# Testing for a Single-Factor Stochastic Volatility in Bivariate Series

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## Abstract

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## 1. Introduction

## 2. Model

## 3. Test Statistic

## 4. Monte Carlo Experiments

- Generate $\left\{{e}_{kt}^{2}\right\}$ from multivariate log-normal random number generator from GAUSS library (The joint probability density function of ${e}_{1t}^{2}$ and ${e}_{2t}^{2}$ is expressed as$$\begin{array}{cc}\hfill f({e}_{1t}^{2},{e}_{2t}^{2})& =\frac{1}{\left(2\pi \right)\sqrt{{\eta}^{2}({\gamma}^{2}-1)}{e}_{1t}^{2}{e}_{2t}^{2}}\hfill \\ & \times exp\left[\frac{\eta \gamma {(log{e}_{1t}^{2}-\mu )}^{2}-2\eta (log{e}_{1t}^{2}-\mu )(log{e}_{2t}^{2}-\mu )+\eta \gamma {(log{e}_{2t}^{2}-\mu )}^{2}}{{\eta}^{2}({\gamma}^{2}-1)}\right]\hfill \end{array}$$
- Generate $\left\{{r}_{kt}^{2}\right\},\phantom{\rule{4pt}{0ex}}\left\{{h}_{kt}\right\}$ from $\left\{{e}_{kt}^{2}\right\},\phantom{\rule{4pt}{0ex}}\left\{{u}_{kt}\right\}$. The processes of $\left\{{r}_{kt}^{2}\right\}$ and $\left\{{h}_{kt}\right\}$ are obtained from the following model;$$\begin{array}{cc}\hfill \left[\begin{array}{c}{r}_{1t}^{2}\\ {r}_{2t}^{2}\end{array}\right]& =\left[\begin{array}{cc}{\psi}_{1}^{2}exp\left({h}_{1t}\right)& 0\\ 0& {\psi}_{2}^{2}exp\left({h}_{2t}\right)\end{array}\right]\left[\begin{array}{c}{e}_{1t}^{2}\\ {e}_{2t}^{2}\end{array}\right],\hfill \end{array}$$$$\begin{array}{cc}\hfill \left[\begin{array}{c}{h}_{1t}\\ {h}_{2t}\end{array}\right]& =\left[\begin{array}{cc}{\varphi}_{1}& 0\\ 0& {\varphi}_{2}\end{array}\right]\left[\begin{array}{c}{h}_{1,t-1}\\ {h}_{2,t-1}\end{array}\right]+\left[\begin{array}{cc}{\omega}_{1}^{1/2}& 0\\ \lambda {\omega}_{1}^{1/2}& {\omega}_{2}^{1/2}\end{array}\right]\left[\begin{array}{c}{u}_{1,t-1}\\ {u}_{2,t-1}\end{array}\right]\hfill \end{array}$$
- Calculate ${\delta}_{k}$ from ${\delta}_{k}=\mu +log{\psi}_{k}^{2}$ and generate $\left\{{y}_{kt}\right\},\phantom{\rule{4pt}{0ex}}\left\{{\xi}_{kt}\right\}$ from ${y}_{kt}=log{r}_{kt}^{2},\phantom{\rule{4pt}{0ex}}{\xi}_{kt}=log{e}_{kt}^{2}-\mu $, respectively.

- Observation equation$$\left[\begin{array}{c}{y}_{1t}\\ {y}_{2t}\end{array}\right]=\left[\begin{array}{c}{\delta}_{1}\\ {\delta}_{2}\end{array}\right]+\left[\begin{array}{c}{h}_{1t}\\ {h}_{2t}\end{array}\right]+\left[\begin{array}{c}{\xi}_{1t}\\ {\xi}_{2t}\end{array}\right],$$
- Transition equation$$\left[\begin{array}{c}{h}_{1t}\\ {h}_{2t}\end{array}\right]=\left[\begin{array}{cc}{\varphi}_{1}& 0\\ 0& {\varphi}_{2}\end{array}\right]\left[\begin{array}{c}{h}_{1,t-1}\\ {h}_{2,t-1}\end{array}\right]+\left[\begin{array}{cc}{\omega}_{1}^{1/2}& 0\\ \lambda {\omega}_{1}^{1/2}& {\omega}_{2}^{1/2}\end{array}\right]\left[\begin{array}{c}{u}_{1,t-1}\\ {u}_{2,t-1}\end{array}\right],$$
- Structure of innovation distribution$$\left[\begin{array}{c}{\xi}_{1t}\\ {\xi}_{2t}\\ {u}_{1t}\\ {u}_{2t}\end{array}\right]\sim \text{i.i.d.}N\left(\left[\begin{array}{c}0\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{cccc}\eta & \eta \gamma & 0& 0\\ \eta \gamma & \eta & 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\right),\phantom{\rule{1.em}{0ex}}\text{for}\phantom{\rule{4pt}{0ex}}t=1,\dots ,T.$$

- Apply the Kalman filtering to $\left\{{y}_{t}\right\}$ under the null hypothesis (10) and estimate the parameters by the maximum likelihood (ML) method.
- Apply the smoothing algorithm to $\left\{{y}_{t}\right\}$ and obtain the conditional moments of $\left\{{h}_{t}\right\}$.
- Calculate the LM test statistic (12).

- Size of the test: For $T=500$, the actual size of the test deviates from the nominal sizes of 5 and 1 percent at most by 3.1 and 1.9 percent, respectively. In particular, when the estimated volatility series are strongly correlated and can be characterized as near unit root processes, the size distortion are increasing. As the sample size increases, namely when $T=750$, the actual rejection rate is closer to the nominal level, as is expected.
- Power under the alternative: For $T=500$, the rejects rate of the null ranges from 12.9 percent to 58.9 percent for the nominal 5 percent significance level. As the sample size increases, the actual rejection rate is increasing. This results indicate that the absolute value of the difference between the null and the alternative is 0.2 or more, the test statistics can discriminate the hypothesis.

γ | ${\varphi}_{1}$ | ${\omega}_{1}$ | $T=500$ | $T=750$ | ||
---|---|---|---|---|---|---|

5% | 1% | 5% | 1% | |||

0.1 | 0.7 | 0.1 | 6.1 | 1.2 | 5.5 | 0.9 |

0 | 0.7 | 0.1 | 5.8 | 1.9 | 5.3 | 1.2 |

−0.1 | 0.7 | 0.1 | 4.6 | 0.8 | 5.1 | 1.1 |

0.1 | 0.9 | 0.1 | 7.2 | 1.8 | 5.7 | 1.4 |

0.1 | 0.95 | 0.1 | 8.1 | 2.9 | 6.5 | 1.8 |

0.1 | 0.7 | 0.2 | 7.1 | 1.6 | 5.4 | 1.1 |

0.1 | 0.7 | 0.3 | 5.1 | 0.7 | 4.9 | 1.2 |

${\varphi}_{2}$ | λ | ${\omega}_{2}$ | $T=500$ | $T=750$ | ||
---|---|---|---|---|---|---|

