"Frontmatter". In: Analysis of Financial Time Series

DURATION MODELS 195For the IBM data employed in the illustration of ADS models, we assumef (t i ) = exp[d(t i )], d(t i ) = β 0 +where7∑β j f j (t i ), (5.32)⎧( )( )ti − 43200 2 ⎨ ti − 38700 2f 1 (t i ) =−, f 3 (t i ) =−if t i < 4320014400⎩75000 otherwise,⎧ ( )( )ti − 48300 2 ⎪⎨ ti − 48600 2−if t i ≥ 43200f 2 (t i ) =−, f 4 (t i ) = 90009300⎪⎩0 otherwise,j=1f 5 (t i ) and f 6 (t i ) are indicator variables for the first and second 5 minutes of marketopening [i.e., f 5 (.) = 1 if and only if t i is between 9:30 am and 9:35 am Eastern(a)(c)-1.0 -0.6 -0.20 100 200 300 400minutes-1.0 -0.6 -0.20 100 200 300 400minutes(b)(d)-2.0 -1.0 0.0-1.0 -0.6 -0.20 100 200 300 400minutes0 100 200 300 400minutesFigure 5.5. Quadratic functions used to remove the deterministic component of IBM intradaytrading durations: (a)–(d) are the functions f 1 (.) to f 4 (.) of Eq. (5.32), respectively.