An Application of Smooth Transition Regression Models to Homeless Research

Jadidzadeh, Ali (2022): An Application of Smooth Transition Regression Models to Homeless Research.

Abstract

This article discusses the limitations of linear models in explaining certain aspects of homelessness-related data and proposes the use of nonlinear models to allow for state-dependent or regime-switching behavior. The threshold autoregressive (TAR) model and its smooth transition autoregressive (STAR) extensions are introduced as a popular class of nonlinear models. The article explains how these models can be applied to univariate time series data to investigate variations in weather conditions on the flow of homeless shelters over time. The objective is to identify the sensitivity of publicly-funded emergency shelter use to changes in weather conditions and better inform social agencies and government funders of predictable and unpredictable changes in demand for shelter beds. The smooth transition regression (STR) model is proposed as a useful tool for investigating nonlinearities in non-autoregressive contexts using both time series and panel data. The article concludes by highlighting the advantages of STR models and their three-stage modeling procedure: model specification, estimation, and evaluation.

• Item Type: MPRA Paper
• Language: English
• Keywords: Homelessness; nonlinear models; smooth transition regression (STR) model.
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; I - Health, Education, and Welfare > I3 - Welfare, Well-Being, and Poverty > I32 - Measurement and Analysis of Poverty

References

Chan, K. S. (1993). Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics, 21(1), 520-533. Davies, R. B. (1987). Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika, 74(1), 33-43. Espinoza, R., Leon, H., & Prasad, A. (2012). When should we worry about inflation? The world bank economic review, 26(1), 100-127. Fahmy, H. (2014). Modelling nonlinearities in commodity prices using smooth transition regression models with exogenous transition variables. Statistical Methods & Applications, 23(4), 577-600. Fischer, S. (1993). The role of macroeconomic factors in growth. Journal of monetary economics, 32(3), 485-512. Franses, P. H., & Van Dijk, D. (2000). Non-linear time series models in empirical finance. Cambridge university press. Glynn, C., & Fox, E. B. (2019). Dynamics of homelessness in urban America. The Annals of Applied Statistics, 13(1), 573-605. Glynn, C., Byrne, T. H., & Culhane, D. P. (2021). Inflection points in community-level homeless rates. The Annals of Applied Statistics, 15(2), 1037-1053. Godfrey, L. G. (1988). Misspecification Tests in Econometrics. Cambridge: Cambridge Universit. González, A., Teräsvirta, T., & van Dijk, D. (2005). Panel Smooth Transition Regression Models. SSE/EFI Working Paper Series in Economics and Finance(604). Granger, C. W., & Teräsvirta, T. (1993). Modelling non-linear economic relationships. Oxford University Press. Hanratty, M. (2017). Do local economic conditions affect homelessness? Impact of area housing market factors, unemployment, and poverty on community homeless rates. Housing Policy Debate, 27(4), 640-655. Jadidzadeh, A., & Kneebone, R. D. (2015). Shelter from the Storm: Weather-Induced Patterns in the Use of Emergency Shelters. SPP Research Paper, 8(6), 1-15. Khan, M. S., & Senhadji, A. S. (2001). Threshold effects in the relationship between inflation and growth. IMF Staff papers, 48(1), 1-21. Kneebone, R. D., & Wilkins, M. (2022). Local conditions and the prevalence of homelessness in Canada. SPP Research Paper, 18(24). Luukkonen, R., Saikkonen, P., & Teräsvirta, T. (1988). Testing linearity against smooth transition autoregressive models. Biometrika, 75(3), 491-499. Teräsvirta, T. (1994). Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association, 89(425), 208-218. Teräsvirta, T. (1998). Modelling economic relationships with smooth transition regressions. In A. Ullah, & D. E. Giles (Eds.), Handbook of Applied Economic Statistics (pp. 507-552). New York: Marcel Dekker. Teräsvirta, T., Tjøstheim, D., & Grange, C. W. (2010). Modelling nonlinear economic time series. New York: Oxford University Press. Tong, H. (1978). On a threshold model. In C. Chen (Ed.), Pattern Recognition and Signal Processing. Amsterdam: Sijhoff & Noordhoff. Tong, H. (1990). Non-linear time series: a dynamical system approach. Oxford university press. van Dijk, D., Teräsvirta, T., & Franses, P. H. (2002). Smooth transition autoregressive models - A survey of recent developments. Econometric Reviews, 21(1), 1-47.