5% | 1% | 5% | 1% | |||

0.5 | 1 | 0 | 25.5 | 10.7 | 36.9 | 17.7 |

0.9 | 1 | 0 | 39.0 | 18.4 | 52.3 | 24.6 |

0.7 | 0.8 | 0 | 12.9 | 1.3 | 15.1 | 5.1 |

0.7 | 0.6 | 0 | 31.5 | 14.1 | 44.4 | 20.9 |

0.7 | 1 | 0.2 | 17.9 | 5.5 | 24.9 | 9.0 |

0.7 | 1 | 0.4 | 58.9 | 32.3 | 79.1 | 52.3 |

## 5. Empirical Analysis

#### 5.1. Univariate Analysis

#### 5.1.1. Data and Descriptive Statistics

Index Number | Ticker | Index name | Market |
---|---|---|---|

1 | HKSPLCI | S&P/HKEx Large Cap Index | Hong Kong (HKG) |

2 | IBOMBSE | BSE 100 Index | India (IND) |

3 | CHSASHR | Shanghai Stock Exchange A Share Index | Shanghai (SHA) |

4 | JAKCOMP | Jakarta Stock Exchange Composite Index | Indonesia (IDN) |

5 | JAPDOWA | Nikkei 225 Stock Average Index | Japan (JPN) |

6 | KOR200I | Korea Stock Exchange KOSPI 200 Index | Korea (KOR) |

7 | FBMKLCI | FTSE Bursa Malaysia KLCI Index | Malaysia (MYS) |

8 | PSECOMP | Philippines Stock Exchange PSEi Index | Philippines (PHL) |

9 | TAIWGHT | FTSE TWSE Taiwan 50 Index | Taiwan (TWN) |

10 | BNGKS50 | Stock Exchange of Thailand SET 50 Index | Thailand (THA) |

11 | SNGPORI | FTSE Straits Times Index | Singapore (SGP) |

Market | Max | Min | Mean | Median | Standard Deviation | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|

Hong Kong | 13.353 | −13.459 | −0.004 | 0.057 | 2.070 | 0.088 | 8.696 |

India | 15.490 | −11.689 | 0.019 | 0.096 | 1.912 | 0.022 | 9.343 |

Shanghai | 9.033 | −9.261 | −0.022 | 0.109 | 2.020 | −0.366 | 5.448 |

Indonesia | 7.623 | −10.954 | 0.064 | 0.181 | 1.740 | −0.635 | 8.652 |

Japan | 13.235 | −12.111 | −0.063 | 0.015 | 1.876 | −0.495 | 10.559 |

Korea | 11.540 | −10.903 | 0.023 | 0.121 | 1.753 | −0.422 | 8.303 |

Malaysia | 4.259 | −9.979 | 0.012 | 0.054 | 0.958 | −1.223 | 14.945 |

Philippines | 9.365 | −13.089 | 0.021 | 0.056 | 1.550 | −0.773 | 10.882 |

Taiwan | 6.525 | −6.735 | −0.009 | 0.110 | 1.549 | −0.342 | 5.054 |

Thailand | 8.916 | −12.563 | 0.036 | 0.053 | 1.782 | −0.477 | 8.384 |

Singapore | 7.531 | −8.696 | −0.014 | 0.012 | 1.533 | −0.118 | 6.576 |

Market | $\mathrm{LB}\left(15\right)$ | ${\mathrm{LB}}^{2}\left(15\right)$ | Market | $\mathrm{LB}\left(15\right)$ | ${\mathrm{LB}}^{2}\left(15\right)$ |
---|---|---|---|---|---|

Hong Kong | $\underset{\left(0.077\right)}{23.359}$ | $\underset{\left(0.000\right)}{\mathit{1101.201}}$ | Malaysia | $\underset{\left(0.009\right)}{\mathit{31.058}}$ | $\underset{\left(0.000\right)}{\mathit{93.300}}$ |

India | $\underset{\left(0.011\right)}{\mathit{30.264}}$ | $\underset{\left(0.000\right)}{\mathit{310.849}}$ | Philippines | $\underset{\left(0.000\right)}{\mathit{40.040}}$ | $\underset{\left(0.000\right)}{\mathit{302.482}}$ |

Shanghai | $\underset{\left(0.047\right)}{\mathit{25.257}}$ | $\underset{\left(0.000\right)}{\mathit{164.299}}$ | Taiwan | $\underset{\left(0.001\right)}{\mathit{36.679}}$ | $\underset{\left(0.000\right)}{\mathit{378.213}}$ |

Indonesia | $\underset{\left(0.000\right)}{\mathit{40.282}}$ | $\underset{\left(0.000\right)}{\mathit{476.883}}$ | Thailand | $\underset{\left(0.000\right)}{\mathit{62.000}}$ | $\underset{\left(0.000\right)}{\mathit{795.580}}$ |

Japan | $\underset{\left(0.480\right)}{14.605}$ | $\underset{\left(0.000\right)}{\mathit{1410.031}}$ | Singapore | $\underset{\left(0.019\right)}{\mathit{28.479}}$ | $\underset{\left(0.000\right)}{\mathit{1180.016}}$ |

Korea | $\underset{\left(0.926\right)}{7.941}$ | $\underset{\left(0.000\right)}{\mathit{816.021}}$ |

#### 5.1.2. Univariate SV Model

- Observation equation$${y}_{it}=\delta +{h}_{it}+{\xi}_{it},$$
- Transition equation$${h}_{it}=\varphi {h}_{i,t-1}+{u}_{i,t-1},\phantom{\rule{1.em}{0ex}}\left|\varphi \right|<1$$
- Structure of innovation distribution$$\left[\begin{array}{c}{\xi}_{it}\\ {u}_{it}\end{array}\right]\sim \text{i.i.d.}N\left(\left[\begin{array}{c}0\\ 0\end{array}\right],\left[\begin{array}{cc}\eta & 0\\ 0& \omega \end{array}\right]\right).$$

Market | $\widehat{\delta}$ | $\widehat{\eta}$ | $\widehat{\varphi}$ | $\widehat{\omega}$ | Market | $\widehat{\delta}$ | $\widehat{\eta}$ | $\widehat{\varphi}$ | $\widehat{\omega}$ |
---|---|---|---|---|---|---|---|---|---|

Hong Kong | −$\underset{\left(0.321\right)}{\mathit{9.572}}$ | $\underset{\left(0.211\right)}{\mathit{5.183}}$ | $\underset{\left(0.006\right)}{\mathit{0.988}}$ | $\underset{\left(0.009\right)}{\mathit{0.023}}$ | Malaysia | −$\underset{\left(0.517\right)}{\mathit{10.095}}$ | $\underset{\left(0.233\right)}{\mathit{5.481}}$ | $\underset{\left(0.002\right)}{\mathit{0.998}}$ | $\underset{\left(0.004\right)}{0.008}$ |

India | −$\underset{\left(0.275\right)}{\mathit{9.635}}$ | $\underset{\left(0.232\right)}{\mathit{5.422}}$ | $\underset{\left(0.010\right)}{\mathit{0.982}}$ | $\underset{\left(0.017\right)}{\mathit{0.031}}$ | Philippines | −$\underset{\left(0.138\right)}{\mathit{10.012}}$ | $\underset{\left(0.225\right)}{\mathit{4.657}}$ | $\underset{\left(0.031\right)}{\mathit{0.918}}$ | $\underset{\left(0.053\right)}{\mathit{0.120}}$ |

Shanghai | −$\underset{\left(0.270\right)}{\mathit{9.034}}$ | $\underset{\left(0.218\right)}{\mathit{5.354}}$ | $\underset{\left(0.001\right)}{\mathit{0.999}}$ | $\underset{\left(0.001\right)}{0.002}$ | Taiwan | −$\underset{\left(0.230\right)}{\mathit{10.204}}$ | $\underset{\left(0.240\right)}{\mathit{5.871}}$ | $\underset{\left(0.011\right)}{\mathit{0.982}}$ | $\underset{\left(0.013\right)}{0.021}$ |

