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Trang 7Note: Page locators followed by
“n” refer to footnotes
A
activation functions, 24–30
Gaussian, 26–28
radial basis, 28–29
ridgelet, 29–30
squasher, 24–28
tansig, 26
Akaike statistic, 86
American options, 138–139
analytic derivatives, 105–107
approximations in
decision-making, 23
arbitrage pricing theory (APT),
47–48, 116, 137–143
arithmetic crossover, 73
asset pricing
arbitrage pricing theory,
47–48, 116, 137–143
capital asset pricing model,
46–48
decision-making in, 46–49
in emerging markets,
122–125
intertemporal capital asset pricing model, 47–48 thick modeling, 48 auto-associative mapping, 44, 46 autocorrelation coefficient, 87 automotive production
forecasting example, 145–155
data used in, 146–148 evaluation of, 150–152 interpretation of, 152–155 MATLAB program notes for, 166
models used in, 148–150 autoregressive models, 14,
55, 177
B
backpropagation method, 69–70 bagging predictors, 78
banking intervention example,
204–209 bank lending, property prices
and, 173–174, 174n, 186–189, 195 233
Trang 8234 Index
BFGS
(Boyden-Fletcher-Goldfarb-Shanno)
algorithm, 69, 78–80
black box criticism, 55–57
Black-Scholes options pricing
(BSOP) model, 116,
137–143
bond ratings, 53
bootstrapping methods
for assessing significance,
108
for in-sample bias, 101–102
for out-of-sample
performance, 202, 204
0.632 bootstrap test, 101–102,
202, 204
bounded rationality assumption,
7
Brock-Deckert-Scheinkman
(BDS) test, 91–92, 94
C
calendar effects, 61–63
call and put options, 1, 138–140
capital asset pricing model
(CAPM), 46–48
capital-asset ratio, 205–206
CAPM beta, 47
chaos theory, 117 See also
stochastic chaos (SC)
model
Chi-squared distribution, 87
Clark-West bias correction test,
98–99
classification networks, 37–38,
49–54, 58
classification problems, 2, 5,
199–210
closed form solutions, 20
conditional variance, 16–17
The Conquest of American
Inflation (Sargent), 56
control, 3
convergence
to absurd results, 105
in genetic algorithms, 75 local, 33–34, 68–71, 76, 105 corporate bonds example,
156–165 data in, 156–158 in-sample performance, 160–162
interpretation of results, 161–165
MATLAB program notes, 166
models used, 157–160 out-of-sample performance, 160–161
covariance stationary time
series, 59–61 credit card risk example,
200–205 crisp logic, 199 crossover, 73–74 cross-section analysis, 14n cross-validation, 101 curse of dimensionality, 18,
41–42, 76
D
data preprocessing, 59–65
in corporate bonds example, 157–158
in out-of-sample evaluation, 95
scaling functions, 64–65, 84 seasonal adjustments, 61–63 stationarity, 59–61
data requirements, 102–103 data scaling, 64–65, 84, 109 decision-making
in asset pricing, 46–49 brain-imaging models of, 23 use of forecasting in, 3–5 deflation forecasting
Trang 9Index 235 Hong Kong example,
168–182
importance of, 167–168
United States example,
174–175
DeLeo scaling function, 64–65
Dickey-Fuller test, 59–61
Diebold-Mariano test, 96–97
dimensionality reduction, 2–3,
41–46, 211–220
dimensionality reduction
mapping, 42, 44
directional accuracy test, 99–100
discrete choice, 49–54
discriminant analysis, 49–50
logit regression, 50–51
multinomial ordered choice,
53–54
neural network models for,
52–53
probit regression, 51–52
Weibull regression, 52
discriminant analysis, 49–50
in banking intervention
example, 207–209
in credit card risk example,
200–204
distorted long-memory (DLM)
model, 115–116,
135–137
dividend payments, 131
Durbin-Watson (DW) test, 87
E
economic bubbles, 135
election tournaments, 74–75
elitism, 75
Ellsberg paradox, 56
Elman recurrent network,
34–38, 58
emerging markets, use of neural
networks in, 8, 122–125
Engle-Ng test of symmetry of
residuals, 89, 94
Euclidean norm, 29 European options, 138 evaluation of network
estimation, 85–111 data requirements, 102–103 implementation strategy, 109–110
in-sample criteria, 85–94 interpretive criteria, 104–108 MATLAB programming code for, 93–94, 107–108
