# Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Data Description

#### 3.2. Methodology

#### 3.2.1. Seasonal and Trend Decomposition Using Loess (STL)

#### 3.2.2. Multifractal Detrended Fluctuation Analysis (MFDFA)

_{s}, while for the segments between $m={N}_{s+1}$ and $m=2{N}_{s}$, this is given by

## 4. Empirical Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Figure A2.**Seasonal and trend decomposition from STL for the return time series for BSE, FTSE, JSE, and TAIEX. The information is the following; original daily returns (1st row), seasonal component (2nd row,) trend component (3rd row), and remainder component (4th row).

**Figure A3.**Seasonal and trend decomposition from STL for the return time series for KSE, PSI, SET, and SSEC. The information is the following; original daily returns (1st row), seasonal component (2nd row,) trend component (3rd row), and remainder component (4th row).

**Figure A4.**MFDFA results for the return time series of BSE, FTSE, JSE, and TAIEX. (

**a**) Fluctuation functions for q = [−10,0,10]. (

**b**) Generalized Hurst exponent depending on q. (

**c**) Mass exponent τ(q). (

**d**) Multifractal spectrum.

**Figure A5.**MFDFA results for the return time series of KSE, PSI, SET, and SSEC. (

**a**) Fluctuation functions for q = [−10,0,10]. (

**b**) Generalized Hurst exponent depending on q. (

**c**) Mass exponent τ(q). (

**d**) Multifractal spectrum.

## Appendix B. BDS Test for Emerging Asian Stock Markets

k | KOSPI | BSE | FTSE | JSE | KSE | PSI | SET | SSEC | TAIEX |
---|---|---|---|---|---|---|---|---|---|

2 | 0.0218 ^{**} | 0.0090 ^{**} | 0.0231 ^{**} | 0.0224 ^{**} | 0.0351 ^{**} | 0.0163 ^{**} | 0.0217 ^{**} | 0.0166 ^{**} | 0.0112 ^{**} |

3 | 0.0507 ^{**} | 0.0210 ^{**} | 0.0444 ^{**} | 0.0445 ^{**} | 0.0660 ^{**} | 0.0307 ^{**} | 0.0474 ^{**} | 0.0375 ^{**} | 0.0250 ^{**} |

4 | 0.0735 ^{**} | 0.0296 ^{**} | 0.0569 ^{**} | 0.0595 ^{**} | 0.0869 ^{**} | 0.0411 ^{**} | 0.0661 ^{**} | 0.0535 ^{**} | 0.0355 ^{**} |

5 | 0.0898 ^{**} | 0.0354 ^{**} | 0.0626 ^{**} | 0.0684 ^{**} | 0.0982 ^{**} | 0.0452 ^{**} | 0.0777 ^{**} | 0.0630 ^{**} | 0.0419 ^{**} |

6 | 0.0992 ^{**} | 0.0362 ^{**} | 0.0636 ^{**} | 0.0708 ^{**} | 0.1034 ^{**} | 0.0461 ^{**} | 0.0845 ^{**} | 0.0680 ^{**} | 0.0436 ^{**} |

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**Figure 1.**Seasonal and trend decomposition from STL for the return time series for the South Korean stock market. The information is the following; original daily returns (1st row), seasonal component (2nd row,) trend component (3rd row), and remainder component (4th row).

**Figure 2.**MFDFA results for the return time series of the Korean market (KOSPI). (

**a**) Fluctuation functions for q = [−10,0,10]. (

**b**) Generalized Hurst exponent depending on q. (

**c**) Mass exponent τ(q). (

**d**) Multifractal spectrum.

S.No. | Country | Index Symbol | Data Range | Observation (Daily) |
---|---|---|---|---|

1 | India | BSE | 24-Feb-2011 to 1-Apr-2020 | 2252 |

2 | Malaysia | FTSE | 20-May-2010 to 2-Apr-2020 | 2441 |

3 | Indonesia | JSE | 4-Jan-2000 to 2-Apr-2020 | 4941 |

4 | South Korea | KOSPI | 4-Jan-2000 to 1-Apr-2020 | 5000 |

5 | Pakistan | KSE | 3-Jan-2000 to 31-Mar-2020 | 5000 |

6 | Philippines | PSE | 2-Nov-2011 to 1-Apr-2020 | 2049 |

7 | Thailand | SET | 4-Jan-2000 to 2-Apr-2020 | 4958 |

8 | China | SSEC | 4-Jan-2000 to 2-Apr-2020 | 4908 |

9 | Taiwan | TAIEX | 17-Mar-2011 to 1-Apr-2020 | 2233 |

Order q | BSE | FTSE | JSE | KOSPI | KSE | PSE | SET | SSEC | TAIEX |

−10 | 0.67 | 0.70 | 0.70 | 0.49 | 0.59 | 0.60 | 0.60 | 0.68 | 0.61 |

−8 | 0.65 | 0.68 | 0.68 | 0.47 | 0.57 | 0.59 | 0.58 | 0.66 | 0.59 |

−6 | 0.62 | 0.65 | 0.66 | 0.46 | 0.55 | 0.57 | 0.56 | 0.65 | 0.58 |

−4 | 0.57 | 0.61 | 0.62 | 0.44 | 0.53 | 0.54 | 0.52 | 0.62 | 0.56 |

−2 | 0.51 | 0.56 | 0.57 | 0.43 | 0.51 | 0.51 | 0.49 | 0.61 | 0.53 |

0 | 0.44 | 0.49 | 0.53 | 0.43 | 0.50 | 0.48 | 0.47 | 0.61 | 0.50 |

2 | 0.37 | 0.41 | 0.51 | 0.39 | 0.46 | 0.41 | 0.44 | 0.58 | 0.44 |

4 | 0.29 | 0.32 | 0.48 | 0.34 | 0.40 | 0.30 | 0.39 | 0.54 | 0.36 |

6 | 0.22 | 0.26 | 0.44 | 0.30 | 0.34 | 0.22 | 0.34 | 0.51 | 0.31 |

8 | 0.18 | 0.22 | 0.41 | 0.28 | 0.31 | 0.18 | 0.31 | 0.48 | 0.27 |

10 | 0.15 | 0.20 | 0.39 | 0.26 | 0.29 | 0.15 | 0.29 | 0.46 | 0.24 |

∆h | 0.52 | 0.50 | 0.31 | 0.23 | 0.30 | 0.46 | 0.31 | 0.22 | 0.37 |

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**MDPI and ACS Style**

Aslam, F.; Latif, S.; Ferreira, P.
Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis. *Symmetry* **2020**, *12*, 1157.
https://doi.org/10.3390/sym12071157

**AMA Style**

Aslam F, Latif S, Ferreira P.
Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis. *Symmetry*. 2020; 12(7):1157.
https://doi.org/10.3390/sym12071157

**Chicago/Turabian Style**

Aslam, Faheem, Saima Latif, and Paulo Ferreira.
2020. "Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis" *Symmetry* 12, no. 7: 1157.
https://doi.org/10.3390/sym12071157