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- Index
Note: Page locators followed by intertemporal capital asset
“n” refer to footnotes. pricing model, 47–48
thick modeling, 48
auto-associative mapping, 44, 46
A
autocorrelation coefficient, 87
activation functions, 24–30
automotive production
Gaussian, 26–28
forecasting example,
radial basis, 28–29 145–155
ridgelet, 29–30
data used in, 146–148
squasher, 24–28
evaluation of, 150–152
tansig, 26
interpretation of, 152–155
Akaike statistic, 86
MATLAB program notes
American options, 138–139
for, 166
analytic derivatives, 105–107
models used in, 148–150
approximations in
autoregressive models, 14,
decision-making, 23
55, 177
arbitrage pricing theory (APT),
47–48, 116, 137–143
arithmetic crossover, 73
B
asset pricing
backpropagation method, 69–70
arbitrage pricing theory,
bagging predictors, 78
47–48, 116, 137–143
banking intervention example,
capital asset pricing model,
204–209
46–48
decision-making in, 46–49 bank lending, property prices
in emerging markets, and, 173–174, 174n,
122–125 186–189, 195
233
- 234 Index
BFGS (Boyden-Fletcher- convergence
Goldfarb-Shanno) to absurd results, 105
algorithm, 69, 78–80 in genetic algorithms, 75
black box criticism, 55–57 local, 33–34, 68–71, 76, 105
Black-Scholes options pricing corporate bonds example,
(BSOP) model, 116, 156–165
137–143 data in, 156–158
bond ratings, 53 in-sample performance,
bootstrapping methods 160–162
for assessing significance, interpretation of results,
108 161–165
for in-sample bias, 101–102 MATLAB program notes,
for out-of-sample 166
performance, 202, 204 models used, 157–160
0.632 bootstrap test, 101–102, out-of-sample performance,
202, 204 160–161
bounded rationality assumption, covariance stationary time
7 series, 59–61
Brock-Deckert-Scheinkman credit card risk example,
(BDS) test, 91–92, 94 200–205
crisp logic, 199
crossover, 73–74
C
cross-section analysis, 14n
calendar effects, 61–63
cross-validation, 101
call and put options, 1, 138–140
curse of dimensionality, 18,
capital asset pricing model
41–42, 76
(CAPM), 46–48
capital-asset ratio, 205–206
D
CAPM beta, 47
data preprocessing, 59–65
chaos theory, 117. See also
in corporate bonds example,
stochastic chaos (SC)
157–158
model
in out-of-sample evaluation,
Chi-squared distribution, 87
95
Clark-West bias correction test,
scaling functions, 64–65, 84
98–99
seasonal adjustments, 61–63
classification networks, 37–38,
stationarity, 59–61
49–54, 58
data requirements, 102–103
classification problems, 2, 5,
data scaling, 64–65, 84, 109
199–210
decision-making
closed form solutions, 20
in asset pricing, 46–49
conditional variance, 16–17
brain-imaging models of, 23
The Conquest of American
Inflation (Sargent), 56 use of forecasting in, 3–5
control, 3 deflation forecasting
- Index 235
Hong Kong example, Euclidean norm, 29
168–182 European options, 138
importance of, 167–168 evaluation of network
United States example, estimation, 85–111
174–175 data requirements, 102–103
DeLeo scaling function, 64–65 implementation strategy,
Dickey-Fuller test, 59–61 109–110
Diebold-Mariano test, 96–97 in-sample criteria, 85–94
dimensionality reduction, 2–3, interpretive criteria,
41–46, 211–220 104–108
dimensionality reduction MATLAB programming
mapping, 42, 44 code for, 93–94,
directional accuracy test, 99–100 107–108
discrete choice, 49–54 out-of-sample criteria,
discriminant analysis, 49–50 94–103
logit regression, 50–51 significance of results, 108
multinomial ordered choice, evolutionary genetic algorithms,
53–54 75
neural network models for, evolutionary stochastic search,
52–53 72–75
probit regression, 51–52 exchange rate forecasting,
Weibull regression, 52 100–101, 103
discriminant analysis, 49–50 expanding window estimation,
in banking intervention 95
example, 207–209 expectations, subjective, 23
in credit card risk example, extreme value theory, 52
200–204
F
distorted long-memory (DLM)
model, 115–116, feedforward networks, 21–24
135–137 analytic derivatives and,
dividend payments, 131 105–106
Durbin-Watson (DW) test, 87 in discrete binary choice,
52–53
E with Gaussian functions,
economic bubbles, 135 26–28
election tournaments, 74–75 with jump connections,
elitism, 75 30–32, 39–40
