# Analysis of Structural Changes in Financial Datasets Using the Breakpoint Test and the Markov Switching Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{1}and U

_{2}are the random errors with normally distributed $\left(0,{\sigma}_{1}^{2}\right)$ and $\left(0,{\sigma}_{2}^{2}\right)$, and B

_{1}and B

_{2}are the coefficients of vector regression with the assumption that $\left({{\rm B}}_{1},{\sigma}_{1}^{2}\right)\ne \left({{\rm B}}_{2},{\sigma}_{2}^{2}\right)$. The probabilities λ and 1 − λ are a random or natural selection for regimes 1 and 2, where the probability λ is an independent state of the system.

## 2. Markov Switching Model

## 3. Methodology

#### 3.1. Data and Variables

#### 3.2. Breakpoint Test

#### 3.2.1. Quandt–Andrews Breakpoint Test

_{0}≤ T ≤ T

_{1}is as follows:

_{0}), c(T

_{0+1}), …, c(T

_{1-1}), c(T

_{1})]

_{0}and T

_{1}are usually the inner 70% of the sample that is excluded from the first 15% and the last 15% of the sample.

#### 3.2.2. Bai–Perron Test

#### 3.3. Co-Integration Test

#### 3.4. Markov Switching Regression Model

## 4. Results and Discussions

_{11}and p

_{22}have a high value; thus, we rejected the null hypothesis of no shifts in the regime.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Fan, J.; Yao, Q. Nonlinear Time Series: Nonparametric and Parametric Methods; Springer: Berlin, Germany, 2005. [Google Scholar]
- Phoong, S.W.; Phoong, S.Y.; Moghavvemi, S.; Phoong, K.H. Multiple Breakpoint Test on Crude Oil Price. Found. Manag.
**2019**, 11, 187–196. [Google Scholar] [CrossRef] [Green Version] - Hamilton, J.D. A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica
**1989**, 57, 357–384. [Google Scholar] [CrossRef] - Krolzig, H.M. Markov-Switching Vector Autoregression; Springer: Berlin, Germany, 1997. [Google Scholar]
- Shaari, M.S.; Hussain, N.E.; Abdullah, H. The effects of oil price shocks and exchange rate volatility on inflation: Evidence from Malaysia. Int. Bus. Res.
**2012**, 5, 106–112. [Google Scholar] [CrossRef] [Green Version] - Siddiqui, M.A.; Butt, S.I.; Gilani, O.; Jamil, M.; Maqsood, A.; Zhang, F. Optimizing Availability of a Framework in Series Configuration Utilizing Markov Model and Monte Carlo Simulation Techniques. Symmetry
**2017**, 9, 96. [Google Scholar] [CrossRef] [Green Version] - Basnet, H.C.; Upadhyaya, K.P. Impact of oil price shocks on output, inflation and the real exchange rate: Evidence from selected ASEAN countries. Appl. Econ.
**2015**, 47, 3078–3091. [Google Scholar] [CrossRef] - David, S.A.; Inácio, C.M.C., Jr.; Tenreiro Machado, J.A. Ethanol Prices and Agricultural Commodities: An Investigation of Their Relationship. Mathematics
**2019**, 7, 774. [Google Scholar] [CrossRef] [Green Version] - Alghalith, M. The interaction between food prices and oil prices. Energy Econ.
**2010**, 32, 1520–1522. [Google Scholar] [CrossRef] - Nazlioglu, S.; Soytas, U. World oil prices and agricultural commodity prices: Evidence from an emerging market. Energy Econ.
**2011**, 33, 488–496. [Google Scholar] [CrossRef] - Nazlioglu, S. World oil and agricultural commodity prices: Evidence from nonlinear causality. Energy Policy
**2011**, 39, 2935–2943. [Google Scholar] [CrossRef] - Rafiq, S.; Salim, R.; Bloch, H. Impact of crude oil price volatility on economic activities: An empirical investigation in the Thai economy. Resour. Policy
**2009**, 34, 121–132. [Google Scholar] [CrossRef] - Zhou, Z.; Jin, Q.; Peng, J.; Xiao, H.; Wu, S. Further Study of the DEA-Based Framework for Performance Evaluation of Competing Crude Oil Prices’ Volatility Forecasting Models. Mathematics
**2019**, 7, 827. [Google Scholar] [CrossRef] [Green Version] - Quandt, R.E. Estimation of the parameters of a linear regression system obeying two separate regime. J. Am. Stat. Assoc.
**1958**, 53, 873–880. [Google Scholar] [CrossRef] - Quandt, R.E. A new approach to estimating switching regression. J. Am. Stat. Assoc.
**1972**, 67, 306–317. [Google Scholar] [CrossRef] - Goldfeld, S.M.; Quandt, R.E. A Markov model for switching regressions. J. Econom.
