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Index ∇f(θ, γ), 359 annualized log return, 30 4(xt), 497 annualized simple return, 29 −1 4 (xt), 500 annualized volatility, 107, 491 ANOVA (analysis of variance), absolute return, 101 415–421, 440 acceptance/rejection method, 317 apply (R function), 150 accredited investor, 18 APT (arbitrage pricing theory), 44 ACF (autocorrelation function), 8, AR model, 534–571 100, 515 AR(1), 536–539 AR model, 541–546 ACF, 538 AR(1), 538 PACF, 539 difference equation, 544 AR(2) MA model, 531 ACF, 543 partial (PACF), 516, 547 AR(p), 534–548 sample (SACF), 100, 519 ACF difference equation, 546 adjusted price, 45–48 order determination, 548 dividend, 46, 134 autocorrelation, 538, 543, 547 effect on option strike, 64 causality, 539 return of capital, 48 explosive, 538 stock split, 45 partial autocorrelation function 2 adjusted R , 423, 468 (PACF), 547 after hours, 10, 37 stationarity, 535 agent-based model, 357 arbitrage, 38 aggregate (R function), 510 statistical, 600 AIC (Akaike information criterion), arbitrage pricing theory (APT), 44 445, 468 ARCH (GARCH see), 576 AICc, 469 ARCH effect, 578 Akaike information criterion (AIC), tests for, 579 445, 468 Archimedean copula, 266 algo (programmed trading), 126 ARFIMA model, 554 alpha, 63, 126 arima (R function), 561 alternative hypothesis, 382 ARIMA model, 553–571 alternative trading system (ATS), order determination, 560, 16, 35, 129 563–565 analysis of variance (ANOVA), arima.sim (R function), 555 415–421, 440 ARMA model, 549–571 Anderson-Darling test, 461 causality, 551 623 624 Index invertibility, 552 Bayes information criterion (BIC), order determination, 557, 560, 468 563–565 Bayesian model, 346, 386–393 ARMAX model, 575 conjugate prior, 388 asymptotic distribution, 270, 271, MCMC, 389 308 Bayesian network, 284 asymptotic inference, 378, 393 bear market, 126 ATS (alternative trading system), Bernoulli distribution, 283, 450 16, 35, 129 beta, 61–63, 126 augmented Dickey-Fuller test, beta distribution, 291 595–596, 598 bias, 347 autocorrelation, 7, 511–513, 518 bootstrap estimate, 395 returns, 99–101 bias-variance tradeoff, 218, 220, 370, tests, 526, 580 379, 402, 463, 465 autocorrelation function (ACF), 8, BIC (Bayes information criterion), 100, 511–513, 515 468 AR model, 541–546 bid/ask, 35 AR(1), 538 bid-ask spread, 37 difference equation, 544 big data, 139 MA model, 531 bill, Treasury, 22 partial (PACF), 516, 547 binary regression, 451 sample (SACF), 100, 519 binary regressor, 415, 419 autocovariance function, 515 binary tree, 281 partial, 516 binomial distribution, 283, 450 sample, 519 binomial tree, 281, 283 autoregressive model, 338, 492, Black Monday (October 19, 1987), 534–571 99, 159 autocorrelation, 538, 543, 547 black swan, 132 stationarity, 535 Black Thursday (October 24, 1929), vector autoregressive model, 159 535, 590 Black Tuesday (October 29, 1929), autoregressive operator, 535 159 multivariate, 536 Black-Scholes-Merton differential equation, 280 backshift operator, B(·), 495, 531, BlackRock iShares, 56 535 BOJ (Bank of Japan), 22 −1 inverse, B (·), 496 bond, 13, 20 multivariate, 497, 531, 536 coupon rate, 26 bagplot, 227, 236 coupon stripping, 28 Bank of Japan (BOJ), 22 coupon yield to maturity, 28 Basel Committee, 19, 119 par value, 21 Basel Accords, 119 price, 28 Basel II, 119 yield to maturity, 28 basis point, 22 zero-coupon, 28 bond, Treasury, 22 Index 625 book value, 38 CDF (cumulative distribution bootstrap, 393–396 function), 211, 249 bias estimate, 395 complementary, 258 boot (R package), 396 CDF-skewing, 302 bootstrap (R package), 396 CDO (collateralized debt obligation), confidence interval, 395 20 variance estimate, 394 Center for Research in Security Bowley’s skewness, 96 Prices (CRSP), 53, 171 box-and-whisker plot, 224, 225 centered data, 208–210, 408 Box-Cox transformation, 345, 422, central limit theorem, 272 579 Chambers, John, 140 Box-Ljung test, 526, 580 change of variables technique, 255 Box-Pierce test, 526 characteristic polynomial, 503, 531, boxplot, 110, 224, 225 533, 535, 539, 543, 545, 546 bivariate, 227, 236 AR model, 535, 543 Brownian motion, 279 discriminant, 504 BUGS (software), 389 MA model, 531, 533 Bulletin Board (OTC), 16 chi-squared distribution, 289, 292, burn-in for a stochastic process, 357 313, 383 Burr distributions, 324 chi-squared test, 457 buyback, stock, 33, 38, 43, 44 Chicago Board Options Exchange (CBOE), 17, 108, 113 Cp, 424, 468 Chicago Mercantile Exchange CAC-40 (index), 59, 166 (CME), 17 calendar spread, 74 Cholesky factor, 269, 310, 320 call option, see option class (R object), 143 call spread, 74 classification model, 337, 449 candlestick graphic, 33, 182 logistic regression, 449 CAPE (Shiller P/E ratio), 43 Clayton copula, 266 capital asset pricing model (CAPM), cleaning data, 183–186 44 missing data, 185 capital market