back start next[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [ 82 ] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] 82 and kurtosis K(m)e where 1 - (ft + a)ma0{m) = m ----- (8.7)1 - (p + a) ) = ( + ) -(3(m) (8.8)K(m)e- 3 + (Ke - 3)/m + 6(Ke - 1){m - 1 - m(fi + g) + (ft + q)m}{q - pa(p + a)} X m2(l -p -a)2(l -2Ba)\Pl + f}\ = 1. Sampling period: 7 years from January I, 1987, to December 31, 1993.Although the coefficient estimates may look quite reasonable for some lower frequencies, the global picture for all frequencies appears quite odd. In particular, the f3i estimates for frequencies higher than 2 hr decrease down to values close to 0.75, whereas the theory, represented by the triangles in Figure 8.1, suggests that [3 \ should tend to one. The triangles are very far from the corresponding black circles. The hypothesis of volatility being generated by only one GARCH(1,1) process is clearly rejected with the high significance of high-frequency data analyzed over 7 years.The results of Figure 8.1 are computed on the basis of the business time introduced at the end of Section 8.2.2. Figure 8.2 shows the corresponding results based on #-time. The time scale & is in fact a better choice because of its better deseasonalization. However, the results of Figure 8.2 are similar to those of Figure 8.1. The strong deviation between theoretical and empirically estimated[start] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [ 82 ] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134]