Penalised regressions vs. autoregressive moving average models for forecasting inflation
This article relates the Seasonal Autoregressive Moving Average Models (SARMA) to linear regression. Based on this relationship, the paper shows that penalized linear models can outperform the out-of-sample forecast accuracy of the best SARMA models in forecasting inflation as a function of past val...
- Autores:
-
Ospina-Holguín, Javier Humberto
Padilla Ospina, Ana Milena
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/6279
- Acceso en línea:
- https://hdl.handle.net/11323/6279
https://doi.org/10.17981/econcuc.41.1.2020.Econ.3
https://repositorio.cuc.edu.co/
- Palabra clave:
- Ridge regression
Penalised linear model
ARMA
SARMA
Inflation forecasting
Regresión de arista
Modelo lineal penalizado
Pronóstico de la inflación
- Rights
- openAccess
- License
- CC0 1.0 Universal
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| dc.title.spa.fl_str_mv |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| dc.title.translated.spa.fl_str_mv |
Regresiones penalizadas vs. modelos autorregresivos de media móvil para pronosticar la inflación |
| title |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| spellingShingle |
Penalised regressions vs. autoregressive moving average models for forecasting inflation Ridge regression Penalised linear model ARMA SARMA Inflation forecasting Regresión de arista Modelo lineal penalizado Pronóstico de la inflación |
| title_short |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| title_full |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| title_fullStr |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| title_full_unstemmed |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| title_sort |
Penalised regressions vs. autoregressive moving average models for forecasting inflation |
| dc.creator.fl_str_mv |
Ospina-Holguín, Javier Humberto Padilla Ospina, Ana Milena |
| dc.contributor.author.spa.fl_str_mv |
Ospina-Holguín, Javier Humberto Padilla Ospina, Ana Milena |
| dc.subject.spa.fl_str_mv |
Ridge regression Penalised linear model ARMA SARMA Inflation forecasting Regresión de arista Modelo lineal penalizado Pronóstico de la inflación |
| topic |
Ridge regression Penalised linear model ARMA SARMA Inflation forecasting Regresión de arista Modelo lineal penalizado Pronóstico de la inflación |
| description |
This article relates the Seasonal Autoregressive Moving Average Models (SARMA) to linear regression. Based on this relationship, the paper shows that penalized linear models can outperform the out-of-sample forecast accuracy of the best SARMA models in forecasting inflation as a function of past values, due to penalization and cross-validation. The paper constructs a minimal functional example using edge regression to compare both competing approaches to forecasting monthly inflation in 35 selected countries of the Organization for Economic Cooperation and Development and in three groups of coun-tries. The results empirically test the hypothesis that penalized linear regression, and edge regression in particular, can outperform the best standard SARMA models calculated through a grid search when fore-casting inflation. Thus, a new and effective technique for forecasting inflation based on past values is provided for use by financial analysts and investors. The results indicate that more attention should be paid to automatic learning techniques for forecasting inflation time series, even as basic as penalized linear regressions, because of their superior empirical performance. |
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2019 |
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2019-11-15 |
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2020-05-19T22:28:57Z |
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2020-05-19T22:28:57Z |
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Ospina-Holguín, J., & Ospina-Holguín, A. (2019). Penalised regressions vs. autoregressive moving average models for forecasting inflation. ECONÓMICAS CUC, 41(1), 65-80. https://doi.org/10.17981/econcuc.41.1.2020.Econ.3 |
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0120-3932, 2382-3860 electrónico |
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10.17981/econcuc.41.1.2020.Econ.3 |
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2382-3860 |
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Corporación Universidad de la Costa |
