American Journal of Applied Mathematics and Statistics, 2016, Vol. 4, No. 5, 136-148 Available online at http://pubs.sciepub.com/ajams/4/5/1 ©Science and Education Publishing DOI:10.12691/ajams-4-5-1 Forecast of Sarima Models: Αn Application to Unemployment Rates of Greece Chaido Dritsaki * Department of Accounting and Finance, University of Applied Sciences of Western Macedonia, Kozani, Greece *Corresponding author: dritsaki@teiwm.gr Abstract The low unemployment rate is one of the main targets of macroeconomic policy for each government. Forecasting unemployment rate is of great importance for each country so as the government can draw up strategies for fiscal policy. The aim of the paper is to find the most suitable model which is adjusted on unemployment rates of Greece using Box-Jenkins methodology and to examine the precision of forecasting on this model. Models’ estimation was made using the non-linear Maximum likelihood optimization methodology (maximum likelihood– ML), whereas covariance matrix is estimated with OPG method using the numerical optimization of Broyden- Fletcher-Goldfarb-Shanno (BFGS) algorithm. Forecasting unemployment rate was made both with dynamic and static process using all criteria of forecasting measures. Keywords: unemployment, SARIMA, Box-Jenkins methodology, forecasting, Greece Cite This Article: Chaido Dritsaki, “Forecast of Sarima Models: Αn Application to Unemployment Rates of Greece.” American Journal of Applied Mathematics and Statistics, vol. 4, no. 5 (2016): 136-148. doi: 10.12691/ajams-4-5-1. 1. Introduction Every economy has a particular population size. Population is distinguished between economically active and non active for economic reasons. Economically active population is the labor force of economy. Thus, labor force considers those that can and want to work. Labor force is divided in two categories: those who already work and called employed and those who don’t work and are called unemployed. Unemployed are those who can and want to work but cannot find a job. Unemployment has three basic economic consequences: • It is regarded as a loss of productive powers • It means wage loss • Puts a strain on government’s budget due to unemployment benefits. The consequences of unemployment are certainly wider because not only it reduces wages but also decreases social position, creates self-respect problems and family matters. In other words, unemployment leads to serious social problems apart from economic ones. The opposition of unemployment is extremely difficult. The measures taken from various governments are divided in two general categories: 1) The measures taken for the increase of total demand and 2) The measures for professional training and re- education on labor force. The measures for total demand are fiscal and monetary. Fiscal measures consist of the increase of government expenditure for public works and the promotion for investments. The aim of these works is the direct growth of employment and wages. Monetary measures aim at interest rate reduction in order to strengthen private investments, production and therefore employment. Fiscal and monetary measures aim at the increase of total demand, thus unemployment decrease which is due to insufficient demand. The insufficient demand is the Keynesian unemployment which comes from the fall of economic activity during the recession stage of economic cycle. Measures of professional formation and re-education facilitate unemployed in the acquisition of professional knowledge and specialization which are necessary in order to be occupied in existing vacancies. It is obvious that these measures aim at the reduction of structural unemployment, created by the disproportion between supply and demand of various specialization. This reduction demands re-education of unemployed in order to acquire the necessary skills where there is scarcity. The measure of unemployment depends on the size of labor force. So, unemployment is measured as percentage (%) of labor force. The unemployment rate is: *100 Number of Unemployed Unemployment rate Labor Force = The progress of unemployment rate has been the central issue of political discussion for many developed countries. However, the behavior of unemployment rate during recession and recovery that followed puzzled researchers and policy makers if there is a change on long run trend of unemployment rate. Given this new situation, policy focuses on the dynamics of unemployment rate after the recession so that they can forecast unemployment rate. Forecasting unemployment rate came to the front from policy makers using autoregressive models as well as structural econometric forecasting models.