Indonesia | −$\underset{\left(0.158\right)}{\mathit{9.943}}$ | $\underset{\left(0.230\right)}{\mathit{5.211}}$ | $\underset{\left(0.023\right)}{\mathit{0.950}}$ | $\underset{\left(0.034\right)}{\mathit{0.062}}$ | Thailand | −$\underset{\left(0.196\right)}{\mathit{9.842}}$ | $\underset{\left(0.213\right)}{\mathit{4.993}}$ | $\underset{\left(0.012\right)}{\mathit{0.969}}$ | $\underset{\left(0.016\right)}{\mathit{0.041}}$ |

Japan | −$\underset{\left(0.238\right)}{\mathit{9.796}}$ | $\underset{\left(0.243\right)}{\mathit{5.593}}$ | $\underset{\left(0.011\right)}{\mathit{0.975}}$ | $\underset{\left(0.019\right)}{\mathit{0.045}}$ | Singapore | −$\underset{\left(0.265\right)}{\mathit{10.003}}$ | $\underset{\left(0.238\right)}{\mathit{5.655}}$ | $\underset{\left(0.011\right)}{\mathit{0.983}}$ | $\underset{\left(0.016\right)}{0.028}$ |

Korea | −$\underset{\left(0.317\right)}{\mathit{10.059}}$ | $\underset{\left(0.221\right)}{\mathit{5.205}}$ | $\underset{\left(0.009\right)}{\mathit{0.986}}$ | $\underset{\left(0.012\right)}{\mathit{0.022}}$ |

**Figure 1.**Stochastic volatilities for the eleven stock indexes. Notes: The figure depicts the stochastic volatilities for the log of squared returns: (from top left to the right and down) Hong Kong, India, Shanghai, Indonesia, Japan, Korea, Malaysia, Philippines, Taiwan, Thailand, and Singapore.

#### 5.2. Bivariate Analysis

#### 5.2.1. Correlation Analysis

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

Hong Kong | 1 | 0.38 | 0.28 | 0.55 | 0.59 | 0.53 | 0.27 | 0.51 | 0.48 | 0.61 | 0.76 |

India | 0.65 | 1 | 0.12 | 0.34 | 0.40 | 0.33 | 0.19 | 0.18 | 0.22 | 0.34 | 0.47 |

Shanghai | 0.51 | 0.32 | 1 | 0.17 | 0.14 | 0.15 | 0.15 | 0.22 | 0.25 | 0.20 | 0.20 |

Indonesia | 0.68 | 0.55 | 0.33 | 1 | 0.53 | 0.45 | 0.33 | 0.38 | 0.54 | 0.56 | 0.60 |

Japan | 0.70 | 0.48 | 0.34 | 0.56 | 1 | 0.69 | 0.24 | 0.42 | 0.43 | 0.56 | 0.50 |

Korea | 0.70 | 0.51 | 0.38 | 0.61 | 0.73 | 1 | 0.26 | 0.32 | 0.54 | 0.36 | 0.62 |

Malaysia | 0.61 | 0.48 | 0.36 | 0.62 | 0.55 | 0.55 | 1 | 0.31 | 0.27 | 0.29 | 0.31 |

Philippines | 0.51 | 0.35 | 0.27 | 0.53 | 0.54 | 0.48 | 0.56 | 1 | 0.36 | 0.61 | 0.32 |

Taiwan | 0.65 | 0.45 | 0.36 | 0.58 | 0.64 | 0.74 | 0.56 | 0.51 | 1 | 0.39 | 0.52 |

Thailand | 0.64 | 0.54 | 0.29 | 0.61 | 0.50 | 0.53 | 0.52 | 0.45 | 0.50 | 1 | 0.63 |

Singapore | 0.84 | 0.66 | 0.38 | 0.69 | 0.67 | 0.71 | 0.63 | 0.44 | 0.64 | 0.64 | 1 |

#### 5.2.2. Bivariate SV Model

- Observation equation$$\left[\begin{array}{c}{y}_{it}\\ {y}_{jt}\end{array}\right]=\left[\begin{array}{c}{\delta}_{1}\\ {\delta}_{2}\end{array}\right]+\left[\begin{array}{c}{h}_{it}\\ {h}_{jt}\end{array}\right]+\left[\begin{array}{c}{\xi}_{it}\\ {\xi}_{jt}\end{array}\right]$$
- Transition equation$$\left[\begin{array}{c}{h}_{it}\\ {h}_{jt}\end{array}\right]=\left[\begin{array}{cc}{\varphi}_{1}& 0\\ 0& {\varphi}_{2}\end{array}\right]\left[\begin{array}{c}{h}_{i,t-1}\\ {h}_{j,t-1}\end{array}\right]+\left[\begin{array}{cc}{\omega}_{1}^{1/2}& 0\\ \lambda {\omega}_{1}^{1/2}& {\omega}_{2}^{1/2}\end{array}\right]\left[\begin{array}{c}{u}_{i,t-1}\\ {u}_{j,t-1}\end{array}\right]$$
- Structure of innovation distribution$$\left[\begin{array}{c}{\xi}_{it}\\ {\xi}_{jt}\\ {u}_{it}\\ {u}_{jt}\end{array}\right]\sim \text{i.i.d.}N\left(\left[\begin{array}{c}0\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{cccc}\eta & \eta \gamma & 0& 0\\ \eta \gamma & \eta & 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right]\right)$$

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | −$\underset{\left(0.30\right)}{\mathit{9.43}}$ | −$\underset{\left(0.36\right)}{\mathit{9.48}}$ | −$\underset{\left(0.48\right)}{\mathit{9.70}}$ | −$\underset{\left(0.26\right)}{\mathit{9.52}}$ | −$\underset{\left(0.31\right)}{\mathit{9.66}}$ | −$\underset{\left(0.42\right)}{\mathit{9.13}}$ | −$\underset{\left(0.26\right)}{\mathit{9.43}}$ | −$\underset{\left(0.27\right)}{\mathit{9.64}}$ | −$\underset{\left(0.25\right)}{\mathit{9.60}}$ | −$\underset{\left(0.28\right)}{\mathit{9.46}}$ | |

IND | −$\underset{\left(0.30\right)}{\mathit{9.53}}$ | −$\underset{\left(0.30\right)}{\mathit{9.54}}$ | −$\underset{\left(0.18\right)}{\mathit{9.75}}$ | −$\underset{\left(0.27\right)}{\mathit{9.70}}$ | −$\underset{\left(0.22\right)}{\mathit{9.75}}$ | −$\underset{\left(0.65\right)}{\mathit{9.00}}$ | −$\underset{\left(0.23\right)}{\mathit{9.63}}$ | −$\underset{\left(0.21\right)}{\mathit{9.73}}$ | −$\underset{\left(0.22\right)}{\mathit{9.76}}$ | −$\underset{\left(0.25\right)}{\mathit{9.68}}$ | |

SHA | −$\underset{\left(0.30\right)}{\mathit{9.40}}$ | −$\underset{\left(0.29\right)}{\mathit{9.31}}$ | −$\underset{\left(0.29\right)}{\mathit{9.51}}$ | −$\underset{\left(0.25\right)}{\mathit{9.39}}$ | −$\underset{\left(0.27\right)}{\mathit{9.68}}$ | −$\underset{\left(0.35\right)}{\mathit{8.66}}$ | −$\underset{\left(0.39\right)}{\mathit{8.84}}$ | −$\underset{\left(0.25\right)}{\mathit{9.65}}$ | −$\underset{\left(0.25\right)}{\mathit{9.63}}$ | −$\underset{\left(0.30\right)}{\mathit{9.33}}$ | |

