Abstract
Interdependencies among neighboring regions appear to be important in forming the shape of local labor markets. Nevertheless, only a few studies exist which have applied spatial models to forecast over small spatial units such as cities, districts or counties. The majority of predictions are developed with quarterly or yearly time series for a country or at regional level. The paper presents the above phenomena and deals with the problem of simultaneous forecasting of the unemployment rate over 35 poviats (districts and cities) in one of the Polish provinces. Two extremely different models with spatial dependencies were developed and estimated in this paper: the Spatial Vector Autoregressions (SpVAR) and the Spatial Artificial Neural Network (SpANN). The 13-month out-of-sample forecast is based on high frequency, raw, monthly panel data extracted from 31 local labor offices. The procedure worked out here allows comparing the forecasting performance of spatial models with their non-spatial and seasonal equivalents. The inclusion of a spatial component into the models significantly improves the accuracy of forecasts; however, the overall performance of SpVAR is 30% better than SpANN.
References
Adhikari, R., and R. Agrawal. 2012. “Forecasting Strong Seasonal Time Series with Artificial Neural Networks.” Journal of Scientific and Industrial Research 71: 657–666.Search in Google Scholar
Anselin, L. 1988. Spatial Econometrics: Methods and Models. Springer Science & Business Media.10.1007/978-94-015-7799-1Search in Google Scholar
Arbia, G., and B. Fingleton. 2008. “New Spatial Econometric Techniques and Applications in Regional Science.” Papers in Regional Science 87: 311–317.10.1111/j.1435-5957.2008.00208.xSearch in Google Scholar
Arellano, M., and S. Bond. 1991. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” Review of Economic Studies 58 (2): 277–297.10.2307/2297968Search in Google Scholar
Baltagi, B. H., B. Fingleton, and A. Pirotte. 2014. “Estimating and Forecasting with a Dynamic Spatial Panel Data Model.” Oxford Bulletin of Economics and Statistics 76 (1): 112–138.10.1111/obes.12011Search in Google Scholar
Beck, N., K. Gleditsch, and K. Beardsly. 2006. “Space is more than Geography: Using Spatial Econometrics in the Study of Political Economy.” International Studies 50: 27–44.10.1111/j.1468-2478.2006.00391.xSearch in Google Scholar
Beenstock, M., and D. Felsenstein. 2007. “Spatial Vector Autoregressions.” Spatial Economic Analysis 2 (2): 167–196.10.1007/978-3-030-03614-0_6Search in Google Scholar
Blanchard, O., and P. Diamond. 1990. “The Cyclical Behovior of the Gross Flows of U.S. Workers.” Brookings Papers on Economic Activity 21 (2): 85–156.10.2307/2534505Search in Google Scholar
Blanchard, O., and L. F. Katz. 1992. “Regional Evolutions.” Brookings Papers on Economic Activity 19921: 1–75.10.2307/2534556Search in Google Scholar
Bottou, L., O. Chapelle, D. DeCoste, and J. Weston. 2007. Large-Scale Kernel Machines. Cambridge, Massachusetts: MIT Press.10.7551/mitpress/7496.001.0001Search in Google Scholar
Canova, F., and M. Ciccarelli. 2013. “Panel Vector Autoregressive Models A Survey.” ECB Working Paper Series 15: 1–53. http://doi.org/10.1108/S0731-9053(2013)0000031006.10.1108/S0731-9053(2013)0000031006Search in Google Scholar
Chen, Y. 2012. “On the Four Types of Weight Functions for Spatial Contiguity Matrix.” Letters in Spatial and Resource Sciences 5 (2): 65–72.10.1007/s12076-011-0076-6Search in Google Scholar
