Palgrave Handbook of Econometrics: Applied Econometrics

1012 Autoregressive Conditional Duration Models

Lag

ACF

–0.10 0.0 0 5 10 15 20 25 30

0.10 0.20

(a) Adjusted durations of IBM stock

Lag

ACF

–0.10 0.0 0 5 10 15 20 25 30

0.10 0.20

(b) Normalized innovations: WACD(1,1) model

Figure 21.2 The sample autocorrelation function of IBM transaction durations from Novem-
ber 1 to November 7, 1990: (a) ACF of the adjusted durations; (b) ACF of the standardized
residual series of a WACD(1,1) model

Table 21.1 Estimation results of EACD(1,1), WACD(1,1) and GACD(1,1)

models for the IBM transaction durations of Example 1

Model Parameters Checking

α 0 α 1 β 1 ακQ( 10 ) Q∗( 10 )

EACD 0.129 0.056 0.905 4.55 5.48

(0.037) (0.009) (0.018) (0.92) (0.86)

WACD 0.125 0.056 0.906 0.880 3.85 5.51

(0.040) (0.010) (0.019) (0.012) (0.92) (0.85)

GACD 0.111 0.056 0.912 0.407 4.016 4.62 5.53

(0.040) (0.010) (0.019) (0.040) (0.730) (0.92) (0.85)

Notes: The adjusted durations are from November 1 to November 7, 1990, with

3,534 observations. The standard errors of the estimates are in parentheses. The

p-values of the Ljung–Box statistics are also in parentheses withQ( 10 )andQ∗( 10 )

for standardized residual series and its squared process, respectively.