IDN | −$\underset{\left(0.23\right)}{\mathit{9.89}}$ | −$\underset{\left(0.17\right)}{\mathit{9.91}}$ | −$\underset{\left(0.22\right)}{\mathit{9.87}}$ | −$\underset{\left(0.20\right)}{\mathit{9.93}}$ | −$\underset{\left(0.19\right)}{\mathit{9.94}}$ | −$\underset{\left(0.25\right)}{\mathit{9.79}}$ | −$\underset{\left(0.14\right)}{\mathit{9.92}}$ | −$\underset{\left(0.17\right)}{\mathit{9.94}}$ | −$\underset{\left(0.18\right)}{\mathit{9.97}}$ | −$\underset{\left(0.19\right)}{\mathit{9.92}}$ | |

JPN | −$\underset{\left(0.29\right)}{\mathit{9.72}}$ | −$\underset{\left(0.25\right)}{\mathit{9.76}}$ | −$\underset{\left(0.25\right)}{\mathit{9.72}}$ | −$\underset{\left(0.20\right)}{\mathit{9.82}}$ | −$\underset{\left(0.22\right)}{\mathit{9.91}}$ | −$\underset{\left(0.31\right)}{\mathit{9.56}}$ | −$\underset{\left(0.18\right)}{\mathit{9.77}}$ | −$\underset{\left(0.21\right)}{\mathit{9.86}}$ | −$\underset{\left(0.20\right)}{\mathit{9.87}}$ | −$\underset{\left(0.24\right)}{\mathit{9.75}}$ | |

KOR | −$\underset{\left(0.29\right)}{\mathit{9.93}}$ | −$\underset{\left(0.23\right)}{\mathit{9.91}}$ | −$\underset{\left(0.25\right)}{\mathit{9.96}}$ | −$\underset{\left(0.21\right)}{\mathit{9.88}}$ | −$\underset{\left(0.23\right)}{\mathit{9.90}}$ | −$\underset{\left(0.27\right)}{\mathit{9.71}}$ | −$\underset{\left(0.18\right)}{\mathit{9.83}}$ | −$\underset{\left(0.40\right)}{\mathit{10.47}}$ | −$\underset{\left(0.23\right)}{\mathit{10.01}}$ | −$\underset{\left(0.24\right)}{\mathit{9.87}}$ | |

MYS | −$\underset{\left(0.39\right)}{\mathit{10.60}}$ | −$\underset{\left(0.50\right)}{\mathit{10.33}}$ | −$\underset{\left(0.37\right)}{\mathit{10.32}}$ | −$\underset{\left(0.22\right)}{\mathit{10.96}}$ | −$\underset{\left(0.29\right)}{\mathit{10.78}}$ | −$\underset{\left(0.28\right)}{\mathit{10.99}}$ | −$\underset{\left(0.79\right)}{\mathit{9.68}}$ | −$\underset{\left(0.27\right)}{\mathit{10.89}}$ | −$\underset{\left(0.20\right)}{\mathit{10.98}}$ | −$\underset{\left(0.55\right)}{\mathit{10.43}}$ | |

PHL | −$\underset{\left(0.23\right)}{\mathit{9.88}}$ | −$\underset{\left(0.22\right)}{\mathit{9.91}}$ | −$\underset{\left(0.33\right)}{\mathit{9.36}}$ | −$\underset{\left(0.15\right)}{\mathit{10.02}}$ | −$\underset{\left(0.16\right)}{\mathit{9.98}}$ | −$\underset{\left(0.18\right)}{\mathit{10.02}}$ | −$\underset{\left(0.63\right)}{\mathit{8.57}}$ | −$\underset{\left(0.18\right)}{\mathit{10.03}}$ | −$\underset{\left(0.16\right)}{\mathit{9.97}}$ | −$\underset{\left(0.22\right)}{\mathit{9.93}}$ | |

TWN | −$\underset{\left(0.30\right)}{\mathit{10.20}}$ | −$\underset{\left(0.25\right)}{\mathit{10.09}}$ | −$\underset{\left(0.25\right)}{\mathit{10.23}}$ | −$\underset{\left(0.20\right)}{\mathit{10.13}}$ | −$\underset{\left(0.21\right)}{\mathit{10.15}}$ | −$\underset{\left(0.34\right)}{\mathit{10.81}}$ | −$\underset{\left(0.27\right)}{\mathit{9.90}}$ | −$\underset{\left(0.17\right)}{\mathit{10.09}}$ | −$\underset{\left(0.22\right)}{\mathit{10.24}}$ | −$\underset{\left(0.26\right)}{\mathit{10.21}}$ | |

THA | −$\underset{\left(0.26\right)}{\mathit{9.84}}$ | −$\underset{\left(0.24\right)}{\mathit{9.78}}$ | −$\underset{\left(0.24\right)}{\mathit{9.91}}$ | −$\underset{\left(0.20\right)}{\mathit{9.85}}$ | −$\underset{\left(0.21\right)}{\mathit{9.83}}$ | −$\underset{\left(0.44\right)}{\mathit{10.80}}$ | −$\underset{\left(0.21\right)}{\mathit{9.66}}$ | −$\underset{\left(0.15\right)}{\mathit{9.74}}$ | −$\underset{\left(0.38\right)}{\mathit{10.54}}$ | −$\underset{\left(0.22\right)}{\mathit{9.83}}$ | |

SGP | −$\underset{\left(0.30\right)}{\mathit{9.93}}$ | −$\underset{\left(0.25\right)}{\mathit{10.02}}$ | −$\underset{\left(0.28\right)}{\mathit{9.92}}$ | −$\underset{\left(0.19\right)}{\mathit{10.08}}$ | −$\underset{\left(0.24\right)}{\mathit{10.05}}$ | −$\underset{\left(0.24\right)}{\mathit{10.17}}$ | −$\underset{\left(0.65\right)}{\mathit{9.44}}$ | −$\underset{\left(0.22\right)}{\mathit{9.98}}$ | −$\underset{\left(0.22\right)}{\mathit{10.09}}$ | −$\underset{\left(0.21\right)}{\mathit{10.13}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | −$\underset{\left(0.30\right)}{\mathit{9.43}}$ | −$\underset{\left(0.36\right)}{\mathit{9.48}}$ | −$\underset{\left(0.48\right)}{\mathit{9.70}}$ | −$\underset{\left(0.26\right)}{\mathit{9.52}}$ | −$\underset{\left(0.31\right)}{\mathit{9.66}}$ | −$\underset{\left(0.42\right)}{\mathit{9.13}}$ | −$\underset{\left(0.26\right)}{\mathit{9.43}}$ | −$\underset{\left(0.27\right)}{\mathit{9.64}}$ | −$\underset{\left(0.25\right)}{\mathit{9.60}}$ | −$\underset{\left(0.28\right)}{\mathit{9.46}}$ | |

IND | −$\underset{\left(0.30\right)}{\mathit{9.41}}$ | −$\underset{\left(0.30\right)}{\mathit{9.22}}$ | −$\underset{\left(0.18\right)}{\mathit{9.89}}$ | −$\underset{\left(0.27\right)}{\mathit{9.69}}$ | −$\underset{\left(0.22\right)}{\mathit{9.85}}$ | −$\underset{\left(0.65\right)}{\mathit{10.31}}$ | −$\underset{\left(0.23\right)}{\mathit{9.87}}$ | −$\underset{\left(0.22\right)}{\mathit{10.06}}$ | −$\underset{\left(0.22\right)}{\mathit{9.72}}$ | −$\underset{\left(0.25\right)}{\mathit{9.96}}$ | |

