The College of Administration and Economics at the University of Baghdad discussed , a master’s thesis in field of Statistics by the student (Mayson Abid Hussein ) and tagged with ( Robust Nonparametric Estimates of Nonstationary Time Series with Application) , Under supervision of (Pro. Dr. Munaf Yosif Hmood )
Time series regard as a One of the important statistical topics that have received great attention by researchers is the time series for their interpretation of phenomena and their behavior. In practice, there are many time series that suffer suffer random changes as a result of changing circumstances over time, which makes them unstable. As a result, the distribution of the data may be unknown and then require appropriate methods for the work of statistical procedures. One of the methods is the parametric methods. Because of the restrictions imposed on the parametric methods, they do not meet the need of the research because they are not flexible in estimating and analyzing the data. Therefore, non- landmark methods have been resorted to in the analysis of time series, which have proven their efficiency in analyzing data without the need for prior assumptions on the researcher. In nonparametric methods, the data and its load of information have become the ones that determine their functional form for the studied society and there are nonparametric for the observations Because estimating the equations of the two regression models of unstable time series leads to obtaining the false regression and to avoid such a problem, the method of cointegration that emerged in the mid-1980s was the most common and used to estimate such models, where the direction of behavior of the study variables in the long term under their change in the short term is known through the application of error correction models. In this letter, some Robust estimation methods ( M Smoother and Lowess Estimator) and Nonrobust (Local Polynomial Estimator and Cubic Spline Estimator) were presented and compared with the ARDL model, which is a parametric method for estimating a common integration regression relationship, and the NARDL model, which is a non-linear method for estimating a common integration regression relationship. The time series stationary test and the regression series residuals stationary test were based on the Philips-Perron test . The most important goal of this thesis is to obtain the best method of estimation in light of the application of the regression relationship of cointegration. Relying on the comparison criterion is the ratio of adjustment of the deviation in the shortـ run to return to the long run .
For the purpose of determining the best estimation methods, they were applied on the monthly time series for two variables, money supply and the variable of bank deposits, which were obtained from the Iraqi Central Bureau of Statistics for the period of time (2010-2015) . From the initial gragh of the data, it was noted that there is a long-run relationship between the two variables of the study, but after conducting the stationary test for the series, it was found that they were unstable at the level I(0). In order to avoid falling into the problem of false regression, it was required to take the first differences I(1)for the time series and ensure their stationarty before estimating the regression relationship. The cointegration test was conducted for all methods and the results showed the limits of the joint integration relationship between the two study variables and that the relationship is significant. Thus, it was possible to estimate the error correction model for each method and calculate the modification percentage. The highest modification rate for the ARDL model method was (0.37) and the lowest time period of (2.7) months. The results of the test showed the lowest MSE error square for the estimated regression relationship between the two study variables that the Locally Weighted Scatter plot Smoothing method (LOWESS) had the lowest value among nonparametric methods. As for the relationship between the variable of money supply and the variable of bank deposits, it was significant in all the estimated models, and that the positive and negative effects of the variable of bank deposits on the variable of money supply were asymmetric according to the Wald Test.