Cleveland, R. B., W. S. Cleveland, J. E. McRae, and I. Terpenning. 1990. “STL: A Seasonal-Trend Decomposition Procedure Based on Loess.” Journal of Official Statistics 6 (1): 3–73.Search in Google Scholar
Cliff, A., and J. K. Ord. 1973. Spatial Autocorrelation. London: Pion.Search in Google Scholar
Corrado, L., and B. Fingleton. 2012. “Where is the Economics in Spatial Econometrics.” Journal of Regional Science 52 (2): 210–239.10.1111/j.1467-9787.2011.00726.xSearch in Google Scholar
Dewachter, H., R. Houssa, and P. Toffano. 2012. “Spatial Propagation of Macroeconomic Shocks in Europe.” Review of World Economics 148 (2): 377–402.10.1007/s10290-012-0118-1Search in Google Scholar
Feng, C., H. Wang, N. Lu, T. Chen, H. He, Y. Lu, and X. Tu. 2014. “Log-Transformation and its Implications for Data Analysis.” Shanghai Arch Psychiatry 26 (2): 105–109.Search in Google Scholar
Fotheringham, S., and P. Rogerson. 2009. The SAGE Handbook of Spatial Analysis. London: SAGE Publications Ltd.10.4135/9780857020130Search in Google Scholar
Giacomini, R., and C. Granger. 2004. “Aggregation of Space-Time Processes.” Journal of Econometrics 118 (1–2): 7–26.10.1016/S0304-4076(03)00132-5Search in Google Scholar
Girardin, E., and K. A. Kholodilin. 2011. “How Helpful are Spatial Effects in Forecasting the Growth of Chinese Provinces?” Journal of Forecast 30: 622–643.10.1002/for.1193Search in Google Scholar
Gnana, K., and S. N. Deepa. 2013. “Review on Methods to Fix Number of Hidden Neurons in Neural Networks.” Mathematical Problems in Engineering 2013, Article ID 425740, 11 pages. doi:10.1155/2013/425740.Search in Google Scholar
Griffith, D. A. 2003 Spatial Autocorrelation and Spatial Filtering. Berlin: Springer.10.1007/978-3-540-24806-4Search in Google Scholar
Gurney, K. N. 2006. “Neural Networks for Perceptual Processing: From Simulation Tools to Theories.” Philosophical Transactions of the Royal Society London B 362: 339–353.10.1017/CBO9780511779145.002Search in Google Scholar
Hampel, K., E. Kunz, M. Schanne, G. Norbert, R. Wapler, and A. Weyh. 2007. “Regional Employment Forecasts with Spatial Interdependencies.” Discussion Paper 02/2007, IAB.Search in Google Scholar
Holly, S., M. Pesaran, and T. Yamagata. 2011. “The Spatial and Temporal Diffusion of House Prices in the UK.” Journal of Urban Economics 69 (1): 2–2310.1016/j.jue.2010.08.002Search in Google Scholar
Hong, J., S. Lee, J. Lim, and J. Kim. 2013. “Application of Spatial Econometrics Analysis for Traffic Accident Prediction Models in Urban Areas.” Proceedings of the Eastern Asia Studies 9: 390–397.Search in Google Scholar
Hyndman, R. 2015. “High-dimensional Autocovariance Matrices and Optimal Linear Prediction.” Electronic Journal of Statistics 9 (1): 792–796. DOI: doi:10.1214/14-EJS953.Search in Google Scholar
Igel, Ch., and M. Hüsken. 2000. “Improving the Rprop Learning Algorithm.” Second International Symposium on Neural Computation, pp. 115–121, ICSC Academic Press.Search in Google Scholar
Igel, Ch, and M. Hüsken. 2003. “Empirical Evaluation of the Improved Rprop Learning Algorithm.” Neurocomputing 50: 105–123. DOI: 10.1016/S0925-2312(01)00700-7.Search in Google Scholar
James, G., D. Witten, T. Hastie, and R. Tibshirani. 2013. An Introduction to Statistical Learning with Applications in R. New York: Springer.10.1007/978-1-4614-7138-7Search in Google Scholar
Kaastra, I., and M. Boyd. 1996. “Designing a Neural Network for Forecasting Financial and Economic Time Series.” Neurocomputing 10 (3): 215–236.10.1016/0925-2312(95)00039-9Search in Google Scholar