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Ospina-Holguín, J., & Ospina-Holguín, A. (2019). Penalised regressions vs. autoregressive moving average models for forecasting inflation. ECONÓMICAS CUC, 41(1), 65-80. https://doi.org/10.17981/econcuc.41.1.2020.Econ.3 0120-3932, 2382-3860 electrónico 10.17981/econcuc.41.1.2020.Econ.3 2382-3860 Corporación Universidad de la Costa 0120-3932 REDICUC - Repositorio CUC |
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Anzola, C., Vargas, P. & Morales, A. (2019). Transición entre sistemas financieros bancarios y bursátiles. Una aproximación mediante modelo de Swithing Markov. Económicas CUC, 40(1), 123–144. https://doi.org/10.17981/econcuc.40.1.2019.08 Box, G. E. P. & Jenkin, G. M. (1976). Time series analysis, forecasting and control. San Francisco: Holden-Day. Burnham, K. P. & Anderson, D. R. (2004). Multimodel inference. Sociological Methods & Research, 33(2), 261–304. https://doi.org/10.1177/0049124104268644 Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431. https://doi.org/10.2307/2286348 Diebold, F. X. & Mariano, R. S. (2002). Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 20(1), 134–144. https://doi. org/10.1198/073500102753410444 Faust, J. & Wright, J. H. (2013). Forecasting Inflation. In, g. Elliott & A. Timmer- mann (Eds.), Handbook of Economic Forecasting, Vol. 2. Part. A (pp. 2–56). Amsterdam: Elsevier. https://doi.org/10.1016/B978-0-444-53683-9.00001-3 Gil, J., Castellanos, D. & gonzalez, D. (2019). Margen de intermediación y concentración bancaria en Colombia: un análisis para el periodo 2000-2017. Económicas CUC, 40(2), 9–30. https://doi.org/10.17981/econcuc.40.2.2019.01 Gómez, C., Sánchez, V. & Millán, E. (2019). Capitalismo y ética: una relación de tensiones. Económicas CUC, 40(2), 31–42. https://doi.org/10.17981/econ- cuc.40.2.2019.02 Gu, S., Kelly, B. T. & Xiu, D. (december, 2018). Empirical Asset Pricing Via Machine Learning [Paper 18-04]. 31st Australasian Finance and Banking Conference, AFBC, Sydney, Australia, 1–79. https://doi.org/10.2139/ssrn.3159577 Hoerl, A. E. & Kennard, R. W. (1970). Ridge Regression: Biased Estimation for Nonor- thogonal Problems. Technometrics, 12(1), 55–67. https://doi.org/10.2307/1267351 Hyndman, R. J. (july, 2013). Facts and fallacies of the AIC. [Online]. Available from https://robjhyndman.com/hyndsight/aic/ Hyndman, R. J. & Khandakar, Y. (2008). Automatic Time Series Forecasting: The forecast Package for R. Journal of Statistical Software, 27(1), 1–22. https://doi. org/10.18637/jss.v027.i03 Kvalseth, T. O. (1985). Cautionary Note about R 2. The American Statistician, 39(4), 279–285. https://doi.org/10.2307/2683704 MacKinnon, J. g. (1996). Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics, 11(6), 601–618. https://doi. org/10.1002/(SICI)1099-1255(199611)11:6<601::AID-JAE417>3.0.CO;2-T Mockus, J. (1989). Bayesian approach to global optimization. Dordrecht: Kluwer Academic Publishers. Mullainathan, S. & Spiess, J. (2017). Machine Learning: An Applied Econometric Approach. Journal of Economic Perspectives, 31(2), 87–106. https://doi.org/10.1257/ jep.31.2.87 OECD. (2019). Inflation (CPI). [indicator]. https://doi.org/10.1787/eee82e6e-en Osborn, D. R., Chui, A. P. L., Smith, J. P. & Birchenhall, C. R. (2009). Seasonality and the order of integration for consumption. Oxford Bulletin of Economics and Statistics, 50(4), 361–377. https://doi.org/10.1111/j.1468-0084.1988.mp50004002.x Quinn, T., Kenny, g. & Meyler, A. (1999). Inflation analysis: An overview. [MPRA Paper No. 11361]. Munich: UTC. Retrieved from https://mpra.ub.uni-muenchen. de/11361/1/MPRA_paper_11361.pdf Santosa, F. & Symes, W. W. (1986). Linear Inversion of Band-Limited Reflection Seismograms. SIAM Journal on Scientific and Statistical Computing, 7(4), 1307–1330. https://doi.org/10.1137/0907087 Tibshirani, R. (1996). Regression Shrinkage and Selection Via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288. https:// doi.org/10.1111/j.2517-6161.1996.tb02080.x Tikhonov, A. N. & Arsenin, V. Y. (1977). Solution of illposed problems. Washington: Winston & Sons. Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320. https://doi.org/10.1111/j.1467-9868.2005.00503.x |