out-of-sample criteria, 94–103
significance of results, 108 evolutionary genetic algorithms,
75 evolutionary stochastic search,
72–75 exchange rate forecasting,
100–101, 103 expanding window estimation,
95 expectations, subjective, 23 extreme value theory, 52
F
feedforward networks, 21–24 analytic derivatives and, 105–106
in discrete binary choice, 52–53
with Gaussian functions, 26–28
with jump connections, 30–32, 39–40 with logsigmoid functions, 24–28, 31
in MATLAB program, 80–82
multilayered, 32–34 with multiple outputs, 36–38
Trang 10236 Index
feedforward networks, contd
in recurrent networks, 34–35
with tansig functions, 26
financial engineering, xii
financial markets
corporate bonds example,
156–165
intrinsic dimensionality in,
41–42
recurrent networks and
memory in, 36
sign of predictions for, 99
volatility forecasting
example, 211–220
finite-difference methods,
106–107
fitness tournaments, 73–75
forecasting, 2
automotive production
example, 145–155
corporate bonds example,
156–165
curse of dimensionality in,
18, 41–42, 76
data requirements in, 103
exchange rate, 100–101, 103
feedback in, 5
financial market volatility
example, 211–220
inflation, 37, 87, 104, 168–182
linear regression model in,
13–15
market volatility example,
211–220
multiple outputs in, 37
out-of-sample evaluation of,
95
predictive stochastic
complexity, 100–101
stochastic chaos model,
117–122
thick model, 77–78
use in decision-making, 3,
167–168
foreign exchange markets, 139n forward contracts, 139n
“free parameters,” 55 fuzzy sets, 199
G
Gallant-Rossi-Tauchen
procedure, 62–63 GARCH nonlinear models,
15–20 development of, 15n GARCH-M, 15–17 integrated, 132 model typology, 20–21 orthogonal polynomials, 18–20
polynomial approximation, 17–18
program notes for, 58 Gaussian function, 26–28, 51 Gaussian transformations, 28 GDP growth rates, 125–128 Geman and Geman theorem, 71 genetic algorithms, 72–75 development of, 6–7 evolutionary, 75 gradient-descent methods with, 75–77
in MATLAB program, 78–80, 83–84 steps in, 72–75 Gensaki interest, 186–188 Gompertz distribution, 52 Gompit regression model, 52 goodness of fit, 86
gradient-descent methods, 75–77 Granger causality test, 195–196
H
Hang Seng index, 170, 172 Hannan-Quinn information
criterion, 85–86
Trang 11Index 237 Harvey-Leybourne-Newbold size
correction, 97
health sciences, classification
in, 2n
Hermite polynomial expansion,
19
Hessian matrix, 67–69, 76
heteroskedasticity, 88–89, 91
hidden layers
jump connections and,
30–32
multilayered feedforward
networks in, 32–34
in principal components
analysis, 42
holidays, data adjustment for,
62–63, 62n
homoskedasticity tests, 88–89,
91
Hong Kong, inflation and
deflation example,
168–182
data for, 168–174
in-sample performance,
177–179
interpretation of results,
178–182
model specification, 174–177
out-of-sample performance,
177–178, 180
Hong Kong, volatility
forecasting example,
212–216
hybridization, 75–77
hyperbolic tangent function, 26
I
implementation strategy,
109–110
import prices, 170–171, 184–185
inflation forecasting
feedforward networks in, 37
Hong Kong example,
168–182
importance of, 167–168 moving averages in, 87 unemployment and, 104
in the United States, 174–175
initial conditions, 65, 118–119 input neurons, 21
in-sample bias, 101–102 in-sample evaluation criteria,
85–94 Brock-Deckert-Scheinkman test, 91–92, 94
Engle-Ng test for symmetry,
89, 94 Hannan-Quinn information statistic, 86
Jarque-Bera statistic, 89–90, 94 Lee-White-Granger test, 32, 90–91, 94
Ljung-Box statistic, 86–88, 94
MATLAB example of, 93–94
McLeod-Li statistic, 88–89, 94
in-sample evaluations
in automotive production example, 150–151
in banking intervention example, 205, 207
in Black-Sholes option pricing models, 140–142
in corporate bond example, 160–162
in credit card risk example, 200–202
in distorted long-memory models, 136–137
in Hong Kong inflation example, 177–179