Elsevier, Neural Networks In Finance 2005_10

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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