test. In this paper, we present a nonparame...In time series modeling, the residuals are often checked for white noise and normality. In practice, the useful tests are Ljung Box test. Mcleod Li test and Lin Mudholkar test. In this paper, we present a nonparametric approach for checking the residuals of time series models. This approach is based on the maximal correlation coefficient ρ 2 * between the residuals and time t . The basic idea is to use the bootstrap to form the null distribution of the statistic ρ 2 * under the null hypothesis H 0:ρ 2 * =0. For calculating ρ 2 * , we proposes a ρ algorithm, analogous to ACE procedure. Power study shows this approach is more powerful than Ljung Box test. Meanwhile, some numerical results and two examples are reported in this paper.展开更多
In this study, the number of sheep and goats in Turkey were analysed by time series analysis method, and the number of great cattle for next years predicted through the most appropriate time series model.Time series w...In this study, the number of sheep and goats in Turkey were analysed by time series analysis method, and the number of great cattle for next years predicted through the most appropriate time series model.Time series was formed using the data on the number of sheep and goats belonging to the period between 1930 and 2014 in Turkey It was determined through autocorrelation function graphic that the series weren't stationary at first, but they became stationary after their first difference were calculated. A stagnancy test was performed through extended Dickey-Fuller test. So as to determine the suitability of the model, it was reviewed if autocorrelation and partial autocorrelation graphs were white noise series and also the results of Box-Ljung test were reviwed. Through the "tested models, the model estimations, of which parameter estimates were significant and Akaike information criterion (AIC) was the smallest, were performed. The most appropriate model in terms of both the number of sheep and goats is first-level integrated moving average model stated as ARIMA(0,1,1). In this model, it was estimated that there would be an increase in the number of sheep and goats in Turkey between the years of 2015 and 2020, however, the increase in the number of sheep would be more than the increase in the number of goats.展开更多
文摘In time series modeling, the residuals are often checked for white noise and normality. In practice, the useful tests are Ljung Box test. Mcleod Li test and Lin Mudholkar test. In this paper, we present a nonparametric approach for checking the residuals of time series models. This approach is based on the maximal correlation coefficient ρ 2 * between the residuals and time t . The basic idea is to use the bootstrap to form the null distribution of the statistic ρ 2 * under the null hypothesis H 0:ρ 2 * =0. For calculating ρ 2 * , we proposes a ρ algorithm, analogous to ACE procedure. Power study shows this approach is more powerful than Ljung Box test. Meanwhile, some numerical results and two examples are reported in this paper.
文摘In this study, the number of sheep and goats in Turkey were analysed by time series analysis method, and the number of great cattle for next years predicted through the most appropriate time series model.Time series was formed using the data on the number of sheep and goats belonging to the period between 1930 and 2014 in Turkey It was determined through autocorrelation function graphic that the series weren't stationary at first, but they became stationary after their first difference were calculated. A stagnancy test was performed through extended Dickey-Fuller test. So as to determine the suitability of the model, it was reviewed if autocorrelation and partial autocorrelation graphs were white noise series and also the results of Box-Ljung test were reviwed. Through the "tested models, the model estimations, of which parameter estimates were significant and Akaike information criterion (AIC) was the smallest, were performed. The most appropriate model in terms of both the number of sheep and goats is first-level integrated moving average model stated as ARIMA(0,1,1). In this model, it was estimated that there would be an increase in the number of sheep and goats in Turkey between the years of 2015 and 2020, however, the increase in the number of sheep would be more than the increase in the number of goats.