SHA | −$\underset{\left(0.30\right)}{\mathit{9.46}}$ | −$\underset{\left(0.29\right)}{\mathit{9.54}}$ | −$\underset{\left(0.29\right)}{\mathit{9.88}}$ | −$\underset{\left(0.25\right)}{\mathit{9.68}}$ | −$\underset{\left(0.27\right)}{\mathit{9.96}}$ | −$\underset{\left(0.35\right)}{\mathit{10.22}}$ | −$\underset{\left(0.38\right)}{\mathit{9.27}}$ | −$\underset{\left(0.25\right)}{\mathit{10.23}}$ | −$\underset{\left(0.25\right)}{\mathit{9.86}}$ | −$\underset{\left(0.30\right)}{\mathit{9.87}}$ | |

IDN | −$\underset{\left(0.23\right)}{\mathit{9.55}}$ | −$\underset{\left(0.17\right)}{\mathit{9.71}}$ | −$\underset{\left(0.22\right)}{\mathit{9.43}}$ | −$\underset{\left(0.19\right)}{\mathit{9.78}}$ | −$\underset{\left(0.19\right)}{\mathit{9.84}}$ | −$\underset{\left(0.25\right)}{\mathit{10.93}}$ | −$\underset{\left(0.15\right)}{\mathit{10.01}}$ | −$\underset{\left(0.17\right)}{\mathit{10.10}}$ | −$\underset{\left(0.18\right)}{\mathit{9.80}}$ | −$\underset{\left(0.19\right)}{\mathit{10.04}}$ | |

JPN | −$\underset{\left(0.29\right)}{\mathit{9.50}}$ | −$\underset{\left(0.25\right)}{\mathit{9.63}}$ | −$\underset{\left(0.25\right)}{\mathit{9.35}}$ | −$\underset{\left(0.20\right)}{\mathit{9.89}}$ | −$\underset{\left(0.22\right)}{\mathit{9.90}}$ | −$\underset{\left(0.31\right)}{\mathit{10.82}}$ | −$\underset{\left(0.18\right)}{\mathit{9.92}}$ | −$\underset{\left(0.21\right)}{\mathit{10.11}}$ | −$\underset{\left(0.20\right)}{\mathit{9.79}}$ | −$\underset{\left(0.24\right)}{\mathit{10.02}}$ | |

KOR | −$\underset{\left(0.29\right)}{\mathit{9.62}}$ | −$\underset{\left(0.23\right)}{\mathit{9.69}}$ | −$\underset{\left(0.25\right)}{\mathit{9.59}}$ | −$\underset{\left(0.21\right)}{\mathit{9.92}}$ | −$\underset{\left(0.23\right)}{\mathit{9.78}}$ | −$\underset{\left(0.27\right)}{\mathit{10.95}}$ | −$\underset{\left(0.18\right)}{\mathit{9.96}}$ | −$\underset{\left(0.40\right)}{\mathit{10.70}}$ | −$\underset{\left(0.23\right)}{\mathit{9.87}}$ | −$\underset{\left(0.24\right)}{\mathit{10.05}}$ | |

MYS | −$\underset{\left(0.39\right)}{\mathit{9.15}}$ | −$\underset{\left(0.50\right)}{\mathit{8.97}}$ | −$\underset{\left(0.37\right)}{\mathit{8.71}}$ | −$\underset{\left(0.22\right)}{\mathit{9.81}}$ | −$\underset{\left(0.29\right)}{\mathit{9.52}}$ | −$\underset{\left(0.27\right)}{\mathit{9.73}}$ | −$\underset{\left(0.79\right)}{\mathit{8.69}}$ | −$\underset{\left(0.27\right)}{\mathit{9.92}}$ | −$\underset{\left(0.20\right)}{\mathit{9.65}}$ | −$\underset{\left(0.55\right)}{\mathit{9.41}}$ | |

PHL | −$\underset{\left(0.23\right)}{\mathit{9.41}}$ | −$\underset{\left(0.22\right)}{\mathit{9.59}}$ | −$\underset{\left(0.33\right)}{\mathit{8.81}}$ | −$\underset{\left(0.16\right)}{\mathit{9.88}}$ | −$\underset{\left(0.16\right)}{\mathit{9.73}}$ | −$\underset{\left(0.18\right)}{\mathit{9.78}}$ | −$\underset{\left(0.63\right)}{\mathit{9.63}}$ | −$\underset{\left(0.18\right)}{\mathit{10.06}}$ | −$\underset{\left(0.16\right)}{\mathit{9.70}}$ | −$\underset{\left(0.22\right)}{\mathit{9.97}}$ | |

TWN | −$\underset{\left(0.30\right)}{\mathit{9.72}}$ | −$\underset{\left(0.25\right)}{\mathit{9.72}}$ | −$\underset{\left(0.25\right)}{\mathit{9.63}}$ | −$\underset{\left(0.20\right)}{\mathit{9.97}}$ | −$\underset{\left(0.21\right)}{\mathit{9.83}}$ | −$\underset{\left(0.34\right)}{\mathit{10.57}}$ | −$\underset{\left(0.27\right)}{\mathit{10.93}}$ | −$\underset{\left(0.17\right)}{\mathit{10.00}}$ | −$\underset{\left(0.22\right)}{\mathit{9.86}}$ | −$\underset{\left(0.25\right)}{\mathit{10.16}}$ | |

THA | −$\underset{\left(0.26\right)}{\mathit{9.60}}$ | −$\underset{\left(0.24\right)}{\mathit{9.73}}$ | −$\underset{\left(0.24\right)}{\mathit{9.55}}$ | −$\underset{\left(0.20\right)}{\mathit{9.92}}$ | −$\underset{\left(0.21\right)}{\mathit{9.80}}$ | −$\underset{\left(0.44\right)}{\mathit{10.86}}$ | −$\underset{\left(0.21\right)}{\mathit{10.99}}$ | −$\underset{\left(0.15\right)}{\mathit{9.94}}$ | −$\underset{\left(0.38\right)}{\mathit{10.87}}$ | −$\underset{\left(0.22\right)}{\mathit{10.07}}$ | |

SGP | −$\underset{\left(0.30\right)}{\mathit{9.43}}$ | −$\underset{\left(0.25\right)}{\mathit{9.62}}$ | −$\underset{\left(0.28\right)}{\mathit{9.26}}$ | −$\underset{\left(0.19\right)}{\mathit{9.92}}$ | −$\underset{\left(0.23\right)}{\mathit{9.71}}$ | −$\underset{\left(0.24\right)}{\mathit{9.86}}$ | −$\underset{\left(0.65\right)}{\mathit{10.44}}$ | −$\underset{\left(0.22\right)}{\mathit{9.90}}$ | −$\underset{\left(0.23\right)}{\mathit{10.09}}$ | −$\underset{\left(0.21\right)}{\mathit{9.77}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | $\underset{\left(0.17\right)}{\mathit{5.38}}$ | $\underset{\left(0.16\right)}{\mathit{5.45}}$ | $\underset{\left(0.16\right)}{\mathit{5.08}}$ | $\underset{\left(0.16\right)}{\mathit{5.49}}$ | $\underset{\left(0.15\right)}{\mathit{5.26}}$ | $\underset{\left(0.16\right)}{\mathit{5.46}}$ | $\underset{\left(0.15\right)}{\mathit{5.07}}$ | $\underset{\left(0.17\right)}{\mathit{5.79}}$ | $\underset{\left(0.16\right)}{\mathit{5.21}}$ | $\underset{\left(0.15\right)}{\mathit{5.08}}$ | |