Khalik Salman, A., L. Arnesson, A. Sörensson, and G. Shukur. 2010. “Estimating International Tourism Demand for Selected Regions in Sweden and Norway with Iterative Seemingly Unrelated Regressions (ISUR).” Scandinavian Journal of Hospitality and Tourism 10 (4): 395–410.10.1080/15022250.2010.484221Search in Google Scholar
Kholodin, K., B. Siliverstos, and S. Kooths. (2007). A Dynamic Panel Data Approach to the Forecasting of the GDP of German Lander. German Institute for Economic Research.Search in Google Scholar
Kriesel, D. 2007. A Brief Introduction to Neural Networks, http://www.dkriesel.com.Search in Google Scholar
Kuethe, T. H., and V. Pede. 2009. Regional Housing Price Cycles: A Spatio-Temporal Analysis Using Us State Level, (09-04). http://ideas.repec.org/p/pae/wpaper/09-04.html.Search in Google Scholar
Lee, L. F., and J. Yu. 2010. “Estimation of Spatial Autoregressive Panel Data Models with Fixed Effects.” Journal of Econometrics 154: 165–185.10.1016/j.jeconom.2009.08.001Search in Google Scholar
Lee, L., and J. Yu. 2015. “Identification of Spatial Durbin Panel Models.” Journal of Applied Econometrics. 31: 133–162. DOI: 10.1002/jae.2450.Search in Google Scholar
Lehmann, R., and K. Wohlrabe. 2015. “Regional Economic Forecasting: State-of-the-Art Methodology and Future Challenges.” Economics and Business Letters 3 (4): 218–231.10.17811/ebl.3.4.2014.218-231Search in Google Scholar
LeSage, J. P. 1999. “The Theory and Practice of Spatial Econometrics.” International Journal of Forecasting 2 (2): 245–246.Search in Google Scholar
Levin, A., Chien-Fu Lin, and Chia-Shang Chu. 2002. “Unit Root Tests in Panel Data: Asymptotic and Finite-Sample Properties.” Journal of Econometrics 108 (1): 1–24.10.1016/S0304-4076(01)00098-7Search in Google Scholar
Lo, S., and S. Andrews. 2015. “To transform or not to transform: using generalized linear mixed models to analyse reaction time data.” Frontiers in Psychology 6: 1171. DOI: 10.3389/fpsyg.2015.01171.Search in Google Scholar PubMed PubMed Central
Lütkepohl, H., and F. Xu. 2012. “The Role of the Log Transformation in Forecasting Economic Variables.” Empirical Economics 42 (3): 619–638.10.1007/s00181-010-0440-1Search in Google Scholar
May, B., N. Korda, A. Lee, and D. Leslie. 2012. “Optimistic Bayesian Sampling in Contextual-Bandit Problems.” The Journal of Machine Learning Research 13 (1): 2069–2106.Search in Google Scholar
Monteiro, J. 2009. “Pollution Havens: a Spatial Panel VAR Approach.” The European Trade Study Group, 1–26. Retrieved from: http://www.etsg.org/ETSG2009/papers/monteiro.pdf.Search in Google Scholar
Moran, P. A. P. 1948. “The Interpretation of Statistical Maps.” Journal of the Royal Statistical Society. Series B (Methodological) 10 (2): 243–251.10.1111/j.2517-6161.1948.tb00012.xSearch in Google Scholar
Moran, P. A. P. 1950. “Notes on Continuous Stochastic Phenomena.” Biometrika 37: 17–23.10.1093/biomet/37.1-2.17Search in Google Scholar
Mutl, J. 2009. “Panel VAR Models with Spatial Dependence.” Institute for Advanced Studies, Economics Series 237: 1–38.Search in Google Scholar
Oancea, B., and S. Ciucu. 2013. “Time Series Forecasting using Neural Networks.” Proceedings of the CKS 2013 International Conference.Search in Google Scholar
O’Hara, R. B., and D. J. Kotze. 2010. “Do Not Log-Transform Count Data.” Methods in Ecology and Evolution 1: 118–122.10.1111/j.2041-210X.2010.00021.xSearch in Google Scholar
Patuelli, R., and M. Mayor. 2012. “Short-Run Regional Forecasts: Spatial Models Through Varying Cross-Sectional and Temporal Dimensions.” Quaderni DSE Working Paper No. 835. http://dx.doi.org/10.2139/ssrn.2084219.10.2139/ssrn.2084219Search in Google Scholar
