01.200.1121.680.0070.660.782
1.270.0780.590.8730.890.4050.750.627
All stocks, 1987 to 19911.24p-value0.091 D1.05p-value0.221 B1.23p-value0.099Di.0.80p-value0.552
1.290.0701.000.2661.260.0840.910.375
0.910.3841.000.2741.060.2081.220.103
0.880.4210.780.5801.320.0601.280.075
1.280.0741.680.0070.650.7871.220.102
1.410.0390.920.3691.270.0780.920.360
2.010.0011.670.0081.100.1760.870.431
1.490.0241.250.0871.260.0850.810.520
1.550.0170.610.8491.670.0071.070.202
1.530.0190.860.4481.810.0031.050.217
All Stocks, 1992 to 19961.21p-value0.108 D0.68p-value0.752 B1.56p-value0.015Di.1.45p-value0.030
1.610.0111.020.2460.850.4700.590.879
0.840.4760.810.5300.710.6880.940.346
0.900.3940.780.5781.000.2750.620.840
0.970.2990.810.5321.100.1801.150.139
0.910.3790.930.3571.040.2311.140.148
1.600.0120.790.5581.430.0340.640.814
1.510.0211.070.2010.930.3520.520.953
1.130.1560.940.3400.900.3920.590.874
1.000.2650.640.8141.440.0311.350.052
104
Advanced Trading Rules
Kolmogorov±Smirnov test still cannot distinguish between the decreasing andincreasing volume-trend conditional distributions, as the last pair of rows ofTable 2.8's ®rst panel indicates.2.5 MONTE CARLO ANALYSISTables 2.9 and 2.10 contain bootstrap percentiles for the Kolmogorov±Smirnov test of the equality of conditional and unconditional one-day returndistributions for NYSE/AMEX and Nasdaq stocks, respectively, from 1962to 1996, for ®ve-year subperiods, and for market-capitalization quintiles,under the null hypothesis of equality. For each of the two sets of market data,two sample sizes, m1 and m2 , have been chosen to span the range of frequencycounts of patterns reported in Tables 2.1 and 2.2. For each sample size mi , weresample one-day normalized returns (with replacement) to obtain a bootstrap sample of mi observations, compute the Kolmogorov±Smirnov teststatistic (against the entire sample of one-day normalized returns), and repeatthis procedure 1000 times. The percentiles of the asymptotic distribution arealso reported for comparison under the column labelled `D'.Tables 2.9 and 2.10 show that for a broad range of sample sizes and acrosssize quintiles, subperiod, and exchanges, the bootstrap distribution of theKolmogorov±Smirnov statistic is well approximated by its asymptoticdistribution, Equation (2.20).2.6 CONCLUSIONSIn this chapter, we have proposed a new approach to evaluating the ecacyof technical analysis. Based on smoothing techniques such as nonparametrickernel regression, our approach incorporates the essence of technical analysis:to identify regularities in the time series of prices by extracting nonlinearpatterns from noisy data. While human judgement is still superior to mostcomputational algorithms in the area of visual pattern recognition, recentadvances in statistical learning theory have had successful applications in®ngerprint identi®cation, handwriting analysis, and face recognition. Technical analysis may well be the next frontier for such methods.We ®nd that certain technical patterns, when applied to many stocks overmany time periods, do provide incremental information, especially forNasdaq stocks. While this does not necessarily imply that technical analysiscan be used to generate `excess' trading pro®ts, it does raise the possibilitythat technical analysis can add value to the investment process.Moreover, our methods suggest that technical analysis can be improved byusing automated algorithms such as ours and that traditional patterns such as
Foundations of technical analysis
105