Ellsberg paradox, 56 with logsigmoid functions,
Elman recurrent network, 24–28, 31
34–38, 58 in MATLAB program,
emerging markets, use of neural 80–82
networks in, 8, 122–125 multilayered, 32–34
Engle-Ng test of symmetry of with multiple outputs,
residuals, 89, 94 36–38
- 236 Index
feedforward networks, contd foreign exchange markets, 139n
in recurrent networks, 34–35 forward contracts, 139n
with tansig functions, 26 “free parameters,” 55
financial engineering, xii fuzzy sets, 199
financial markets
corporate bonds example,
G
156–165
Gallant-Rossi-Tauchen
intrinsic dimensionality in,
procedure, 62–63
41–42
GARCH nonlinear models,
recurrent networks and
15–20
memory in, 36
development of, 15n
sign of predictions for, 99
GARCH-M, 15–17
volatility forecasting
integrated, 132
example, 211–220
model typology, 20–21
finite-difference methods,
orthogonal polynomials,
106–107
18–20
fitness tournaments, 73–75
polynomial approximation,
forecasting, 2
17–18
automotive production
program notes for, 58
example, 145–155
Gaussian function, 26–28, 51
corporate bonds example,
Gaussian transformations, 28
156–165
curse of dimensionality in, GDP growth rates, 125–128
18, 41–42, 76 Geman and Geman theorem, 71
data requirements in, 103 genetic algorithms, 72–75
exchange rate, 100–101, 103 development of, 6–7
feedback in, 5 evolutionary, 75
financial market volatility gradient-descent methods
example, 211–220 with, 75–77
inflation, 37, 87, 104, 168–182 in MATLAB program,
linear regression model in, 78–80, 83–84
13–15 steps in, 72–75
market volatility example, Gensaki interest, 186–188
211–220 Gompertz distribution, 52
multiple outputs in, 37 Gompit regression model, 52
out-of-sample evaluation of, goodness of fit, 86
95 gradient-descent methods, 75–77
predictive stochastic Granger causality test, 195–196
complexity, 100–101
stochastic chaos model,
H
117–122
Hang Seng index, 170, 172
thick model, 77–78
use in decision-making, 3, Hannan-Quinn information
167–168 criterion, 85–86
- Index 237
Harvey-Leybourne-Newbold size importance of, 167–168
correction, 97 moving averages in, 87
health sciences, classification unemployment and, 104
in, 2n in the United States,
Hermite polynomial expansion, 174–175
19 initial conditions, 65, 118–119
Hessian matrix, 67–69, 76
input neurons, 21
heteroskedasticity, 88–89, 91
in-sample bias, 101–102
hidden layers
in-sample evaluation criteria,
jump connections and,
85–94
30–32
Brock-Deckert-Scheinkman
multilayered feedforward
test, 91–92, 94
networks in, 32–34
Engle-Ng test for symmetry,
in principal components
89, 94
analysis, 42
Hannan-Quinn information
holidays, data adjustment for,
statistic, 86
62–63, 62n
Jarque-Bera statistic,
homoskedasticity tests, 88–89,
89–90, 94
91
Hong Kong, inflation and Lee-White-Granger test, 32,
deflation example, 90–91, 94
168–182 Ljung-Box statistic, 86–88,
data for, 168–174 94
in-sample performance, MATLAB example of,
177–179 93–94
interpretation of results, McLeod-Li statistic, 88–89,
178–182 94
model specification, 174–177 in-sample evaluations
out-of-sample performance,
in automotive production
177–178, 180
example, 150–151
Hong Kong, volatility
in banking intervention
forecasting example,
example, 205, 207
212–216
in Black-Sholes option
hybridization, 75–77
pricing models,
hyperbolic tangent function, 26
140–142
I in corporate bond example,
160–162
implementation strategy,
in credit card risk example,
109–110
200–202
import prices, 170–171, 184–185
in distorted long-memory
inflation forecasting
models, 136–137
feedforward networks in, 37
in Hong Kong inflation
Hong Kong example,
example, 177–179
168–182
- 238 Index
L
in-sample evaluations, contd
in Hong Kong volatility lagged values
forecasting example, in Elman recurrent network,
213–214 34–36
in Japan inflation example, in evaluating models, 116
189–191 in implementation, 109
in Markov regime switching in Ljung-Box Q-statistic,
models, 128–130 87–88
in stochastic chaos models, in nonlinear principal
118–120 components, 49
in stochastic volatility/jump predictive stochastic
diffusion models, complexity, 100–101
123–124
Laguerre polynomial expansion,
in United States volatility
19
forecasting example,
land price index (Japan),
216–218
186–189, 193
in volatility regime
latent variables, 23