line, 72 CME (Chicago Mercantile capitalization, market, 32 Exchange), 17 CAPM (capital asset pricing model), CME Group, 17 44 coefficient of multiple correlation, Case-Shiller Index, 168 417 cash settlement, 64 coefficient of multiple determination, Cauchy distribution, 293 417 causality, 528, 537, 539, 551 coherent measure, 118, 257 CBOE (Chicago Board Options cointegration, 599–602 Exchange), 17, 108, 113 Engle-Granger test, 600 CBOE SKEW Index, 113 Johansen test, 600 CBOE Volatility Index, 108–111, 166 Phillips-Ouliaris test, 600 CCF (cross-correlation function), 517 collateralized debt obligation (CDO), sample, 519 20 626 Index COMEX, 17 correlation, 83, 85, 208, 210, comma separated file (CSV), 162–163 261–263, 584–591 header, 163 among assets in financial crises, Commodity Futures Trading 127, 130, 276 Commission (CFTC), 18 autocorrelation, 100 complementary cumulative distribution, 408–409, 584–591 distribution function Kendall’s tau, 98, 399 (CCDF), 258 Pearson correlation coefficient, composite hypothesis, 381 83 composition of functions, 495 sample, 83, 408 compound distribution, 307 Spearman’s rank correlation, 97, compounding, 26 399 continuous, 28 spurious, 584 computational inference, 378, 393 tail dependence, 127, 130, 276, conditional distribution, 6, 260, 310, 402 513 test, 409 conditional heteroscedasticity, correlogram, 519 575–583 coupon bond, 21 conditional value at risk, 119, 404 coupon rate, 26 confidence interval, 379, 448 coupon stripping, 28 basic bootstrap, 395 Cov(·, ·) (covariance, see), 4 conjugate prior, 388 covariance, 82, 208, 210, 261–263 consistency, 348 covered call, 74 consistent estimator, 348 Cox-Ross-Rubinstein (CRR) model, constrained optimization, 359, 362 282 feasible set, 362 Cram´er-von Mises test, 461 Consumer Price Index (CPI), 168 CRAN (Comprehensive R Archive continuous compounding, 28 Network), 146 continuous data, 206 credit rating agency, 19 continuous distribution, 252, 285 cross-correlation function (CCF), contour plot, 235 513, 517 Cook’s distance, 433, 440, 443 sample, 519 copula, 264–267, 310, 321, 334, 350 cross-correlogram, 519, 522 Archimedean, 266 cross-covariance function, 513 copula (R package), 350 sample, 519 definition, 265 cross-validation, 463–467 fitting, 350 k-fold, 465 Gaussian, 266 leave out one (LOOCV), 464 normal, 266 crossover, 122 Cor(·, ·) (correlation, see), 4 CRSP (Center for Research in Cornish-Fisher expansion, 406 Security Prices), 53, 171 corporate bond, 25 database, 53, 171 seasoned, 26 cryptocurrency, 14, 38 correction, 25 CSV file (comma separated file), 162–163 Index 627 header, 163 Nasdaq daily, 50, 55, 85, 86, 98, cumsum (R function), 154 127 cumulative distribution function Nasdaq daily 1987-2017, 83 (CDF), 211, 249 S&P 500 daily, 50, 53, 55, 61, complementary, 258 83, 85, 89, 90, 92, 98–101, currency exchange rates, 167, 168 108, 127, 569, 579 CVaR, 119, 404 S&P 500 monthly, 93, 102, 105 S&P 500 Total Return daily, 53, D’Agostino-Pearson test, 461 56 DAG (directed acyclic graph), 388 S&P 500 weekly, 93, 105 daily log return, 30 SKEW daily, 108 dark pool, 16, 35, 129 SPY daily, 56 data, 2 T-Bill, 3-month monthly, 22 continuous, 206 USDollar/Euro daily, 14, 601 copyright, 164 VIX daily, 108, 110 derived, 158 yield curves, 24, 25 discrete, 206 date data, 156, 174 observed, 158 in data frames, 161 repository, 163 in xts objects, 174 data cleansing, 183–186 ISO 8601, 157, 176 data quality, 197, 481 POSIX, 157, 176 missing data, 185 DAX (index), 59, 166 data frame, 152–153, 161 death cross, 123 stringsAsFactors, 152, 163 deleted residual, 429, 464 converting to xts object, 174 delta (Greek), 65, 75, 137 data-generating process, 2, 311 density plot, 79, 226 model, 311 bivariate, 227 data reduction, 341 derivative, 13, 63–66 data structure, 160 descriptive statistics, 94, 205 data wrangling and munging, 183 detrending, 505, 508 datasets deviance, 373, 451, 468 CanadaDollar/USDollar daily, deviance residual, 374, 451 601 df (degrees of freedom), 289 Dow Jones daily, 50, 55, 85, 98, DFBETAS, 433, 440, 443 127 DFFITS, 433, 440, 443 Dow Jones daily 1987-2017, 83 Dickey-Fuller test, 595 GLD daily, 85 augmented, 595–596 INTC daily, 9, 34, 39, 51, 70, 76, diff (R function), 154, 174, 176, 499 77, 79, 80, 85, 86, 88, 98, cumsum, 154 124, 127 diffinv, 154 INTC daily 2017, 61 on xts object, 155, 174 INTC monthly, 9 difference equation, 501–505, 545, INTC price adjustments, 47, 48 546 INTC weekly, 9 difference operator, 4(·) or (1 − B), 497 628 Index fractional differencing, 498 lognormal, 286, 288, 313 differential scaling, 302 Lorentz, 286 diffusion process, 279, 280, 490 multinomial, 284, 294, 313 dimension reduction, 341 multivariate normal, 287, 295, directed acyclic graph (DAG), 388 313 discount rate, 22 multivariate t, 295, 313 discounted cash flow,
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