Table 2.9 Bootstrap percentiles for the Kolmogorov±Smirnov test of the equality of conditional andunconditional one-day return distributions for NYSE/AMEX and Nasdaq stocks from 1962 to 1996, andfor size quintiles, under the null hypothesis of equality. For each of the two sets of market data, two samplesizes, m1 and m2 , have been chosen to span the range of frequency counts of patterns reported in Table 2.1.For each sample size mi , we resample one-day normalized returns (with replacement) to obtain abootstrap sample of mi observations, compute the Kolmogorov±Smirnov test statistic (against theentire sample of one-day normalized returns), and repeat this procedure 1000 times. The percentiles ofthe asymptotic distribution are also reported for comparison
NYSE/AMEX samplePercentile
Nasdaq sample
Dm1 ;n
m2
Dm2 ;n
D
m1
Dm1 ;n
m2
Dm2 ;n
D
All stocks, 1962 to 19960.0120760.4330.0520760.5150.1020760.5680.5020760.8270.9020761.2190.9520761.3850.9920761.608
725725725725725725725
0.4350.5350.5900.8361.2371.3951.611
0.4410.5200.5710.8281.2241.3581.628
1320132013201320132013201320
0.4300.5140.5730.8401.2441.3731.645
414414414414414414414
0.4380.5220.5660.8261.2291.3401.600
0.4410.5200.5710.8281.2241.3581.628
Smallest quintile, 1962 to 19960.013200.456780.053200.535780.103200.586780.503200.848780.903201.231780.953201.357780.993201.66178
0.4060.5020.5590.8141.2041.3301.590
0.4410.5200.5710.8281.2241.3581.628
218218218218218218218
0.4590.5330.5900.8471.2291.3811.708
41414141414141
0.4360.4980.5430.8011.2161.3321.571
0.4410.5200.5710.8281.2241.3581.628
2nd quintile, 1962 to 19960.014200.4450.054200.5300.104200.5800.504200.8310.904201.1970.954201.3490.994201.634
146146146146146146146
0.4280.5050.5530.8231.2101.3431.626
0.4410.5200.5710.8281.2241.3581.628
305305305305305305305
0.4580.5570.6100.8621.2651.4071.686
68686868686868
0.4260.5010.5590.8041.2101.4091.614
0.4410.5200.5710.8281.2241.3581.628
3rd quintile, 1962 to 19960.014580.4420.054580.5160.104580.5590.504580.8380.904581.2160.954581.4060.994581.660
145145145145145145145
0.4580.5080.5570.8351.2511.3971.661
0.4410.5200.5710.8281.2241.3581.628
279279279279279279279
0.4640.5390.5860.8321.2201.3571.606
105105105105105105105
0.4250.5250.5700.8181.2331.3551.638
0.4410.5200.5710.8281.2241.3581.628
m1
(continued)
106
Advanced Trading RulesTable 2.9 (continued)
NYSE/AMEX samplePercentile
Nasdaq sample
Dm1 ;n
m2
Dm2 ;n
D
m1
Dm1 ;n
m2
Dm2 ;n
D
4th quintile, 1962 to 19960.014240.4290.054240.5060.104240.5520.504240.8230.904241.1970.954241.3360.994241.664
173173173173173173173
0.4180.5160.5590.8151.1831.3131.592
0.4410.5200.5710.8281.2241.3581.628
303303303303303303303
0.4540.5260.5630.8401.2171.3501.659
92929292929292
0.4460.5060.5540.8181.1781.3271.606
0.4410.5200.5710.8281.2241.3581.628
Largest quintile, 1962 to 19960.015610.421 1670.055610.509 1670.105610.557 1670.505610.830 1670.905611.218 1670.955611.369 1670.995611.565 167
0.4250.5000.5540.8171.2021.3081.615
0.4410.5200.5710.8281.2241.3581.628
308308308308308308308
0.4410.5200.5730.8421.2311.4081.724
108108108108108108108
0.4290.5080.5580.8161.2261.3571.630
0.4410.5200.5710.8281.2241.3581.628
m1
head-and-shoulders and rectangles, while sometimes eective, need not beoptimal. In particular, it may be possible to determine `optimal patterns' fordetecting certain types of phenomena in ®nancial time series, e.g., an optimalshape for detecting stochastic volatility or changes in regime. Moreover,patterns that are optimal for detecting statistical anomalies need not beoptimal for trading pro®ts, and vice versa. Such considerations may lead toan entirely new branch of technical analysis, one based on selecting patternrecognition algorithms to optimize speci®c objective functions. We hope toexplore these issues more fully in future research.