switching models, 132
learning parameters, 69
interest rate forecasting, 37, 146
leave out one method, 101
interpretive criteria, 104–108
Lee-White-Granger test, 32,
intertemporal capital asset
90–91, 94
pricing model
Legendre polynomial expansion,
(ICAPM), 47–48
19
intrinsic dimensionality, 41–42
likelihood functions, 16–17
linear ARX model, 14n
J
linear discriminant analysis,
jacobian matrix, 107–108 49–50
Japan, inflation and deflation linear models, 13–15
model for, 182–196 advantages of, 15
data in, 184–189 in automotive production
in-sample performance, forecasting, 148–152
189–190 as benchmark, xii
interpretation of results, in corporate bond example,
191–196 159–165
model specification, 189 in Hong Kong inflation
proposed remedies, 182–184 example, 176–180
Jarque-Bera statistic, in Japan inflation example,
89–90, 94 189–192
jump connections, use of residuals from, 32, 34
30–32, 39–40 linear principal components
analysis (PCA), 42–43,
K 211–220
linear scaling functions, 64
kurtosis, 90
- Index 239
linear smooth-transition regime in-sample diagnostic
switching system, 40 statistics in, 93–94
Ljung-Box Q-statistic, 87–88, 94 main script functions in,
142–143
local convergence problem
models in, 58
absurd results, 105
numerical optimization
multiple hidden layers and,
example, 78–80
32, 33
polynomial and network
in nonlinear optimization
approximation
methods, 68–71, 76
example, 80–83
local gradient-based search, 67
stochastic chaos model
logistic estimation, 53–54
in, 117
logistic regression, 52–53
Texas bank failures in, 210
logit regression, 50–51
maximum likelihood estimation,
in banking intervention
88
example, 207–209
McLeod and Li test, 88–89, 94
in credit card risk example,
model typology, 20–21
200–205
modified Diebold-Mariano
logsigmoid (squasher) function,
(MDM) statistic, 97
24–28, 31
moving average filters, 63
logsigmoid transition function,
moving-average processes,
39
34–35, 87–88
loss function minimization,
moving window estimation,
66–67
95–96
multilayered feedforward
M
networks, 32–34
Markov chain property, 71
multi-layer perception (MLP)
Markov regime switching (MRS) network, 25, 29
model, 115, 125–130
multiperceptron networks, 22
MATLAB program
multiple outputs, 36–38
analytic and finite
mutation operation, 74
differences in, 107–108
automobile industry
N
program in, 166
neglected nonlinearity, 90–91
availability of, xiv
nested classification, 53
corporate bonds program
nested evaluation models, 98–99
in, 166
neural linguistics, 22
evaluation tests in, 110–111
neural network approach
evolutionary computation
in, 83–84 advantages over nonlinear
regression, 33
German credit card defaults
in, 210 bounded rationality
assumption in, 7
inflation/deflation programs
in, 197 data requirements, 102–103
- 240 Index
neural network approach, contd nonlinearity, tests to determine,
in detecting neglected 90–92
nonlinearity, 90–91 nonlinear principal components
differences from classical analysis (NLPCA),
models, 7 44–46, 211–220
in discrete choice, 52–53 nonstationary series, 60
model typology, 20–21 normal distributions, 89–90
terminology in, 6 normal (Gaussian) function,
neural network 26–28
smooth-transition
O
regime switching
system (NNRS), 39–40 options pricing
in automotive production Black-Scholes model, 116,
example, 150–155 137–143
in corporate bond example, seasonal adjustment in, 63
160–165 SVJD model for, 123
in Hong Kong inflation ordinary least squares (OLS)
example, 176–182 estimators, 20
in Japan inflation example, orthogonal polynomials, 18–20,
189–196 80–82
neural network types, 21–38 orthogonal regression, 42–43
classification networks, out-of-sample evaluation
37–38 criteria, 94–103
feedforward networks, 21–24 data requirements, 102–103
jump connections, 30–32, Diebold-Mariano test, 96–97
39–40 in nested models, 98–99
multiple outputs in, 36–38 predictive stochastic
radial basis functions, 28–29 complexity, 100–101
recurrent networks, 34–36 recursive methodology,
ridgelet function, 29–30 95–96
squasher functions, 24–28 root mean squared error
Nikkei index, 186–187 statistic, 96, 219n, 220
nonlinear estimation, 65–77 sign prediction success
genetic algorithms, 67, ratios, 99–100
72–75, 78–80, 83–84 out-of-sample evaluations