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Ospina-Holguín, Javier HumbertoPadilla Ospina, Ana Milena2020-05-19T22:28:57Z2020-05-19T22:28:57Z2019-11-15Ospina-Holguín, J., & Ospina-Holguín, A. (2019). Penalised regressions vs. autoregressive moving average models for forecasting inflation. ECONÓMICAS CUC, 41(1), 65-80. https://doi.org/10.17981/econcuc.41.1.2020.Econ.30120-3932, 2382-3860 electrónicohttps://hdl.handle.net/11323/6279https://doi.org/10.17981/econcuc.41.1.2020.Econ.310.17981/econcuc.41.1.2020.Econ.32382-3860Corporación Universidad de la Costa0120-3932REDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This article relates the Seasonal Autoregressive Moving Average Models (SARMA) to linear regression. Based on this relationship, the paper shows that penalized linear models can outperform the out-of-sample forecast accuracy of the best SARMA models in forecasting inflation as a function of past values, due to penalization and cross-validation. The paper constructs a minimal functional example using edge regression to compare both competing approaches to forecasting monthly inflation in 35 selected countries of the Organization for Economic Cooperation and Development and in three groups of coun-tries. The results empirically test the hypothesis that penalized linear regression, and edge regression in particular, can outperform the best standard SARMA models calculated through a grid search when fore-casting inflation. Thus, a new and effective technique for forecasting inflation based on past values is provided for use by financial analysts and investors. The results indicate that more attention should be paid to automatic learning techniques for forecasting inflation time series, even as basic as penalized linear regressions, because of their superior empirical performance.Este artículo relaciona los Modelos Autorregresivos Estacionales de Media Móvil (SARMA) con la regresión lineal. Sobre la base de esta relación, el documento muestra que los modelos lineales penalizados pueden superar la precisión del pronóstico fuera de la muestra de los mejores modelos SARMA al pronosticar la inflación en función de valo-res pasados, debido a la penalización y a la validación cruzada. El artí-culo construye un ejemplo funcional mínimo utilizando la regresión de arista para comparar ambos enfoques que compiten al pronosticar la inflación mensual en 35 países seleccionados de la Organización para la Cooperación y el Desarrollo Económico y en tres grupos de países. Los resultados verifican empíricamente la hipótesis de que la regre-sión lineal penalizada, y la regresión de arista en particular, puede superar a los mejores modelos estándar SARMA calculados a través de una búsqueda de cuadrícula cuando se pronostica la inflación. Así, se proporciona una técnica nueva y efectiva para pronosticar la infla-ción basada en valores pasados para el uso de analistas financieros e inversores. Los resultados indican que se debe prestar más atención a las técnicas de aprendizaje automático para el pronóstico de series de tiempo de la inflación, incluso tan básicas como las regresiones linea-les penalizadas, debido a su rendimiento empírico superior.Ospina, Javier H.-will be generated-orcid-0000-0002-0103-3280-600Padilla Ospina, Ana Milena-will be generated-orcid-0000-0003-3859-8741-600application/pdfengCorporación Universidad de la CostaECONÓMICAS CUC; Vol. 41, Núm. 1 (2020)ECONÓMICAS CUCECONÓMICAS CUCAnzola, C., Vargas, P. & Morales, A. (2019). Transición entre sistemas financieros bancarios y bursátiles. Una aproximación mediante modelo de Swithing Markov. Económicas CUC, 40(1), 123–144. https://doi.org/10.17981/econcuc.40.1.2019.08Box, G. E. P. & Jenkin, G. M. (1976). Time series analysis, forecasting and control. San Francisco: Holden-Day.Burnham, K. P. & Anderson, D. R. (2004). Multimodel inference. Sociological Methods & Research, 33(2), 261–304. https://doi.org/10.1177/0049124104268644Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427–431. https://doi.org/10.2307/2286348Diebold, F. X. & Mariano, R. S. (2002). Comparing Predictive Accuracy. Journal of Business & Economic Statistics, 20(1), 134–144. https://doi. org/10.1198/073500102753410444Faust, J. & Wright, J. H. (2013). Forecasting Inflation. In, g. Elliott & A. Timmer- mann (Eds.), Handbook of Economic Forecasting, Vol. 2. Part. A (pp. 2–56). Amsterdam: Elsevier. https://doi.org/10.1016/B978-0-444-53683-9.00001-3Gil, J., Castellanos, D. & gonzalez, D. (2019). Margen de intermediación y concentración bancaria en Colombia: un análisis para el periodo 2000-2017. Económicas CUC, 40(2), 9–30. https://doi.org/10.17981/econcuc.40.2.2019.01Gómez, C., Sánchez, V. & Millán, E. (2019). Capitalismo y ética: una relación de tensiones. Económicas CUC, 40(2), 31–42. https://doi.org/10.17981/econ- cuc.40.2.2019.02Gu, S., Kelly, B. T. & Xiu, D. (december, 2018). Empirical Asset Pricing Via Machine Learning [Paper 18-04]. 