Foundations of technical analysis
107
Table 2.10 Bootstrap percentiles for the Kolmogorov±Smirnov test of the equality of conditional andunconditional one-day return distributions for NYSE/AMEX and Nasdaq stocks from 1962 to 1996, for®ve-year subperiods, under the null hypothesis of equality. For each of the two sets of market data, twosample sizes, m1 and m2 , have been chosen to span the range of frequency counts of patterns reported inTable 2.1. For each sample size mi , we resample one-day normalized returns (with replacement) to obtaina bootstrap sample of mi observations, compute the Kolmogorov±Smirnov test statistic (against the entiresample of one-day normalized returns), and repeat this procedure 1000 times. The percentiles of theasymptotic distribution are also reported for comparison
NYSE/AMEX samplePercentile
Nasdaq sample
Dm1 ;n
m2
Dm2 ;n
D
m1
Dm1 ;n
m2
Dm2 ;n
D
All stocks, 1962 to 19660.013560.4310.053560.5160.103560.5760.503560.8270.903561.2330.953561.3590.993561.635
85858585858585
0.4270.5090.5590.8131.2211.3631.711
0.4410.5200.5710.8281.2241.3581.628
342342342342342342342
0.4600.5390.5890.8491.2421.3841.582
72727272727272
0.4170.5010.5650.8021.1921.3391.684
0.4410.5200.5710.8281.2241.3581.628
All stocks, 1967 to 19710.012580.4320.052580.5220.102580.5880.502580.8410.902581.1940.952581.3150.992581.703
112112112112112112112
0.4230.5080.5620.8191.2531.3851.563
0.4410.5200.5710.8281.2241.3581.628
227227227227227227227
0.4350.5120.5710.8111.1791.3461.625
65656565656565
0.4240.4980.5460.8121.2191.3571.669
0.4410.5200.5710.8281.2241.3581.628
All stocks, 1972 to 19760.012230.4390.052230.5180.102230.5880.502230.8540.902231.2490.952231.4060.992231.685
82828282828282
0.4400.5030.5540.7981.2081.3641.635
0.4410.5200.5710.8281.2241.3581.628
58585858585858
0.4330.4950.5420.7931.1681.2721.618
25252525252525
0.4050.4790.5260.7831.2031.3451.616
0.4410.5200.5710.8281.2241.3581.628
All stocks, 1977 to 19810.012900.4260.052900.5190.102900.5730.502900.8410.902901.2620.952901.3830.992901.598
110110110110110110110
0.4350.5040.5550.7931.1841.3421.645
0.4410.5200.5710.8281.2241.3581.628
96969696969696
0.4300.5040.5700.8211.1971.3521.540
36363636363636
0.4170.4850.5420.8101.2011.3711.545
0.4410.5200.5710.8281.2241.3581.628
m1
(continued)
108
Advanced Trading RulesTable 2.10 (continued)
NYSE/AMEX samplePercentile
Nasdaq sample
Dm1 ;n
m2
Dm2 ;n
D
m1
Dm1 ;n
m2
Dm2 ;n
D
All stocks, 1982 to 19860.013130.4620.053130.5420.103130.5850.503130.8440.903131.2660.953131.3970.993131.727
106106106106106106106
0.4370.5060.5590.8191.2201.3691.615
0.4410.5200.5710.8281.2241.3581.628
120120120120120120120
0.4480.5140.5790.8251.2531.3661.692
44444444444444
0.4170.4990.5550.8021.1971.3371.631
0.4410.5200.5710.8281.2241.3581.628
All Stocks, 1987 to 19910.012870.4430.052870.5130.102870.5650.502870.8370.902871.2000.952871.3360.992871.626
98989898989898
0.4490.5220.5660.8131.2171.3481.563
0.4410.5200.5710.8281.2241.3581.628
312312312312312312312
0.4550.5420.6100.8781.3191.4571.701
50505050505050
0.4320.5170.5630.8141.2161.3231.648
0.4410.5200.5710.8281.2241.3581.628
All Stocks, 1992 to 19960.013890.4380.053890.5220.103890.5670.503890.8240.903891.2200.953891.3210.993891.580
102102102102102102102
0.4320.5060.5580.8181.2131.3101.616
0.4410.5200.5710.8281.2241.3581.628
361361361361361361361
0.4470.5180.5590.8171.2261.3531.617
87878787878787
0.4280.4920.5500.7991.2161.3411.572
0.4410.5200.5710.8281.2241.3581.628
m1
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