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(f) Hidden Markov model with the five components independent model (AIC and<br />

BIC selection)<br />

The estimated covariance matrix and the estimated correlation matrix are given below:<br />

⎡2.2087<br />

⎢<br />

0.0629<br />

⎢<br />

⎢⎣<br />

0.0590<br />

0.0629<br />

0.2893<br />

− 0.0476<br />

0.0590 ⎤<br />

− 0.0476<br />

⎥<br />

⎥<br />

24.6595⎥⎦<br />

⎡1<br />

⎢<br />

⎢<br />

⎢⎣<br />

0.0787<br />

1<br />

0.0080 ⎤<br />

− 0.0178<br />

⎥<br />

.<br />

⎥<br />

1 ⎥⎦<br />

(g) Hidden Markov model with the four components restricted model (AIC and<br />

BIC selection)<br />

The estimated covariance matrix and the estimated correlation matrix are given below:<br />

⎡1.6483<br />

⎢<br />

0.1311<br />

⎢<br />

⎢⎣<br />

0.7095<br />

0.1311<br />

0.4815<br />

1.1935<br />

0.7095 ⎤<br />

1.1935<br />

⎥<br />

⎥<br />

26.7686⎥⎦<br />

⎡1<br />

⎢<br />

⎢<br />

⎢⎣<br />

0.1471<br />

1<br />

0.1068⎤<br />

0.3324<br />

⎥<br />

.<br />

⎥<br />

1 ⎥⎦<br />

(h) Hidden Markov model with the four components common model (BIC<br />

selection)<br />

The estimated covariance matrix and the estimated correlation matrix are given below:<br />

⎡ 2.1514<br />

⎢<br />

− 0.0550<br />

⎢<br />

⎢⎣<br />

0.0904<br />

− 0.0550<br />

0.2740<br />

− 0.0053<br />

0.0904 ⎤<br />

− 0.0053<br />

⎥<br />

⎥<br />

21.2568⎥⎦<br />

⎡1<br />

⎢<br />

⎢<br />

⎢⎣<br />

− 0.0716<br />

1<br />

0.0134 ⎤<br />

− 0.0022<br />

⎥<br />

.<br />

⎥<br />

1 ⎥⎦<br />

158

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