Abstract
This paper develops a framework for the analysis of state-space models combined with Kalman and smoothed Kalman filters for the estimation of unknown states, and parameters, determining the accuracy of the algorithms, with the purpose of analyzing some time series of the macroeconomy of Ecuador. This methodology plays an important role in the area of economics and finance and has many advantages because it allows describing how observed macroeconomic variables can be related to potentially unobserved state variables, determining the evolution in real time, estimating unobserved trends, changes of structures and make forecasts in future times. To achieve the objectives, three models are proposed: the first model is used to estimate the Ecuador’s gross domestic product. The second model combines a state space model with the classic ARIMA (p, q, r) model to adjust the GDP rate and finally it is considered a model for the simultaneous stress time series analysis related to: consumer price index, industrial production index and active interest rate. In all the cases studied, the estimates obtained reflect the real behavior of the Ecuadorian economy. The square root of the mean square error was used as a measure of goodness of fit to measure the quality of estimation of the algorithms, obtaining small errors.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kalman, R.: New approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng. 82(Series D), 35–45 (2016)
Kalman, R., Bucy, R.: New results in linear filtering and prediction theory. J. Basic Eng. Trans. ASME Ser. D 83, 95–108 (2016)
Anderson, B., Moore, J.: Optimal Filtering. Prentice Hall, New Jersy (1979)
Harvey, A.: Forecasting, Stuctural Time Series and the Kalman Filter, 1st edn. Cambridge University Press, UK (1989)
West, M., Harrison, J.: Bayesian Forecasting and Dynamic Model, 2nd edn. Springer, New York (1989)
Carter, C., Kohn, R.: On Gibbs sampling for state space models. Biometrika 81(3), 541–553 (1994)
Box, G., Jenkins, G.: Time Series Analysis Forecasting and Control. San Francisco (1970)
Ball, F., Rice, J.: Stochastic models for ion channels: introduction and bibliography. Biometrika 112, 189 (1992)
Hodgson, M.: A Bayesian restoration of an ion channel signal. J. Roy. Stat. Soc. Ser. B 61, 95–114 (1999)
Boys, R., Henderson, D., Wilkinson, D.: Detecting homogeneous segments in DNA sequences by using hidden Markov models. J. Roy. Stat. Soc. Ser. C 49, 269–285 (2000)
Juang, B., Rabiner, L.: Hidden Markov models for speech recognition. Technometrics 33, 251–272 (1991)
Hull, J., White, A.: The pricing of options on assets with stochastic volatilities. J. Financ. 42, 281–300 (1987)
Chen, J., Gupta, A.: Testing and locating changepoints with application to stock prices. J. Am. Stat. Assoc. 92, 739–747 (1997)
Infante, S., Rojas, J., Hernández, A., Cartaya, V.: AModelos de espacio estado basados en la distribución normal inversa gaussiana: una aplicación al análisis de series de tiempo de la economía venezolana estadística. Rev. Inst. Interamericano Estadística 61(178), 5–36 (2010)
Estévez, G., Infante, S., Sáez, F.: Estimation of general equilibium model in dynamic economies using Markov chain monte carlo methods. Rev. Mat. Teoría Aplicaciones 19(1), 7–36 (2012)
Trosel, Y., Hernandez, A., F., Infante, S.: Estimación de modelos de volatilidad estocástica vía filtro auxiliar de partículas. Rev. Mat. Teoría Aplicaciones 26(1), 45–81 (2019). https://doi.org/10.15517/rmta.v26i1.35518
Infante, S., Gomez, E., Sánchez, L., Hernández, A.: An estimation of the industrial production dynamic in the mercosur countries using the markov switching model. Rev. Electrón. Comun. Trabajos ASEPUMA Rect@ 20, 21–42 (2019a)
Infante, S., Luna, C., Sánchez, L., Hernández, A.: Estimation of stochastic volatility models using optimized filtering algorithms. Aust. J. Stat. 48, 73–96 (2019b)
Roth, M.: Advanced Kalman filtering approaches to Bayesian state estimation. LiU-Tryck, Sweden (2017)
Infante, S., Sánchez, L., Hernández, A., Marcano, J.: Sequential Monte Carlo filters with parameters learning for commodity pricing models. Stat. Optim. Inf. Comput. 9(3), 694–716 (2021). https://doi.org/10.19139/soic-2310-5070-814
Ruey, S., Rong, C.: Nonlinear Time Series Analysis, 1st edn. Wiley, Hoboken (2019)
Petropoulos, F., Spiliotis, E.: The wisdom of the data: getting the most out of univariate time series forecasting. Forecasting 3, 478–497 (2021). https://doi.org/10.3390/forecast3030029
Petris, G.: An R package for dynamic linear models. J. Stat. Softw. 2(5), 99–110 (2010)
Shumway, R., Stoffer, D.: Time Series Analysis and Its Applications, 4th edn. Springer, New York (2016). https://doi.org/10.1007/978-3-319-52452-8
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Bautista Vega, H., Infante, S., Amaro, I.R. (2021). Estimation of the State Space Models: An Application in Macroeconomic Series of Ecuador. In: Salgado Guerrero, J.P., Chicaiza Espinosa, J., Cerrada Lozada, M., Berrezueta-Guzman, S. (eds) Information and Communication Technologies. TICEC 2021. Communications in Computer and Information Science, vol 1456. Springer, Cham. https://doi.org/10.1007/978-3-030-89941-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-89941-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-89940-0
Online ISBN: 978-3-030-89941-7
eBook Packages: Computer ScienceComputer Science (R0)