Patuelli, R., S. Longhi, A. Reggiani, and P. Nijkamp. 2005. Forecasting Regional Employment in Germany by Means of Neural Networks and Genetic Algorithms, (0511002), 1–23. http://ideas.repec.org/p/wpa/wuwpco/0511002.html.Search in Google Scholar
Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-Section Dependence.” Journal of Applied Econometrics 22: 265–312.10.1002/jae.951Search in Google Scholar
Riedmiller, M. 1994. “Advanced Supervised Learning in Multi-Layer Perceptrons – from Backpropagation to Adaptive Learning Algorithms.” International Journal of Computer Standards and Interfaces 16: 265–278.10.1016/0920-5489(94)90017-5Search in Google Scholar
Riedmiller, M., and H. Braun. 1993. “A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algorithm.” EEE International Conference on Neural Networks, 586–599.Search in Google Scholar
Schanne, N., R. Wappler, and A. Weyh. 2010. “Regional Unemployment Forecasts with Spatial Interdependencies.” International Journal of Forecasting 26 (4): 908–926.10.1016/j.ijforecast.2009.07.002Search in Google Scholar
Schurmann, T., and P. Grassberger. 1996. “Entropy Estimation of Symbol Sequences.” Chaos 6: 41–427.10.1063/1.166191Search in Google Scholar PubMed
Seymen, A. 2008. “A Critical Note on the Forecast Error Variance Decomposition.” SSRN Electronic Journal 1–17. http://doi.org/10.2139/ssrn.1266093.10.2139/ssrn.1266093Search in Google Scholar
Shimer, R. 2005. “The Cyclical Behavior of Equilibrium Unemployment and Vacancies.” American Economic Review 95 (1): 25–49.10.1257/0002828053828572Search in Google Scholar
Sims, Ch. A., ed. 1994. Advances in Econometrics. Cambridge Books, Cambridge University Press.Search in Google Scholar
Stoyan, D., G. Upton, and B. Fingleton. 1986. Spatial Data Analysis, vol. 1: Point Pattern and Quantitative Data. Chichester/New York/Brisbane/Toronto/Singapore: J. Wiley & Sons, 1985.Search in Google Scholar
Telser, L. G. 1964. “Iterative Estimation of a Set of Linear Regression Equations.” Journal of American Statistical Association 59: 845–862.10.1080/01621459.1964.10480731Search in Google Scholar
Vega, S., and J. P. Elhorst. 2014. “Modelling Regional Labour Market Dynamics in Space and Time.” Papers in Regional Science 93 (4): 819–842.10.1111/pirs.12018Search in Google Scholar
Viton, P. A. 2010. “Notes on Spatial Econometric Models.” City and Regional Planning 870 (3): 9–10.Search in Google Scholar
Wozniak, M. 2015. “Can Stochastic Equilibrium Search Model Fit Transition Economies?.” Acta Oeconomica 65 (4): 567–591.10.1556/032.65.2015.4.4Search in Google Scholar
Xu, W., Z. Li, and Q. Chen. 2012. Forecasting the Unemployment Rate by Neural Networks Using Search Engine Query Data, Hawaii International Conference on System Sciences.10.1109/HICSS.2012.284Search in Google Scholar
Zhang, Z. 2016. “Neural Networks: Further Insights into Error Function, Generalized Weights and Others.” Annals of Translational Medicine 4 (16): 300.10.21037/atm.2016.05.37Search in Google Scholar
Zhang, G., B. Eddy Patuwo, and Michael Y. Hu. 1998. “Forecasting with Artificial Neural Networks: The State of the Art.” International Journal of Forecasting 14 (1): 35–62.10.1016/S0169-2070(97)00044-7Search in Google Scholar
Zhang, Y, Z. Zhang, and D. Wei. 2012. “Centrality Measure in Weighted Networks Based on an Amoeboid Algorithm.” Journal of Information & Computational Science 9 (2): 369–376.Search in Google Scholar
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