Brazilian Journal of Probability and Statistics

The Split-BREAK model

Vladica Stojanović, Biljana Popović, and Predrag Popović

Full-text: Open access

Abstract

A special type of the stochastic STOPBREAK process, which behaves properly when applied to time series data with emphatic permanent fluctuations, is presented. A good dynamic behavior is induced by the threshold regime and named the Split-BREAK process. General properties of this threshold STOPBREAK process are investigated, as well as some estimation procedures for the parameters of the process presented. A Monte Carlo simulation of the process is given and its application to the share trading on the Belgrade Stock Exchange illustrated.

Article information

Source
Braz. J. Probab. Stat., Volume 25, Number 1 (2011), 44-63.

Dates
First available in Project Euclid: 3 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1291387773

Digital Object Identifier
doi:10.1214/09-BJPS025

Mathematical Reviews number (MathSciNet)
MR2746492

Zentralblatt MATH identifier
1298.62158

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Split-BREAK process Noise-indicator Split-MA(1) process

Citation

Stojanović, Vladica; Popović, Biljana; Popović, Predrag. The Split-BREAK model. Braz. J. Probab. Stat. 25 (2011), no. 1, 44--63. doi:10.1214/09-BJPS025. https://projecteuclid.org/euclid.bjps/1291387773


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References

  • Billingsley, P. (1961). The Lindeberg–Levy theorem for martingales. Proceedings of the American Mathematical Society 12 788–792.
  • Engle, R. F. and Smith, A. D. (1999). Stochastic permanent breaks. The Review of Economics and Statistics 81 553–574.
  • Fuller, W. A. (1976). Introduction to Statistical Time Series. Wiley, New York.
  • González, A. (2004). A smooth permanent surge process. SSE/EFI Working Paper Series in Economics and Finance, No. 572. Stockhölm.
  • Gonzalo, J. and Martinez, O. (2006). Large shocks vs. small shocks (Or does size matter? May be so). Journal of Econometrics 135 311–347.
  • Hafner, C. M. (1998). Durations, volume and prediction of financial returns in transaction time. In Symposium on Microstructure and High Frequency Data. Paris.
  • Lawrence, A. J. and Lewis, P. A. W. (1992). Reversed residuals in autoregressive time series analysis. Journal of Time Series Analysis 13 253–266.
  • Nicholls, D. and Quinn, B. (1982). Random Coefficient Autoregressive Models: An Introduction. Lecture Notes in Statistics 11. Springer, New York.
  • Popović, B. Č. and Stojanović, V. (2005). Split-ARCH. PLISKA Studia Mathematica Bulgarica 17 201–220.
  • Popović, B. Č. (1992). The first order RC autoregressive time series. Scientific Review 2122 131–136.
  • Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.
  • Stojanović, V. and Popović, B. (2005). Thresholds STOPBREAK Process like a stochastic model of the financial sequences dynamics (in Serbian). In Proceedings of the Conference SYM-OP-IS 505–508.