hybridization, 75–77 in automotive production
initial conditions in, 65–66 example, 151–153
local gradient-based in banking intervention
searches, 67 example, 207–208
MATLAB examples of, in Black-Sholes option
78–83 pricing models,
simulated annealing, 67, 142–143
70–72, 78–80 in corporate bond example,
thick modeling, 77–78 160–161, 163
- Index 241
in credit card risk example, portfolio management,
202–205 forecasting in, 4
predictive stochastic complexity
in distorted long-memory
(PSC), 100–101
models, 137–138
price equalization, 168
in Hong Kong inflation
price gap, Hong Kong, 170,
example, 177–178, 180
172–173
in Hong Kong volatility
price puzzle, 188
forecasting example,
pricing of risk, 1–2, 5
214–215
pricing options
in Japan inflation example,
Black-Scholes model, 116,
190–192
137–143
in Markov regime switching
seasonal adjustment in, 63
methods, 130–131
SVJD model for, 123
in stochastic chaos models,
principal components
120–122
in asset pricing, 46–49
in stochastic volatility/jump
intrinsic dimensionality in,
diffusion models,
41–42
125–126
linear, 42–43
in United States volatility
nonlinear, 44–46
forecasting example,
program notes for, 58
218–219
principal components analysis
in volatility regime
(PCA), 42–43, 211–220
switching models,
principle of functional
132–134
integration, 23
out-of-sample predictions, 3
principle of functional
output gap, 169–170, 184–185
segregation, 23
output neurons, 21–22
probit regression, 51–52
in banking intervention
P
example, 207–209
parallel processing, 21–22 in credit card risk example,
parallel processing advantage, 22 200–205
parametric models, 20 put options, 1, 138–140
Pesaran-Timmerman directional
accuracy test, 99–100
Q
Petersohn scaling function,
quasi-Newton algorithm, 67–69,
64, 84
78–80, 83
Phillips and Perron test, 61
Phillips curve model, 56, 169,
R
174
Poisson jump process, 122 radial basis function (RBF)
polynomial approximation, network, 28–29
17–18 random shocks, 34, 47, 70, 117,
polynomial expansions, 18–20 149
- 242 Index
reconstruction mapping, 42, 44 in Japan inflation example,
189–196
recurrent networks, 34–36
softmax function, 53–54
recursive methodology, 95–96
sparse data sets, 42
regime switching models
squasher functions, 24–28, 31
Markov, 115, 125–130
stationarity, 59–61
smooth-transition, 38–40
stochastic chaos (SC) model,
volatility, 115, 130–134
115, 117–122
regularization term, 86n
stochastic search methods
residuals, use of, 32, 34, 85, 89
evolutionary, 72–75
ridgelet networks, 29–30
simulated annealing, 67,
robust regression, 45–46
70–72, 78–80
root mean squared error
stochastic volatility/jump
statistic, 96, 219n, 220
diffusion (SVJD)
R-squared coefficient, 86
model, 115, 122–125
strike price, 140, 140n
S
swap-options (swaptions), 48
saddle points, 65–66, 69 symmetry of residuals, 89
Sargent, Thomas J., The synapses, 22
Conquest of American
Inflation, 56
T
Schwartz statistic, 86
tanh function, 26
seasonal adjustments, 61–63
tansig function, 26
semi-parametric models,
Tchebeycheff polynomial
17–18, 20
expansion, 18–19, 19n
serial independence tests, 86–89
terminology, 6
shuffle crossover, 73
thick model forecasts, 77–78, 110
sieve estimator, 23–24
thick modeling, 48, 77–78
significance of results, 108
threshold responses, 24–25
sign prediction success ratios,
time-series recency effect, 103
99–100
times-series examples, 145–166
simulated annealing, 67, 70–72,
automotive production
78–80
forecasts, 145–155
single-point crossover, 73
corporate bonds, 156–165
skewness, 90
times-series models, 14, 14n
smooth-transition regime
transition function, 38–40
switching models,
t statistic, 108
38–40
in automotive production
U
example, 149–155
in corporate bond example, uncertainty, model, 55–56
159–165 United States, volatility
in Hong Kong inflation forecasting example,
example, 176–182 216–220
- Index 243
unit labor costs, 170–171, volatility regime switching
184, 186 (VRS), 115, 130–134
unit root processes, 60, 135,
W
135n
unsupervised training, 41 Weibull regression, 52
in banking intervention
example, 207–209
V in credit card risk example,
vector autoregressive models 200–205
(VAR), 168, 188 Weierstrass Theorem, 17–18
vocabulary of neural networks, 6 welfare index, 4–5
nguon tai.lieu . vn
