Modeling golden and dollar data by robust simulation-based estimation

Rahimpoor, Ahad; Yarmohamadi, Masoud; Chinipardaz, Rahim; Shadrokh, Ali

doi:10.22055/jqe.2019.27757.1980

Modeling golden and dollar data by robust simulation-based estimation

https://doi.org/10.22055/jqe.2019.27757.1980

Volume 17, Issue 1 - Serial Number 64

Vol. 17, No. 1, Spring 2020

Winter 2020

Pages 35-60

Quarterly Journal of Quantitative Economics (JQE)

Document Type : Research Paper

Authors

Ahad Rahimpoor ¹

Masoud Yarmohamadi ²

Rahim Chinipardaz ³

Ali Shadrokh ⁴

¹ Department of statistics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran

² Associate Professor, Department of statistics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran.

³ Professor, Department of statistics, Shahid Chamran University, Ahwaz, Iran

⁴ Associate Professor, Department of statistics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran

Abstract

Multivariate time series data are often modeled using vector autoregressive moving average (VARMA) model. However, the presence of outliers can violate the stationary assumption and may lead to wrong modeling, biased estimation of parameters and inaccurate prediction. Therefore, a new robust simulation-based estimation for parameters of the VARMA model was introduced in this research. The simulation-based estimation as a kind of indirect estimation uses the estimation of the simple vector autoregressive (VAR) model with large order rather than the estimation of the complex VARMA model. To do this, the VAR model was first fitted on observation. Then, the data from different VARMA models were simulated and on each simulated data, the VAR model was fitted. The simulation-based method is based on the distance between the estimation of the VAR model on the simulation and observation data. The values of the parameters that use the VARMA model in the simulation and provide the minimum distance are indeed the estimates of the VARMA model parameters. Thus, if the estimates of VAR model are solid, we expect the VARMA model to be stable as well. For this reason, the robust BMM method of Muler and Yohai (2013) was used to estimate the VAR model. The simulation-based estimator has asymptotic normality and consistency properties. In addition, the simulation study in the data without outliers showed that the ratio of the mean square error of this estimator to the conditional maximum likelihood estimator was between 0.6 and 0.7 which is allowable for a robust estimator. Besides, when the 0.05 data is contaminated by the outliers, the mean square error of the robust simulation-based estimator is lower than the conditional maximum likelihood estimator.
As a real example, the gold and dollar price data in the Tehran free market were collected and investigated weekly in the period 2013-2018. It should be noted that gold and dollar prices are often affected by economic, political, and war crises which, in turn, create outliers. Thus, a robust method was used to reduce the bad effects of these outliers to estimate the model correctly. As gold and dollar prices are highly correlated, the VARMA model can be used to predict the gold and dollar interactions. Fitting the VARMA (1, 1) model to these data shows that the variance of the gold price error in the robust model to the conditional maximum likelihood reduced by 38%. However, the variance of dollar error in the robust model to the maximum conditional likelihood reduced by 30%. In other words, using robust method leads to better predictions with less variance. According to the fitted vector model, the gold price forecast for each week was obtained using the gold price of the previous week and the gold and dollar errors of the previous week. Besides, a forecast of the dollar for each week was obtained by the dollar and dollar error of the previous week.