IND | $\underset{\left(0.16\right)}{\mathit{5.26}}$ | $\underset{\left(0.16\right)}{\mathit{5.86}}$ | $\underset{\left(0.17\right)}{\mathit{5.67}}$ | $\underset{\left(0.19\right)}{\mathit{6.10}}$ | $\underset{\left(0.17\right)}{\mathit{5.57}}$ | $\underset{\left(0.18\right)}{\mathit{5.84}}$ | $\underset{\left(0.16\right)}{\mathit{5.36}}$ | $\underset{\left(0.17\right)}{\mathit{5.74}}$ | $\underset{\left(0.17\right)}{\mathit{5.42}}$ | $\underset{\left(0.17\right)}{\mathit{5.53}}$ | |

SHA | $\underset{\left(0.17\right)}{\mathit{5.46}}$ | $\underset{\left(0.16\right)}{\mathit{5.50}}$ | $\underset{\left(0.16\right)}{\mathit{5.43}}$ | $\underset{\left(0.17\right)}{\mathit{5.70}}$ | $\underset{\left(0.17\right)}{\mathit{5.74}}$ | $\underset{\left(0.16\right)}{\mathit{5.60}}$ | $\underset{\left(0.17\right)}{\mathit{5.29}}$ | $\underset{\left(0.16\right)}{\mathit{5.73}}$ | $\underset{\left(0.16\right)}{\mathit{5.60}}$ | $\underset{\left(0.16\right)}{\mathit{5.48}}$ | |

IDN | $\underset{\left(0.16\right)}{\mathit{5.50}}$ | $\underset{\left(0.17\right)}{\mathit{5.50}}$ | $\underset{\left(0.16\right)}{\mathit{5.40}}$ | $\underset{\left(0.18\right)}{\mathit{5.60}}$ | $\underset{\left(0.15\right)}{\mathit{5.39}}$ | $\underset{\left(0.16\right)}{\mathit{5.40}}$ | $\underset{\left(0.16\right)}{\mathit{5.33}}$ | $\underset{\left(0.17\right)}{\mathit{5.59}}$ | $\underset{\left(0.16\right)}{\mathit{5.24}}$ | $\underset{\left(0.15\right)}{\mathit{5.23}}$ | |

JPN | $\underset{\left(0.16\right)}{\mathit{5.40}}$ | $\underset{\left(0.17\right)}{\mathit{5.75}}$ | $\underset{\left(0.16\right)}{\mathit{5.56}}$ | $\underset{\left(0.16\right)}{\mathit{5.38}}$ | $\underset{\left(0.16\right)}{\mathit{5.56}}$ | $\underset{\left(0.17\right)}{\mathit{5.62}}$ | $\underset{\left(0.16\right)}{\mathit{5.28}}$ | $\underset{\left(0.18\right)}{\mathit{6.01}}$ | $\underset{\left(0.17\right)}{\mathit{5.55}}$ | $\underset{\left(0.16\right)}{\mathit{5.54}}$ | |

KOR | $\underset{\left(0.15\right)}{\mathit{5.17}}$ | $\underset{\left(0.17\right)}{\mathit{5.63}}$ | $\underset{\left(0.16\right)}{\mathit{5.59}}$ | $\underset{\left(0.16\right)}{\mathit{5.33}}$ | $\underset{\left(0.16\right)}{\mathit{5.47}}$ | $\underset{\left(0.17\right)}{\mathit{5.56}}$ | $\underset{\left(0.17\right)}{\mathit{5.46}}$ | $\underset{\left(0.15\right)}{\mathit{5.36}}$ | $\underset{\left(0.16\right)}{\mathit{5.26}}$ | $\underset{\left(0.15\right)}{\mathit{5.38}}$ | |

MYS | $\underset{\left(0.16\right)}{\mathit{5.54}}$ | $\underset{\left(0.17\right)}{\mathit{5.66}}$ | $\underset{\left(0.17\right)}{\mathit{5.47}}$ | $\underset{\left(0.17\right)}{\mathit{5.54}}$ | $\underset{\left(0.17\right)}{\mathit{5.56}}$ | $\underset{\left(0.16\right)}{\mathit{5.54}}$ | $\underset{\left(0.15\right)}{\mathit{5.15}}$ | $\underset{\left(0.16\right)}{\mathit{5.71}}$ | $\underset{\left(0.17\right)}{\mathit{5.50}}$ | $\underset{\left(0.16\right)}{\mathit{5.37}}$ | |

PHL | $\underset{\left(0.16\right)}{\mathit{5.22}}$ | $\underset{\left(0.16\right)}{\mathit{5.29}}$ | $\underset{\left(0.15\right)}{\mathit{5.34}}$ | $\underset{\left(0.16\right)}{\mathit{5.08}}$ | $\underset{\left(0.17\right)}{\mathit{5.39}}$ | $\underset{\left(0.16\right)}{\mathit{5.29}}$ | $\underset{\left(0.16\right)}{\mathit{5.28}}$ | $\underset{\left(0.18\right)}{\mathit{5.67}}$ | $\underset{\left(0.16\right)}{\mathit{4.94}}$ | $\underset{\left(0.16\right)}{\mathit{5.24}}$ | |

TWN | $\underset{\left(0.16\right)}{\mathit{5.41}}$ | $\underset{\left(0.16\right)}{\mathit{5.48}}$ | $\underset{\left(0.16\right)}{\mathit{5.68}}$ | $\underset{\left(0.16\right)}{\mathit{5.49}}$ | $\underset{\left(0.17\right)}{\mathit{6.07}}$ | $\underset{\left(0.16\right)}{\mathit{5.38}}$ | $\underset{\left(0.16\right)}{\mathit{5.58}}$ | $\underset{\left(0.17\right)}{\mathit{5.45}}$ | $\underset{\left(0.17\right)}{\mathit{5.75}}$ | $\underset{\left(0.16\right)}{\mathit{5.65}}$ | |

THA | $\underset{\left(0.15\right)}{\mathit{5.17}}$ | $\underset{\left(0.16\right)}{\mathit{5.37}}$ | $\underset{\left(0.17\right)}{\mathit{5.66}}$ | $\underset{\left(0.16\right)}{\mathit{5.26}}$ | $\underset{\left(0.16\right)}{\mathit{5.51}}$ | $\underset{\left(0.15\right)}{\mathit{5.25}}$ | $\underset{\left(0.16\right)}{\mathit{5.48}}$ | $\underset{\left(0.16\right)}{\mathit{5.03}}$ | $\underset{\left(0.17\right)}{\mathit{5.64}}$ | $\underset{\left(0.16\right)}{\mathit{5.28}}$ | |

SGP | $\underset{\left(0.15\right)}{\mathit{5.08}}$ | $\underset{\left(0.17\right)}{\mathit{5.50}}$ | $\underset{\left(0.16\right)}{\mathit{5.64}}$ | $\underset{\left(0.15\right)}{\mathit{5.32}}$ | $\underset{\left(0.18\right)}{\mathit{5.64}}$ | $\underset{\left(0.16\right)}{\mathit{5.52}}$ | $\underset{\left(0.16\right)}{\mathit{5.52}}$ | $\underset{\left(0.15\right)}{\mathit{5.15}}$ | $\underset{\left(0.17\right)}{\mathit{5.88}}$ | $\underset{\left(0.16\right)}{\mathit{5.50}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | $\underset{\left(0.03\right)}{\mathit{0.15}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.13}}$ | $\underset{\left(0.03\right)}{\mathit{0.09}}$ | $\underset{\left(0.03\right)}{\mathit{0.18}}$ | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | |

