recent developments in high frequency financial ... - Index of

Modelling financial transaction price movements: a dynamic integer count data model 191
JBX HAL
Fig. 9 Autocorrelation functions of the squared residuals of the entire ICH models for Jack in the
Box Inc. (JBX) and Halliburton pCompany
ffiffi (HAL). The dashed lines mark off the approximate
99% confidence interval 2:58 n
However, the null of absence of serial correlation in w i and w i 2 has to be rejected at
all standard significance levels.
To assess the ability of the ICH model to characterize the density of the price
change process, we extend the density forecast test by Diebold et al. (1998)
originally developed for continuous densities processes to the case of discrete ones.
For discrete data generating processes the key assumption that the cumulative
density function of the true data generating process has to be invertible is violated.
Our modification of the density forecast test rests on the idea of a continuization by
adding random noise to the discrete random variable under consideration such that
Table 5 Properties of the raw series and the ICH model residuals for Jack in the Box Inc. (JBX)
and Halliburton Company (HAL)
JBX HAL JBX HAL
Price changes y i
Squared price changes y i 2
Q(30) (p-value) 107.8 (0.000) 186.4 (0.000) 100.8 (0.000) 996.2 (0.000)
Q(50) (p-value) 134.9 (0.000) 212.4 (0.000) 141.2 (0.000) 1105.2 (0.000)
Mean 0.009 −0.009
Variance 11.34 7.526
Residuals wi
Squared residuals wi
Q(30) (p-value) 50.9 (0.000) 44.9 (n.a.*) 31.3 (0.000) 29.2 (n.a.*)
Q(50) (p-value) 78.5 (0.000) 59.1 (0.000) 58.5 (0.000) 49.2 (0.000)
Mean 0.006 0.008
Variance 1.042 1.019
*Number of parameters are larger than the number of included lags