Keywords

Outlier

robustness

simulation-based

VARMA model

Subjects

Econometrics

- Ben, M.G., Martinez, E.J., & Yohai, V.J. (1999). Robust Estimation in Vector Autoregressive Moving-Average Time Series Models. Journal of Time Series Analysis, 20(4), 381-399. ##- Ben, M.G., Villar, A.J., & Yohai, V.J. (2001). Robust Estimation in Vector Autoregressive Models Based on a Robust Scale. Estadística, 53, 397–434. ##- Brockwell, P.J., & Davis, R.A. (1991). Time Series: Theory and Methods. New York: Springer-Verlag. ##- Chen, C., & Liu, L. (1993). Joint Estimation of Model Parameters and Outlier Effects in Time Series. Journal of the American Statistical Association, 88(421), 284–297. ##- Croux, C., & Joossens, K. (2008). Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure. In: COMPSTAT 2008: Proceedings in Computational Statistics, 489–501. ##- Delavari, M. & Roshani, B.N. (2012). Investigating Factors Affecting the Future Volatility of Gold Coin Prices. Financial Economy (Financial Economy and Development), 6(19), 29-58. in Persion. ##- Ehsanifar, M., & Rasi, R.E. (2015). Forecasting Currency Exchange Rate in Capital Market using Autoregressive Moving Average Regression and Neural Network Models(Case Study: Australian Dollar, Canadian Dollar, Japanese Yen and British Pound). Financial Knowledge of Securities Analysis, 8(27), 35-51. in Persion. ##- Gourieroux, C., Monfort, A., & Renault, A.E. (1993). Indirect Inference. Journal of Applied Econometrics, 8, 85-118. ##- Gourieroux, C., & Monfort, A. (1996). Simulation-Based Econometric Methods. Oxford: Oxford University Press. ##- Henze, N., & Zirkler, B. (1990). A Class of Invariant Consistent Tests for Multivariate Normality. Communications in Statistics-Theory and Method, 19(10), 3595-3618. ##- Hosseinioun, N.S., Behname, M, & Ebrahimi S.T. (2016). Volatility Transmission of the Rate of Returns in Iranian Stock, Gold and Foreign Currency Markets. Iranian Journal of Economic Research, 21(66), 123-150. in Persion. ##- Hosseini, S.S., & Rezai, A. (2017). Forecasting the Official Exchange Rate in Iran using ARIMA Auto Regression Model with Intervention Factors and Comparison with Random Step Model. New Economy And Trade, 12(1), 51-80. in Persion. ##- Huber, P. (1981). Robust Statistics. Wiley, New York. ##- Jahanbin, G. (2012). Detection of Outliers in ARMA Models (Unpublished Master's thesis), Department of Statistics, College of Science, Shiraz university. in Persion. ##- Keshideh, M.D., & Asl, N.M. (2011). Introducing FOREX Market and Identify Factors in Forecasting Exchange Rates in Iran. Journal of Financial Economics (Financial Economics and Development) , 5(14), 138-161. in Persion. ##- Khashai, M., & Bijari, M. (2008). Gold Price Forecasting using Combined Models of Classic Autoregressive Integrated Moving Average Model with Fuzzy Logic. Journal of Isfahan University (Humanities), 3(31), 151-162. in Persion. ##- Li, W.K., & Hui, Y.V. (1989). Robust Multiple Time Series Modelling. Biometrika, 76, 309-315. ##- Luna, X., & Genton, M.G. (2001). Robust Simulation-Based Estimation of ARMA Models. Journal of Computational and Graphical Statistics, 10, 370–387. ##- Lutkepohl, H. (2006). New Introduction to Multiple Time Series Analysis. Berlin and Heidelberg: Springer. ##- Muler, N., & Yohai, V.J. (2013). Robust Estimation for Vector Autoregressive Models. Computational Statistics and Data Analysis, 65, 68–79. ##- Nezhad, M.Z., Majidi, A.F., & Rezaei, R. (2009). Forcasting Exchange Rate with Artificial Neural Network (ANN) and Autoregressive Integrated Moving Average Process (ARIMA). Journal of Quantitative Economics (Quarterly Journal of Economics Review), 5(4), 107-130. in Persion. ##- Plakanadaras, V. (2015). Forecasting Financial Time Series with Machin Learning Techniques (Unpublished Doctoral Dissertation), Department of Economics, Democritus University of Thrace, Greece. ##- Shirazi, H., & Nasrollahi, K. (2014). Monetary Models and Exchange Rate Forecast in Iran: from theory to empirical evidences. Quarterly Journal of Fiscal and Economic Policies, 1(4), 5-24. in Persion. ##- Smith, A.A. (1993). Estimating Nonlinear Time Series Models using Simulated Vector Autoregressions. Journal of Applied Econometrics, 8, S63-S84. ##- Tajalli, N. (2017). Forecasting Gold Price Fluctuations using ANN-GARCH Combined Model (Unpublished Master's thesis), Management Group, Faculty of Economics, Management and Commerce, Tabriz University. in Persion. ##- Tehrani, R., & Khosroshahi, S.A. (2017). Fluctuation Transfer and the Interaction of Stock Markets, Currency and Gold. Financial Management Perspective, 7(18), 9-31. in Persion. ##- Tsay, R., Pena, D., & Pankratz, A. (2000). Outliers in Multivariate Time Series. Biometrika, 87, 789-804. ##- Ursu, E., & Péreau, J-C. (2014). Robust Modelling of Periodic Vector Autoregressive Time Series. Journal of Statistical Planning and Inference, 155, 93–106. ##- Yarmohammadi, M., & Mahmoudvand, R. (2016). Exchange RatePrediction using Singular Spectrum Analysis. Quarterly Journal of Applied Economics Studiesin Iran, 5(18), 133-146. in Persion. ##- Yohai, V.J. (1987). High Breakdown Point and High Efficiency Estimates for Regression. Annals of Statistics, 15, 642–656. ##- Zarei, M. (2017). Gold Price Forecasting using ANN, ANFIS and SVM Comparison Methods (Unpublished Master's thesis), management Group, Faculty of Economics, Management and Commerce, Tabriz University. in Persion. ##

XML

PDF 894.92 K

Extended Abstract

Full Text in second language