IND | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | −$\underset{\left(0.03\right)}{0.01}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.02\right)}{\mathit{0.06}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.02\right)}{\mathit{0.08}}$ | $\underset{\left(0.03\right)}{0.01}$ | $\underset{\left(0.02\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{\mathit{0.08}}$ | $\underset{\left(0.03\right)}{\mathit{0.15}}$ | |

SHA | $\underset{\left(0.02\right)}{\mathit{0.10}}$ | −$\underset{\left(0.03\right)}{0.02}$ | $\underset{\left(0.02\right)}{0.02}$ | $\underset{\left(0.03\right)}{0.05}$ | $\underset{\left(0.02\right)}{0.05}$ | $\underset{\left(0.02\right)}{0.02}$ | $\underset{\left(0.03\right)}{0.02}$ | $\underset{\left(0.03\right)}{0.04}$ | −$\underset{\left(0.02\right)}{0.01}$ | $\underset{\left(0.03\right)}{\mathit{0.05}}$ | |

IDN | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.03\right)}{0.02}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.03\right)}{\mathit{0.08}}$ | $\underset{\left(0.02\right)}{\mathit{0.18}}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | |

JPN | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.02\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{0.04}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.02\right)}{\mathit{0.16}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | |

KOR | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.02\right)}{\mathit{0.18}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.09}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | |

MYS | $\underset{\left(0.03\right)}{\mathit{0.15}}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.02\right)}{\mathit{0.13}}$ | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | $\underset{\left(0.03\right)}{\mathit{0.05}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.03\right)}{\mathit{0.08}}$ | $\underset{\left(0.02\right)}{\mathit{0.15}}$ | |

PHL | $\underset{\left(0.03\right)}{\mathit{0.09}}$ | $\underset{\left(0.03\right)}{0.04}$ | $\underset{\left(0.03\right)}{0.01}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.03\right)}{0.05}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | −$\underset{\left(0.03\right)}{0.01}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | |

TWN | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.02\right)}{\mathit{0.06}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | $\underset{\left(0.03\right)}{\mathit{0.18}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.03\right)}{\mathit{0.09}}$ | $\underset{\left(0.02\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{\mathit{0.17}}$ | |

THA | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | $\underset{\left(0.03\right)}{\mathit{0.11}}$ | $\underset{\left(0.03\right)}{0.00}$ | $\underset{\left(0.03\right)}{\mathit{0.10}}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{\mathit{0.09}}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{0.00}$ | $\underset{\left(0.03\right)}{\mathit{0.07}}$ | $\underset{\left(0.03\right)}{\mathit{0.16}}$ | |

SGP | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.18}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.00\right)}{\mathit{0.20}}$ | $\underset{\left(0.03\right)}{\mathit{0.14}}$ | $\underset{\left(0.03\right)}{\mathit{0.19}}$ | $\underset{\left(0.03\right)}{\mathit{0.13}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.02\right)}{\mathit{0.17}}$ | $\underset{\left(0.02\right)}{\mathit{0.13}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | |

IND | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | |

SHA | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | |

IDN | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.03\right)}{\mathit{0.92}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | |

JPN | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | |

KOR | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | |

MYS | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | |

PHL | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.02\right)}{\mathit{0.94}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.02\right)}{\mathit{0.95}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | |

TWN | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.00\right)}{\mathit{1.00}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.02\right)}{\mathit{0.96}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | |

THA | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.02\right)}{\mathit{0.95}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | |

SGP | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.00\right)}{\mathit{0.99}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ | $\underset{\left(0.01\right)}{\mathit{0.98}}$ | $\underset{\left(0.01\right)}{\mathit{0.97}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

HKG | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.00\right)}{\mathit{0.01}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | |

IND | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.02\right)}{\mathit{0.06}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{0.02}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | |

SHA | $\underset{\left(0.00\right)}{\mathit{0.01}}$ | $\underset{\left(0.00\right)}{0.00}$ | $\underset{\left(0.00\right)}{\mathit{0.01}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.00\right)}{0.01}$ | $\underset{\left(0.00\right)}{0.01}$ | $\underset{\left(0.00\right)}{0.01}$ | $\underset{\left(0.00\right)}{0.00}$ | $\underset{\left(0.00\right)}{\mathit{0.01}}$ | $\underset{\left(0.00\right)}{0.01}$ | |

IDN | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{0.02}$ | $\underset{\left(0.04\right)}{\mathit{0.11}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | |

JPN | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | |

KOR | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.00\right)}{0.01}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.03\right)}{\mathit{0.05}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | |

MYS | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.00\right)}{0.00}$ | $\underset{\left(0.01\right)}{0.02}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.03\right)}{\mathit{0.06}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.02\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | |

PHL | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | $\underset{\left(0.00\right)}{0.00}$ | $\underset{\left(0.03\right)}{\mathit{0.08}}$ | $\underset{\left(0.02\right)}{\mathit{0.06}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.02\right)}{\mathit{0.05}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | $\underset{\left(0.02\right)}{\mathit{0.07}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | |

TWN | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.00\right)}{0.00}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.01}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | |

THA | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.00\right)}{0.01}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.02\right)}{\mathit{0.06}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | |

SGP | $\underset{\left(0.01\right)}{\mathit{0.03}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{0.01}$ | $\underset{\left(0.01\right)}{\mathit{0.05}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.02\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.04}}$ | $\underset{\left(0.01\right)}{\mathit{0.02}}$ | $\underset{\left(0.01\right)}{\mathit{0.03}}$ |

Market | HKG | IND | SHA | IDN | JPN | KOR | MYS | PHL | TWN | THA | SGP |
---|---|---|---|---|---|---|---|---|---|---|---|

Hong Kong | $\underset{\left(0.12\right)}{5.87}$ | $\underset{\left(0.00\right)}{\mathit{16.15}}$ | $\underset{\left(0.00\right)}{\mathit{15.85}}$ | $\underset{\left(0.05\right)}{\mathit{7.87}}$ | $\underset{\left(0.01\right)}{\mathit{10.50}}$ | $\underset{\left(0.01\right)}{\mathit{12.25}}$ | $\underset{\left(0.00\right)}{\mathit{17.62}}$ | $\underset{\left(0.01\right)}{\mathit{11.79}}$ | $\underset{\left(0.00\right)}{\mathit{20.50}}$ | $\underset{\left(0.54\right)}{2.17}$ | |

India | $\underset{\left(0.19\right)}{4.76}$ | $\underset{\left(0.00\right)}{\mathit{13.47}}$ | $\underset{\left(0.03\right)}{\mathit{9.12}}$ | $\underset{\left(0.01\right)}{\mathit{12.40}}$ | $\underset{\left(0.02\right)}{\mathit{9.69}}$ | $\underset{\left(0.01\right)}{\mathit{12.17}}$ | $\underset{\left(0.02\right)}{\mathit{10.27}}$ | $\underset{\left(0.04\right)}{\mathit{8.54}}$ | $\underset{\left(0.04\right)}{\mathit{8.14}}$ | $\underset{\left(0.37\right)}{3.14}$ | |

Shanghai | $\underset{\left(0.00\right)}{\mathit{15.71}}$ | $\underset{\left(0.01\right)}{\mathit{11.57}}$ | $\underset{\left(0.00\right)}{\mathit{14.82}}$ | $\underset{\left(0.00\right)}{\mathit{28.21}}$ | $\underset{\left(0.00\right)}{\mathit{25.44}}$ | $\underset{\left(0.00\right)}{\mathit{13.56}}$ | $\underset{\left(0.01\right)}{\mathit{12.06}}$ | $\underset{\left(0.01\right)}{\mathit{11.62}}$ | $\underset{\left(0.00\right)}{\mathit{30.07}}$ | $\underset{\left(0.02\right)}{\mathit{10.22}}$ | |

