Forecast of Sarima Models: Αn Application to Unemployment Rates of Greece

Chaido Dritsaki^1,

¹Department of Accounting and Finance, University of Applied Sciences of Western Macedonia, Kozani, Greece

Cite this paper

Chaido Dritsaki. Forecast of Sarima Models: Αn Application to Unemployment Rates of Greece. American Journal of Applied Mathematics and Statistics. 2016; 4(5):136-148. doi: 10.12691/AJAMS-4-5-1

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

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Akaike, H. “A New Look at the Statistical Model Identification”, IEEE Transaction on Automatic Control, 19(6), 716-723, 1974.
[2]	Box, G. E. P. and Jenkins, G. M. Time Series Analysis, Forecasting and Control. Holden-Day, San Francisco, 1976.
[3]	Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. Time Series Analysis, Forecasting and Control, 3rd ed., Prentice Hall, Englewood Clifs, Brockwell, Peter J., 1994.
[4]	Brida, J. G. and Garrido, N. “Tourism Forecasting using SARIMA Models in Chilenean Regions”, International Journal of Leisure and Tourism Marketing, 2(2):176-190, 2009.
[5]	Broyden, C. G. “The convergence of a class of double-rank minimization algorithms”, Journal of the Institute of Mathematics and Its Applications. 6, 76-90, 1970.
[6]	Dickey, D. and Fuller, W. A. “Distribution of the Estimators for Autoregressive Time Series with a Unit Root”, Journal of the American Statistical Association, 74 (366), 427-431, 1979.
[7]	Dickey, D., and Fuller, W.A. “Likelihood ratio statistics for autoregressive time series with a unit root”, Econometrica, 49(4), 1057-1072, 1981.
[8]	Dobre, I. and Alexandrou, A.A., “Modelling unemployment rate using Box-Jenkins procedure”, Journal of Applied Quantitative Methods, Vol.3 No.2, pp.156-166, 2008.
[9]	Dritsaki, C. “Box–Jenkins Modelling of Greek Stock Prices Data”, International Journal of Economics and Financial Issues, 5(3), 740-747, 2015.
[10]	Etuk, E.H. “The Fitting of a SARIMA model to Monthly Naira-Euro Exchange Rates”, Mathematical Theory and Modeling, 3(1): 17-26, 2013
[11]	Etuk, E.H. “An Additive SARIMA Model for Daily Exchange Rates of the Malaysian Ringgit (MYR) and Nigerian Naira (NGN)”, International Journal of Empirical Finance 2(4): 193-201, 2014.
[12]	Etuk, E.H, Uchendu, B., and Edema, U.V. “ARIMA fit to Nigerian unemployment data”, Journal of Basic and Applied Scientific Research, 2(6), 5964-5970, 2012.
[13]	Fannoh, R., Otieno Orwa G, and Mungatu, G. J. K. “Modeling the Inflation Rates in Liberia SARIMA Approach”, International Journal of Science and Research, 3(6): 1360-1367, 2012.
[14]	Fletcher, R. “A New Approach to Variable Metric Algorithms”, Computer Journal, 13(3), 317-322, 1970.
[15]	Funke, M. “Time-series Forecasting of the German Unemployment Rate”, Journal of Forecasting, 11, 111-125, 1992.
[16]	Gikungu, S.W., A. G. Waititu, and Kihoro, J. M. “Forecasting inflation rate in Kenya using SARIMA model”, American Journal of Theoretical and Applied Statistics, 4(1): 15-18, 2015.
[17]	Goldfarb, D. “A Family of Variable Metric Updates Derived by Variational Means”, Mathematics of Computation, 24(109), 23-26, 1970.
[18]	Kanlapat Mahipan, Nipaporn Chutiman, and Bungon Kumphon. “A Forecasting Model for Thailand’s Unemployment Rate”, Modern Applied Science, 7(7): 10-16, 2013.
[19]	Ljung, G. M., and Box, G. E. P. “On a Measure of a Lack of Fit in Time Series Models”, Biometrika, 65 (2), 297-303, 1978.
[20]	MacKinnon, J.G. “Numerical distribution functions for unit root and cointegration tests”, Journal of Applied Econometrics, 11(6), 601-618, 1996.
[21]	Nasiru S. and Sarpong, S. “Empirical Approach to Modelling and Forecasting Inflation in Ghana”, Current Research Journal of Economic Theory 4(3): 83-87, 2012
[22]	Newey, W. K. and D. McFadden, Large sample estimation and hypothesis testing, in Handbook of Econometrics, Chapter 36, Vol.4, pp.2111-2245, Elsevier, 1994.
[23]	Newey, W.K. and K. D. West “Automatic lag selection in covariance matrix estimation”, Review of Economic Studies, 61, 631-653, 1994.
[24]	Nkwatoh, L. S. “Forecasting Unemployment Rates in Nigeria Using Univariate Time Series Models”, International Journal of Business and Commerce 1(12): 33-46, 2012.
[25]	Olsson, Α. “Forecasting using the Phillips curve II”, 2016. Available at: http://samastockholm.com/home/2016/2/8/forecasting-using-the-phillips-curve.
[26]	Pankratz, A. Forecasting with Univariate Box-Jenkins Models: Concepts and Cases. John Wiley & Sons, Inc. USA, 1983.
[27]	Phillips, P.C., and Perron, P. “Testing for a unit root in time series regression”, Biometrika, 75(2), 335-46, 1988.
[28]	Shanno, D.F. “Conditioning of quasi-Newton methods for function minimization”, Mathematics of Computation, 24(111), 647-656, 1970.
[29]	Stoklasová, R. “Model of the unemployment rate in the Czech Republic”, in 30th International Conference Mathematical Methods in Economics, Karviná, Czech Republic, 11-13 September, 2012.
[30]	Theil, H. Economic Forecasts and Policy. Second Edition, North Holland Publishing Company, Amsterdam, 1961.
[31]	Yu-Wei Chang and Meng-Yuan Liao. “A Seasonal ARIMA Model of Tourism Forecasting: The Case of Taiwan”, Asia Pacific Journal of Tourism Research, 15(2):215-221, 2010.