**1973**, 1, 3–16. [Google Scholar] [CrossRef] - Cosslett, S.R.; Lee, L.F. Serial correlation in the latent discrete variable models. J. Econom.
**1985**, 27, 79–97. [Google Scholar] [CrossRef] - Kim, C.J. Dynamic linear models with Markov-switching. J. Econom.
**1994**, 60, 1–22. [Google Scholar] [CrossRef] - Phoong, S.W.; Ismail, M.T.; Sek, S.K. Linear Vector Error Correction Model versus Markov Switching Vector Error Correction Model to Investigate Stock Market Behaviour. Asian Acad. Manag. J. Account. Financ.
**2014**, 10, 133–149. [Google Scholar] - Ardia, D.; Bluteau, K.; Boudt, K.; Leopoldo, C. Forecasting risk with Markov-switching GARCH models:A large-scale performance study. Int. J. Forecast.
**2018**, 34, 733–747. [Google Scholar] [CrossRef] - Caporale, G.; Zekokh, T. Modelling volatility of cryptocurrencies using Markov-Switching GARCH models. Res. Int. Bus. Financ.
**2019**, 48, 143–155. [Google Scholar] [CrossRef] - Berument, M.; Ceylan, N.; Dogan, N. The Impact of Oil Price Shocks on the Economic Growth of Selected MENA Countries. Energy J.
**2010**, 31, 149–176. [Google Scholar] - Arezki, R.; Jakab, Z.; Laxton, D.; Matsumoto, A.; Nurbekyan, A.; Wang, H.; Yao, J. Oil Prices and the Global Economy. Int. Monet. Fund
**2017**, 17, 1–30. [Google Scholar] [CrossRef] - Shahbaz, M.; Lean, H.H. Does financial development increase energy consumption? The role of industrialization and urbanization in Tunisia. Energy Policy
**2012**, 40, 473–479. [Google Scholar] [CrossRef] [Green Version] - Gómez, M.; Ciarreta, A.; Zarraga, A. Linear and nonlinear causality between energy consumption and economic growth: The case of Mexico 1965–2014. Energies
**2018**, 11, 784. [Google Scholar] [CrossRef] [Green Version] - Gómez, M.; Rodríguez, J.C. Energy Consumption and Financial Development in NAFTACountries, 1971–2015. Appl. Sci.
**2019**, 9, 302. [Google Scholar] [CrossRef] [Green Version] - De Martino, I. Decaying Dark Energy in Light of the Latest Cpsmological Dataset. Symmetry
**2018**, 10, 372. [Google Scholar] [CrossRef] [Green Version] - Farah, P.D. Five Years of China WTO Membership: EU and US Perceptives about China’s Compliance with Transparency Commitments and the Transitional Review Mechanism. Leg. Issuses Econ. Integr.
**2006**, 33, 263–304. [Google Scholar] - Neftci, S.N. Are economic time series asymmetric over the business cycle? J. Political Econ.
**1984**, 92, 306–328. [Google Scholar] [CrossRef] - Brunner, A.D. Conditional symmetries in real GNP: A semi nonparametric approach. J. Bus. Econ. Stat.
**1992**, 10, 65–72. [Google Scholar] - Laredic, S.; Mignon, V. The impact of oil prices on GDP in European countries: An empirical investigation based on asymmetric cointegration. Energy Policy
**2006**, 34, 3910–3915. [Google Scholar] [CrossRef] - Gadea, M.D.; Gómez-Loscos, A.; Montañés, A. Oil Price and Economic Growth: A Long Story? Econometrics
**2016**, 4, 41. [Google Scholar] [CrossRef] [Green Version] - Benhmad, F. Dynamic cyclical comovements betweem oil prices and US GDP: A wavelet perspective. Energy Policy
**2013**, 57, 141–151. [Google Scholar] [CrossRef] - Rafiq, S.; Bloch, H. Explaining commodity prices through asymmetric oil shocks: Evidence from nonlinear models. Resour. Policy
**2016**, 50, 34–48. [Google Scholar] [CrossRef] [Green Version] - Miao, D.W.C.; Wu, C.C.; Su, Y.K. Regime-switching in volatility and correlation structure using range-based models with Markov-switching. Econ. Model.
**2013**, 31, 87–93. [Google Scholar] [CrossRef] - Balcilar, M.; Eyden, R.; Uwilingiye, J.; Gupta, R. The Impact of Oil Price on South African GDP Growth: A Bayesian Markov Switching VAR Analysis. Afr. Dev. Rev.
**2017**, 29, 319–336. [Google Scholar] [CrossRef] - Ayodeji, I.O. A Three-State Markov-Modulated Switching Model for Exchange Rates. J. Appl. Math.
**2016**, 2016, 5061749. [Google Scholar] [CrossRef] [Green Version]

Mean | Standard Deviation | Skewness | Kurtosis | Jarqua–Bera | |
---|---|---|---|---|---|