Indonesia | $\underset{\left(0.00\right)}{\mathit{16.05}}$ | $\underset{\left(0.00\right)}{\mathit{16.45}}$ | $\underset{\left(0.00\right)}{\mathit{19.05}}$ | $\underset{\left(0.00\right)}{\mathit{21.95}}$ | $\underset{\left(0.01\right)}{\mathit{11.65}}$ | $\underset{\left(0.01\right)}{\mathit{11.46}}$ | $\underset{\left(0.85\right)}{\mathit{0.82}}$ | $\underset{\left(0.39\right)}{\mathit{2.99}}$ | $\underset{\left(0.71\right)}{\mathit{1.36}}$ | $\underset{\left(0.06\right)}{\mathit{7.23}}$ | |

Japan | $\underset{\left(0.15\right)}{5.25}$ | $\underset{\left(0.01\right)}{\mathit{11.56}}$ | $\underset{\left(0.00\right)}{\mathit{23.54}}$ | $\underset{\left(0.01\right)}{\mathit{12.09}}$ | $\underset{\left(0.02\right)}{\mathit{9.81}}$ | $\underset{\left(0.00\right)}{\mathit{20.83}}$ | $\underset{\left(0.00\right)}{\mathit{16.69}}$ | $\underset{\left(0.68\right)}{\mathit{1.50}}$ | $\underset{\left(0.00\right)}{\mathit{18.92}}$ | $\underset{\left(0.01\right)}{\mathit{11.72}}$ | |

Korea | $\underset{\left(0.00\right)}{\mathit{14.87}}$ | $\underset{\left(0.03\right)}{\mathit{8.98}}$ | $\underset{\left(0.00\right)}{\mathit{26.10}}$ | $\underset{\left(0.01\right)}{\mathit{11.86}}$ | $\underset{\left(0.01\right)}{\mathit{11.65}}$ | $\underset{\left(0.01\right)}{\mathit{12.38}}$ | $\underset{\left(0.04\right)}{\mathit{8.60}}$ | $\underset{\left(0.25\right)}{4.11}$ | $\underset{\left(0.29\right)}{\mathit{3.73}}$ | $\underset{\left(0.11\right)}{6.07}$ | |

Malaysia | $\underset{\left(0.00\right)}{\mathit{13.21}}$ | $\underset{\left(0.06\right)}{7.57}$ | $\underset{\left(0.00\right)}{\mathit{12.86}}$ | $\underset{\left(0.01\right)}{\mathit{12.20}}$ | $\underset{\left(0.00\right)}{\mathit{20.56}}$ | $\underset{\left(0.04\right)}{\mathit{8.26}}$ | $\underset{\left(0.01\right)}{\mathit{10.59}}$ | $\underset{\left(0.19\right)}{4.77}$ | $\underset{\left(0.00\right)}{\mathit{19.65}}$ | $\underset{\left(0.38\right)}{3.09}$ | |

Philippines | $\underset{\left(0.00\right)}{\mathit{13.26}}$ | $\underset{\left(0.05\right)}{\mathit{8.04}}$ | $\underset{\left(0.19\right)}{4.72}$ | $\underset{\left(0.70\right)}{1.42}$ | $\underset{\left(0.00\right)}{\mathit{21.23}}$ | $\underset{\left(0.00\right)}{\mathit{14.92}}$ | $\underset{\left(0.03\right)}{\mathit{9.26}}$ | $\underset{\left(0.03\right)}{\mathit{9.22}}$ | $\underset{\left(0.28\right)}{3.84}$ | $\underset{\left(0.10\right)}{6.35}$ | |

Taiwan | $\underset{\left(0.00\right)}{\mathit{13.56}}$ | $\underset{\left(0.17\right)}{4.97}$ | $\underset{\left(0.04\right)}{\mathit{8.19}}$ | $\underset{\left(0.96\right)}{0.28}$ | $\underset{\left(0.12\right)}{5.75}$ | $\underset{\left(0.79\right)}{1.04}$ | $\underset{\left(0.66\right)}{\mathit{1.59}}$ | $\underset{\left(0.67\right)}{1.54}$ | $\underset{\left(0.14\right)}{5.47}$ | $\underset{\left(0.42\right)}{2.84}$ | |

Thailand | $\underset{\left(0.01\right)}{\mathit{12.78}}$ | $\underset{\left(0.04\right)}{\mathit{8.48}}$ | $\underset{\left(0.00\right)}{\mathit{30.63}}$ | $\underset{\left(0.24\right)}{4.17}$ | $\underset{\left(0.00\right)}{\mathit{20.87}}$ | $\underset{\left(0.16\right)}{5.11}$ | $\underset{\left(0.00\right)}{\mathit{24.85}}$ | $\underset{\left(0.42\right)}{2.83}$ | $\underset{\left(0.06\right)}{7.43}$ | $\underset{\left(0.02\right)}{\mathit{10.34}}$ | |

Singapore | $\underset{\left(0.30\right)}{3.67}$ | $\underset{\left(0.85\right)}{0.79}$ | $\underset{\left(0.00\right)}{\mathit{14.34}}$ | $\underset{\left(0.20\right)}{4.63}$ | $\underset{\left(0.02\right)}{\mathit{10.31}}$ | $\underset{\left(0.66\right)}{1.59}$ | $\underset{\left(0.40\right)}{2.95}$ | $\underset{\left(0.02\right)}{\mathit{9.66}}$ | $\underset{\left(0.20\right)}{4.67}$ | $\underset{\left(0.04\right)}{\mathit{8.49}}$ |

No. | Pair of markets | No. | Pair of markets |
---|---|---|---|

1 | Hong Kong and India | 9 | Korea and Taiwan |

2 | Hong Kong and Singapore | 10 | Korea and Thailand |

3 | India and Singapore | 11 | Korea and Singapore |

4 | Indonesia and Philippines | 12 | Malaysia and Taiwan |

5 | Indonesia and Taiwan | 13 | Malaysia and Singapore |

6 | Indonesia and Thailand | 14 | Philippines and Thailand |

7 | Indonesia and Singapore | 15 | Taiwan and Thailand |

8 | Japan and Taiwan | 16 | Taiwan and Singapore |

## 6. Conclusions

## Acknowledgements

## Conflicts of Interest

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## Appendix

## A. Derivation of Scores

#### A.1. Integration by Parts Formula

#### A.2. Scores of ${\rho}_{1}$ and ${\rho}_{2}$

#### A.3. Score of λ

#### A.4. Score of ${\omega}_{2}$

#### A.5. Scores of ${\delta}_{1}$

#### A.6. Score of ${\delta}_{2}$

#### A.7. Score of η

#### A.8. Score of γ

#### A.9. Score of ${\omega}_{1}$

## B. Conditional Moments of State Variables

© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Chiba, M.; Kobayashi, M. Testing for a Single-Factor Stochastic Volatility in Bivariate Series. *J. Risk Financial Manag.* **2013**, *6*, 31-61.
https://doi.org/10.3390/jrfm6010031

**AMA Style**

Chiba M, Kobayashi M. Testing for a Single-Factor Stochastic Volatility in Bivariate Series. *Journal of Risk and Financial Management*. 2013; 6(1):31-61.
https://doi.org/10.3390/jrfm6010031

**Chicago/Turabian Style**

Chiba, Masaru, and Masahito Kobayashi. 2013. "Testing for a Single-Factor Stochastic Volatility in Bivariate Series" *Journal of Risk and Financial Management* 6, no. 1: 31-61.
https://doi.org/10.3390/jrfm6010031