Financial Risk Manager Part 1

Financial Risk Manager Part 1

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The following sample autocorrelation estimates are obtained using 200 data points:

Lag123
Coefficient0.3-0.15-0.10

Compute the value of the Box-Pierce Q-statistic.

TTanishq

Explanation:

The Box-Pierce Q-statistic is given by:

QBP=nβˆ‘Οk2Q_{BP} = n \sum \rho_k^2

Where nn is the sample size and ρ\rho represents the autocorrelations.

Therefore, QBP=200(0.32+(βˆ’0.15)2+(βˆ’0.10)2)=24.5Q_{BP} = 200(0.3^2 + (-0.15)^2 + (-0.10)^2) = 24.5

Calculation breakdown:

  • 0.32=0.090.3^2 = 0.09
  • (βˆ’0.15)2=0.0225(-0.15)^2 = 0.0225
  • (βˆ’0.10)2=0.01(-0.10)^2 = 0.01
  • Sum = 0.09 + 0.0225 + 0.01 = 0.1225
  • QBP=200Γ—0.1225=24.5Q_{BP} = 200 \times 0.1225 = 24.5
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