LOGOP | 4.32 | 0.37 | −0.34 | 1.81 | 2.85 |

MYGDP | 71,410.50 | 5296.73 | −0.39 | 2.29 | 1.66 |

Quandt–Andrews Unknown Breakpoint Test | |||
---|---|---|---|

Null Hypothesis: No Breakpoints within 15% Trimmed Data | |||

Varying Regressors: All Equation Variables | |||

Statistic | Value | Prob. | |

Maximum LR F-statistic (2012Q2) | 21.39673 | 0.0000 | |

Maximum Wald F-statistic (2012Q2) | 42.79346 | 0.0000 | |

Exp LR F-statistic | 8.147680 | 0.0000 | |

Exp Wald F-statistic | 18.32268 | 0.0000 | |

Ave LR F-statistic | 9.538625 | 0.0001 | |

Ave Wald F-statistic | 19.07725 | 0.0001 |

Multiple Breakpoint Tests | |||
---|---|---|---|

Bai–Perron Tests of L+1 vs. L Sequentially Determined Breaks | |||

Break Test Options: Trimming 0.15, Max. Breaks 5, Sig. Level 0.05 | |||

Sequential F-statistic determined breaks: | 2 | ||

Scaled | Critical | ||

Break Test | F-statistic | F-statistic | Value ** |

0 vs. 1 * | 21.39673 | 42.79346 | 11.47 |

1 vs. 2 * | 7.279554 | 14.55911 | 12.95 |

2 vs. 3 | 4.667017 | 9.334033 | 14.03 |

Break dates: | |||

Sequential | Repartition | ||

1 | 2012Q2 | 2012Q2 | |

2 | 2015Q3 | 2015Q3 |

Unrestricted Co-Integration Rank Test (Trace) | ||||
---|---|---|---|---|

Hypothesized | Trace | 0.05 | ||

No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |

None | 0.226176 | 12.01652 | 20.26184 | 0.4473 |

At most 1 | 0.092458 | 3.298539 | 9.164546 | 0.5264 |

Hypothesized | Max. Eigenvalue | 0.05 | ||

No. of CE(s) | Eigenvalue | Statistic | Critical Value | Prob.** |

None | 0.226176 | 8.717976 | 15.89210 | 0.4647 |

At most 1 | 0.092458 | 3.298539 | 9.164546 | 0.5264 |

Method: Markov Switching Regression (BFGS/Marquardt Steps) | ||||
---|---|---|---|---|

Number of states: 2 | ||||

Initial probabilities obtained from ergodic solution | ||||

Ordinary standard errors and covariance using a numeric Hessian | ||||

Random search: 25 starting values with 10 iterations using 1 standard | ||||

deviation (rng = kn, seed = 1,560,858,386) | ||||

Convergence achieved after 28 iterations | ||||

Variable | Coefficient | Std. Error | z-Statistic | Prob. |

Regime 1 | ||||

LOGOP | 10,254.71 | 1877.429 | 5.462102 | 0.0000 |

C | 29,104.07 | 7933.635 | 3.668440 | 0.0002 |

Regime 2 | ||||

LOGOP | 21,525.61 | 6420.504 | 3.352635 | 0.0008 |

C | −30,461.34 | 29431.43 | −1.034993 | 0.3007 |

Constant Markov Transition Probabilities | ||||
---|---|---|---|---|

Sample: 2010Q1 2018Q4 | ||||

Included observations: 36 | ||||

P(i, k) = P(s(t) = k | s(t − 1) = i) | ||||

(row = i/column = j) | ||||

1 | 2 | |||

All periods | 1 | 0.975638 | 0.024362 | |

2 | 0.043480 | 0.956520 | ||

Expected duration: Constant Markov transition | ||||

probabilities | ||||

Sample: 2010Q1 2018Q4 | ||||

Included observations: 36 | ||||

Constant expected durations: | ||||

1 | 2 | |||

All periods | 41.04773 | 22.9920 |

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**MDPI and ACS Style**

Phoong, S.W.; Phoong, S.Y.; Phoong, K.H.
Analysis of Structural Changes in Financial Datasets Using the Breakpoint Test and the Markov Switching Model. *Symmetry* **2020**, *12*, 401.
https://doi.org/10.3390/sym12030401

**AMA Style**

Phoong SW, Phoong SY, Phoong KH.
Analysis of Structural Changes in Financial Datasets Using the Breakpoint Test and the Markov Switching Model. *Symmetry*. 2020; 12(3):401.
https://doi.org/10.3390/sym12030401

**Chicago/Turabian Style**

Phoong, Seuk Wai, Seuk Yen Phoong, and Kok Hau Phoong.
2020. "Analysis of Structural Changes in Financial Datasets Using the Breakpoint Test and the Markov Switching Model" *Symmetry* 12, no. 3: 401.
https://doi.org/10.3390/sym12030401