90.5336.277
0.0270.8400.3512.243
All stocks, 1967 to 1971Mean0.000S.D.1.000Skew.0.734Kurt.5.194
0.1270.8640.0971.060
0.1140.8051.0802.509
0.1210.9950.5740.380
0.0161.0130.8432.928
0.0450.9761.60710.129
0.0770.9550.5451.908
0.1541.0160.8101.712
0.1361.1181.9255.815
0.0000.8820.4651.585
0.0060.9300.4312.476
All stocks, 1972 to 1976Mean0.000S.D.1.000Skew.0.466Kurt.17.228
0.0140.5750.2812.194
0.0890.9080.9731.828
0.4030.5691.1760.077
0.0340.8030.0460.587
0.1320.6180.0640.444
0.4220.8301.5032.137
0.0760.8862.72813.320
0.1080.9102.0479.510
0.0040.9240.5511.434
0.1630.5640.7912.010
All stocks, 1977 to 1981Mean0.000S.D.1.000Skew.1.092Kurt.20.043
0.0250.7690.2301.618
0.2121.0251.5164.397
0.1121.0910.7313.766
0.0560.8380.3680.460
0.1100.6830.4300.962
0.0860.8340.2494.722
0.0551.0362.3919.137
0.1771.0472.57110.961
0.0810.9861.5207.127
0.0400.8800.2913.682(continued)
Table 2.4 (continued)
Moment
Raw
HS
IHS
BTOP
BBOT
TTOP
TBOT
RTOP
RBOT
DTOP
DBOT
All stocks, 1982 to 1986Mean0.000S.D.1.000Skew.1.267Kurt.21.789
0.1471.0731.4004.899
0.2041.4422.19210.530
0.1370.8040.0010.863
0.0011.0400.0480.732
0.0530.9821.3708.460
0.0221.1581.6907.086
0.0280.9100.1200.780
0.1160.8300.0480.444
0.2240.8680.0011.174
0.0521.0820.0910.818
All stocks, 1987 to 1991Mean0.000S.D.1.000Skew.0.104Kurt.12.688
0.0120.9070.3263.922
0.1201.1360.9765.183
0.0800.9250.3421.839
0.0310.8260.2340.734
0.0521.0070.2482.796
0.0380.8781.0022.768
0.0980.9360.2331.038
0.0491.0000.0232.350
0.0480.7720.1050.313
0.1220.8600.3752.598
All stocks, 1992 to 1996Mean0.000S.D.1.000Skew.0.036Kurt.5.377
0.1190.9260.0792.818
0.0580.8540.0150.059
0.0330.9641.3997.584
0.0131.1060.1580.626
0.0781.0930.1272.019
0.0860.9010.1501.040
0.0060.9730.2831.266
0.0110.8790.2361.445
0.0030.9320.0391.583
0.1050.8750.0970.205
Table 2.5 Goodness-of-®t diagnostics for the conditional one-day normalized returns, conditional on ten technical indicators, for a sample of 350 NYSE/AMEXstocks from 1962 to 1996 (ten stocks per size-quintile with at least 80 per cent non-missing prices are randomly chosen in each ®ve-year subperiod, yielding 50 stocksper subperiod over seven subperiods). For each pattern, the percentage of conditional returns that fall within each of the ten unconditional-return deciles is tabulated.If conditioning on the pattern provides no information, the expected percentage falling in each decile is 10 per cent. Asymptotic z-statistics for this null hypothesis arereported in parentheses, and the  2 goodness-of-®tness test statistic Q is reported in the last column with the p-value in parentheses below the statistic. The tentechnical indicators are as follows: head-and-shoulders (HS), inverted head-and-shoulders (IHS), broadening top (BTOP), broadening bottom (BBOT), triangletop (TTOP), triangle bottom (TBOT), rectangle top (RTOP), rectangle bottom (RBOT), double top (DTOP), and double bottom (DBOT)
DecilePattern
1
HS
8.9( 1.49)8.6( 2.05)9.4( 0.57)11.5(1.28)7.8( 2.94)8.9( 1.35)8.4( 2.27)8.6( 2.01)8.2( 2.92)9.7( 0.48)
IHSBTOPBBOTTTOPTBOTRTOPRBOTDTOPDBOT
210.4(0.56)9.7( 0.36)10.6(0.54)9.9( 0.10)10.4(0.42)10.6(0.72)9.9( 0.10)9.6( 0.56)10.9(1.36)9.9( 0.18)
3
4
5
6
7
8
9
10
Q(p-Value)