31st Australasian Finance and Banking Conference, AFBC, Sydney, Australia, 1–79. https://doi.org/10.2139/ssrn.3159577Hoerl, A. E. & Kennard, R. W. (1970). Ridge Regression: Biased Estimation for Nonor- thogonal Problems. Technometrics, 12(1), 55–67. https://doi.org/10.2307/1267351Hyndman, R. J. (july, 2013). Facts and fallacies of the AIC. [Online]. Available from https://robjhyndman.com/hyndsight/aic/Hyndman, R. J. & Khandakar, Y. (2008). Automatic Time Series Forecasting: The forecast Package for R. Journal of Statistical Software, 27(1), 1–22. https://doi. org/10.18637/jss.v027.i03Kvalseth, T. O. (1985). Cautionary Note about R 2. The American Statistician, 39(4), 279–285. https://doi.org/10.2307/2683704MacKinnon, J. g. (1996). Numerical distribution functions for unit root and cointegration tests. Journal of Applied Econometrics, 11(6), 601–618. https://doi. org/10.1002/(SICI)1099-1255(199611)11:6<601::AID-JAE417>3.0.CO;2-TMockus, J. (1989). Bayesian approach to global optimization. Dordrecht: Kluwer Academic Publishers.Mullainathan, S. & Spiess, J. (2017). Machine Learning: An Applied Econometric Approach. Journal of Economic Perspectives, 31(2), 87–106. https://doi.org/10.1257/ jep.31.2.87OECD. (2019). Inflation (CPI). [indicator]. https://doi.org/10.1787/eee82e6e-enOsborn, D. R., Chui, A. P. L., Smith, J. P. & Birchenhall, C. R. (2009). Seasonality and the order of integration for consumption. Oxford Bulletin of Economics and Statistics, 50(4), 361–377. https://doi.org/10.1111/j.1468-0084.1988.mp50004002.xQuinn, T., Kenny, g. & Meyler, A. (1999). Inflation analysis: An overview. [MPRA Paper No. 11361]. Munich: UTC. Retrieved from https://mpra.ub.uni-muenchen. de/11361/1/MPRA_paper_11361.pdfSantosa, F. & Symes, W. W. (1986). Linear Inversion of Band-Limited Reflection Seismograms. SIAM Journal on Scientific and Statistical Computing, 7(4), 1307–1330. https://doi.org/10.1137/0907087Tibshirani, R. (1996). Regression Shrinkage and Selection Via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58(1), 267–288. https:// doi.org/10.1111/j.2517-6161.1996.tb02080.xTikhonov, A. N. & Arsenin, V. Y. (1977). Solution of illposed problems. Washington: Winston & Sons.Zou, H. & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(2), 301–320. https://doi.org/10.1111/j.1467-9868.2005.00503.x141Revista Económicas CUCCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2ECONÓMICAS CUChttps://revistascientificas.cuc.edu.co/economicascuc/article/view/2657Ridge regressionPenalised linear modelARMASARMAInflation forecastingRegresión de aristaModelo lineal penalizadoPronóstico de la inflaciónPenalised regressions vs. autoregressive moving average models for forecasting inflationRegresiones penalizadas vs. modelos autorregresivos de media móvil para pronosticar la inflaciónArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionPublicationORIGINALPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdfPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdfapplication/pdf900642https://repositorio.cuc.edu.co/bitstreams/64533127-6918-4906-b23a-6356e49e57b6/download04394b497fa7f9568f344ddeed5f1541MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.cuc.edu.co/bitstreams/19ad13c2-a475-4ce0-aec4-84fbb866a823/download42fd4ad1e89814f5e4a476b409eb708cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/2a2fb5ff-e2e1-4a8d-9904-5ab8bca6bd82/download8a4605be74aa9ea9d79846c1fba20a33MD53THUMBNAILPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdf.jpgPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdf.jpgimage/jpeg66284https://repositorio.cuc.edu.co/bitstreams/6eea842b-e705-4fd5-889d-382b66c2b166/downloadb90dede79c10c40cd9f666718a5c0842MD54TEXTPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdf.txtPenalised regressions vs. autoregressive moving average models for forecasting inflation.pdf.txttext/plain35903https://repositorio.cuc.edu.co/bitstreams/b8220bbc-a0fd-448c-83fc-06b69381622f/download17d175a86cb9452d5030a6ffa51fc266MD5511323/6279oai:repositorio.cuc.edu.co:11323/62792024-09-17 10:52:33.519http://creativecommons.org/publicdomain/zero/1.0/CC0 1.0 Universalopen.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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 |