Palgrave Handbook of Econometrics: Applied Econometrics

1018 Autoregressive Conditional Duration Models

Index

Duration

0 20406080100

0 5000 10000 15000 20000

(a) Trade duration

Index

Time from start

0 5000 10000 15000 20000

0 2000 4000 6000 8000

(b) Time from start, before noon

Index

Time to close

0 5000 10000 15000 20000

0 2000 6000 10000 14000

(c) Time to close, after noon

Figure 21.8 Time plots of durations for the G.M. stock from December 1 to December 5,
2003; (a) observed trade durations (positive only); (b) and (c) the time functionO(ti)and
time functionC(ti)of equation (21.12)

time plots ofO(ti)andC(ti)of the GM stock transactions. Figure 21.8(a) shows the
observed trade durations as in Figure 21.7(a). From the plots, the use ofO(ti)and
C(ti)is justified.
Consider the multiple linear regression:

ln(zi)=β 0 +β 1 o(ti)+β 2 c(ti)+ei, (21.13)

whereo(ti)=O(ti)/10000 andc(ti)=C(ti)/10000. Letβˆibe the ordinary least
squares estimates of the above linear regression. The residual is then given by:

ˆei=ln(zi)−βˆ 0 −βˆ 1 o(ti)−βˆ 2 c(ti).

The adjusted durations then become:

xˆi=exp(eˆi). (21.14)

For the GM stock transactions, the estimates of theβiare 1.015(0.012), 0.133(0.028)
and 0.313(0.016), respectively, where the numbers in parentheses denote standard
errors. All estimates are statistically significant at the usual 1% level. Note that