11.2(1.49)9.4( 0.88)10.6(0.54)13.0(2.42)10.9(1.03)10.9(0.99)9.2( 1.10)7.8( 3.30)9.6( 0.64)10.0( 0.04)
11.7(2.16)11.2(1.60)11.9(1.55)11.1(0.95)11.3(1.46)12.2(2.36)10.5(0.58)10.5(0.60)12.4(3.29)10.9(1.37)
12.2(2.73)13.7(4.34)8.7( 1.25)7.8( 2.30)9.0( 1.30)9.2( 0.93)12.5(2.89)12.9(3.45)11.8(2.61)11.4(1.97)
7.9( 3.05)7.7( 3.44)6.6( 3.66)9.2( 0.73)9.9( 0.13)8.7( 1.57)10.1(0.16)10.8(1.07)7.5( 4.39)8.5( 2.40)
9.2( 1.04)9.1( 1.32)9.2( 0.71)8.3( 1.70)10.0( 0.04)9.3( 0.83)10.0( 0.02)11.6(1.98)8.2( 2.92)9.2( 1.33)
10.4(0.48)11.1(1.38)13.7(2.87)9.0( 1.00)10.7(0.77)11.6(1.69)10.0( 0.02)9.3( 0.99)11.3(1.83)10.0(0.04)
10.8(1.04)9.6( 0.62)9.2( 0.71)10.7(0.62)10.5(0.60)8.7( 1.57)11.4(1.70)10.3(0.44)10.3(0.46)10.7(0.96)
7.1( 4.46)10.0( 0.03)10.1(0.06)9.6( 0.35)9.7( 0.41)9.8( 0.22)8.1( 2.69)8.7( 1.91)9.7( 0.41)9.8( 0.33)
39.31(0.000)40.95(0.000)23.40(0.005)16.87(0.051)12.03(0.212)17.12(0.047)22.72(0.007)33.94(0.000)50.97(0.000)12.92(0.166)
Table 2.6 Goodness-of-®t diagnostics for the conditional one-day normalized returns, conditional on ten technical indicators, for a sample of 350 Nasdaq stocksfrom 1962 to 1996 (ten stocks per size-quintile with at least 80 per cent non-missing prices are randomly chosen in each ®ve-year subperiod, yielding 50 stocks persubperiod over seven subperiods). For each pattern, the percentage of conditional returns that fall within each of the ten unconditional-return deciles is tabulated. Ifconditioning on the pattern provides no information, the expected percentage falling in each decile is 10 per cent. Asymptotic z-statistics for this null hypothesis arereported in parentheses, and the  2 goodness-of-®tness test statistic Q is reported in the last column with the p-value in parentheses below the statistic. The tentechnical indicators are as follows: head-and-shoulders (HS), inverted head-and-shoulders (IHS), broadening top (BTOP), broadening bottom (BBOT), triangletop (TTOP), triangle bottom (TBOT), rectangle top (RTOP), rectangle bottom (RBOT), double top (DTOP), and double bottom (DBOT)
DecilePattern
1
2
3
4
5
6
7
8
9
10
Q(p-Value)
HS
10.8(0.76)9.4( 0.56)11.6(1.01)11.4(1.00)10.7(0.67)9.9( 0.11)11.2(1.28)8.9( 1.35)11.0(1.12)10.9(0.98)
10.8(0.76)14.1(3.35)12.3(1.44)11.4(1.00)12.1(1.89)11.3(1.14)10.8(0.92)12.3(2.52)12.6(2.71)11.5(1.60)
13.7(3.27)12.5(2.15)12.8(1.71)14.8(3.03)16.2(4.93)15.6(4.33)8.8( 1.40)8.9( 1.35)11.7(1.81)13.1(3.09)
8.6( 1.52)8.0( 2.16)7.7( 1.73)5.9( 3.91)6.2( 4.54)7.9( 2.24)8.3( 2.09)8.9( 1.45)9.0( 1.18)8.0( 2.47)
8.5( 1.65)7.7( 2.45)8.2( 1.32)6.7( 2.98)7.9( 2.29)7.7( 2.39)10.2(0.25)11.6(1.81)9.2( 0.98)8.1( 2.35)
6.0( 5.13)4.8( 7.01)6.8( 2.62)9.6( 0.27)8.7( 1.34)5.7( 5.20)7.1( 3.87)8.9( 1.35)5.5( 6.76)7.1( 3.75)
6.0( 5.13)6.4( 4.26)4.3( 5.64)5.7( 4.17)4.0( 8.93)5.3( 5.85)7.7( 2.95)7.0( 4.19)5.8( 6.26)7.6( 3.09)
12.5(2.30)13.5(2.90)13.3(1.97)11.4(1.00)12.5(2.18)14.6(3.64)9.3( 0.75)9.5( 0.66)11.6(1.73)11.5(1.60)
13.5(3.10)12.5(2.15)12.1(1.30)9.8( 0.12)11.4(1.29)12.0(1.76)15.3(4.92)13.6(3.85)12.3(2.39)12.8(2.85)
9.7( 0.32)11.3(1.14)10.9(0.57)13.2(2.12)10.2(0.23)10.0(0.01)11.3(1.37)10.3(0.36)11.3(1.47)9.3( 0.78)
64.41(0.000)75.84(0.000)34.12(0.000)43.26(0.000)92.09(0.000)85.26(0.000)57.08(0.000)45.79(0.000)71.29(0.000)51.23(0.000)
IHSBTOPBBOTTTOPTBOTRTOPRBOTDTOPDBOT
Foundations of technical analysis
93
returns, i.e., fewer patterns, the corresponding test statistics might be subjectto greater sampling variation and lower power. However, this explanationcan be ruled out from the frequency counts of Tables 2.1 and 2.2 ± thenumber of patterns in the NYSE/AMEX sample is considerably larger thanthose of the Nasdaq sample for all ten patterns. Tables 2.5 and 2.6 seem tosuggest important dierences in the informativeness of technical indicatorsfor NYSE/AMEX and Nasdaq stocks.Tables 2.7 and 2.8 report the results of the Kolmogorov±Smirnov test(Equation (2.9)) of the equality of the conditional and unconditional returndistributions for NYSE/AMEX (Table 2.7) and Nasdaq (Table 2.8) stocks,respectively, from 1962 to 1996, in ®ve-year subperiods, and in marketcapitalization quintiles. Recall that conditional returns are de®ned as the oneday return starting three days following the conclusion of an occurrence of apattern. The p-values are with respect to the asymptotic distribution of theKolmogorov±Smirnov test statistic given in Equation (2.20).Table 2.7 shows that for NYSE/AMEX stocks, ®ve of the ten patterns ±HS, BBOT, RTOP, RBOT, and DTOP ± yield statistically signi®cant teststatistics, with p-values ranging from 0.000 for RBOT to 0.021 for DTOPpatterns. However, for the other ®ve patterns, the p-values range from 0.104for IHS to 0.393 for TTOP, which implies an inability to distinguish betweenthe conditional and unconditional distributions of normalized returns.When we also condition on declining volume trend, the statistical signi®cance declines for most patterns, but the statistical signi®cance of TBOTpatterns increases. In contrast, conditioning on increasing volume trend yieldsan increase in the statistical signi®cance of BTOP patterns. This dierencemay suggest an important role for volume trend in TBOT and BTOPpatterns. The dierence between the increasing and decreasing volumetrend conditional distributions is statistically insigni®cant for almost all thepatterns (the sole exception is the TBOT pattern). This drop in statisticalsigni®cance may be due to a lack of power of the Kolmogorov±Smirnov testgiven the relatively small sample sizes of these conditional returns (see Table2.1 for frequency counts).Table 2.8 reports corresponding results for the Nasdaq sample, and as inTable 2.6, in contrast to the NYSE/AMEX results, here all the patterns arestatistically signi®cant at the 5 per cent level. This is especially signi®cantbecause the the Nasdaq sample exhibits far fewer patterns than the NYSE/AMEX sample (see Tables 2.1 and 2.2), hence the Kolmogorov±Smirnov testis likely to have lower power in this case.As with the NYSE/AMEX sample, volume trend seems to providelittle incremental information for the Nasdaq sample except in one case:increasing volume and BTOP. And except for the TTOP pattern, the
Table 2.7 Kolmogorov±Smirnov test of the equality of conditional and unconditional one-day return distributions for NYSE/AMEX stocks from 1962 to 1996, in®ve-year subperiods, and in size quintiles. Conditional returns are de®ned as the daily return three days following the conclusion of an occurrence of one of tentechnical indicators: head-and-shoulders (HS), inverted head-and-shoulders (IHS), broadening top (BTOP), broadening bottom (BBOT), triangle top (TTOP),triangle bottom (TBOT), rectangle top (RTOP), rectangle bottom (RBOT), double top (DTOP), and double bottom (DBOT). All returns have been normalizedby subtraction of their means and division by their standard deviations. p-values are with respect to the asymptotic distribution of the Kolmogorov±Smirnov teststatistic. The symbols ` D' and ` B' indicate that the conditional distribution is also conditioned on decreasing and increasing volume trend, respectively
Statistic
HS
IHS
BTOP
BBOT
TTOP
TBOT
RTOP
RBOT
DTOP
DBOT
1.220.1040.950.3271.050.2200.540.935
1.150.1390.440.9891.330.0590.590.879
1.760.0040.620.8391.590.0130.940.342
0.900.3930.730.6570.920.3680.750.628
1.090.1851.330.0591.290.0731.370.046
1.840.0021.370.0471.130.1560.790.557
2.450.0001.770.0041.240.0901.200.111
1.510.0210.960.3190.740.6380.820.512
1.060.2150.780.5790.840.4810.710.698
Smallest quintile, 1962 to 19960.591.19p-value0.8720.116 D0.670.80p-value0.7650.540 B0.430.95p-value0.9940.325Di.0.520.48p-value0.9510.974
0.720.6791.160.1360.670.7561.140.151
1.200.1140.690.7231.030.2360.680.741
0.980.2901.000.2710.470.9810.480.976
1.430.0331.460.0290.880.4230.980.291
1.090.1881.310.0650.510.9590.980.294
1.190.1200.940.3390.930.3560.790.552
0.840.4851.120.1650.940.3421.160.133
0.780.5830.730.6630.580.8920.620.840
2nd quintile, 1962 to 19961.82p-value0.003 D1.62p-value0.010
0.930.3530.880.427
0.920.3650.420.994
0.820.5050.910.378
0.840.4850.900.394
0.880.4170.710.703
1.290.0730.860.443
1.460.0291.500.022
0.840.4780.970.298
All stocks, 1962 to 19961.89p-value0.002 D1.49p-value0.024 B0.72p-value0.671Di.0.88p-value0.418
1.630.0101.030.242
1.630.0100.940.334
0.960.3171.040.228
0.830.4970.710.687
0.890.4071.220.102
0.980.2890.920.361
1.190.1190.990.276
1.150.1410.790.564
0.960.3171.180.126
0.990.2860.680.745
3rd quintile, 1962 to 19960.83p-value0.502 D0.95p-value0.326 B1.05p-value0.223Di.1.02p-value0.246
1.560.0160.940.3461.430.0331.140.148
1.000.2660.660.7750.930.3500.450.986
1.280.0740.760.6131.140.1470.480.974
0.570.9030.610.8540.630.8260.500.964
1.030.2430.820.5200.800.5440.890.413
1.960.0011.450.0310.930.3540.660.774
1.500.0231.610.0120.780.5780.910.383
1.550.0161.170.1310.590.8780.720.670
1.140.1501.010.2580.860.4501.150.143
4th quintile, 1962 to 19960.72p-value0.683 D1.01p-value0.255 B0.93p-value0.349Di.1.10p-value0.175
0.610.8520.950.3300.660.7720.970.301
1.290.0710.830.5041.290.0720.640.804
0.840.4790.960.3110.960.3161.160.138
0.610.8550.780.5851.160.1371.310.065
0.840.4800.840.4870.690.7310.780.571
1.370.0481.340.0560.640.8100.640.806
1.370.0470.720.6801.160.1360.920.363
0.720.6820.620.8410.690.7200.660.780
0.530.9431.010.2580.850.4681.100.176
Largest quintile, 1962 to 19961.251.16p-value0.0880.136 D1.120.90p-value0.1640.386 B0.810.93p-value0.5220.350Di.0.710.54p-value0.6990.934
0.980.2870.570.9060.830.4950.590.874
0.480.9770.780.5800.610.8540.640.800
0.500.9640.640.8060.690.7290.760.607
0.800.54