Index
ACD, see Autoregressive conditional durationActivation function, see Neural networkAirline model, 75Akaike information criterion (AIC), 41, 356Arbitrage, 391Autoregressive conditional hetereoscedastic
(ARCH) effect, 101Autoregressive conditional hetereoscedastic
(ARCH) model, 102estimation, 107
t distribution, 108GED innovation, 108normal, 107
Arranged autoregression, 189Augmented DickeyFuller test, 69Autocorrelation function (ACF), 26Autoregressive conditional duration (ACD)
model, 227exponential, 228generalized Gamma, 229threshold, 236Weibull, 228
Autoregressive integrated moving-average(ARIMA) model, 67
Autoregressive model, 32estimation, 43forecasting, 47order, 41stationarity, 40
Autoregressive moving-average(ARMA) model, 56
forecasting, 61
Back propagation (BP) neural network, 180Back-shift operator, 36Bartletts formula, 27
Analysis of Financial Time Series, Second Edition By Ruey S. TsayCopyright 2005 John Wiley & Sons, Inc.
Bayesian information criterion(BIC), 42
Bidask bounce, 211Bidask spread, 211Bilinear model, 156BlackScholes
differential equation, 263BlackScholes formula
European call option, 97, 265European put option, 265
Brownian motion, 255geometric, 258standard, 253
Business cycle, 37
Canonical correlation analysis, 385Characteristic equation, 40Characteristic root, 36, 40Cholesky decomposition, 350, 397, 455Co-integration, 82, 376Co-integration test
maximum eigenvalue, 385trace, 385
Common factor, 477Common trend, 378Companion matrix, 354Compounding, 4Conditional distribution, 8Conditional forecast, 48Conditional heteroscedasticity, 86
HAC covariance estimator, 86Conditional heteroscedasticity ARMA
(CHARMA) model, 131Conditional likelihood method, 53Conjugate prior, see Distribution
601
602 INDEX
Correlationcoefcient, 25constant, 459time-varying, 464
Cost-of-carry model, 390Covariance matrix, 340Cross-correlation matrix, 340, 341Cross-validation, 170
Data3M stock return, 19, 59, 66, 164Cisco stock return, 260, 472, 480Citi-Group stock return, 19Civilian employment number, 412consumer price index, 412equal-weighted index, 19, 52, 54, 91, 157, 190GE stock return, 591Hewlett-Packard stock return, 423Hong Kong market index, 445IBM stock return, 19, 28, 126, 135, 136, 161,
180, 190, 259, 292, 295, 298, 300, 307,313, 323, 343, 423, 462, 478, 573
IBM transactions, 213, 215, 219, 223, 234, 240Intel stock return, 19, 100, 109, 299, 423, 472,
480Japan market index, 445Johnson and Johnsons earning, 72Mark/Dollar exchange rate, 104Merrill Lynch stock return, 423Microsoft stock return, 19Morgan Stanley Dean Witter stock return, 423SP 500 excess return, 116, 132SP 500 index futures, 390, 392SP 500 index return, 135, 138, 141, 343, 462,
472, 478, 569, 573, 586SP 500 spot price, 392U.S. 3-month treasury bill rate, 173U.S. government bond, 21, 345, 431U.S. interest rate, 21, 80, 556, 564U.S. monthly unemployment rate, 159U.S. real GNP, 38, 165U.S. unemployment rate, 194value-weighted index, 19, 28, 41, 91, 126, 190
Data augmentation, 544Decomposition model, 221Descriptive statistics, 19Diagonal VEC model, 447DickeyFuller test, 68Differencing, 68
seasonal, 74Distribution
beta, 549conjugate prior, 548double exponential, 276
Frechet family, 303gamma, 243, 549generalized error, 108generalized extreme value, 302generalized Gamma, 245generalized Pareto, 320, 330inverted chi-squared, 551Laplacian, 275multivariate t , 482multivariate normal, 399, 549negative binomial, 550Poisson, 550posterior, 548prior, 548Weibull, 244
Diurnal pattern, 212Donskers theorem, 254Duration
between trades, 215model, 225
DurbinWatson statistic, 85
EGARCH model, 124forecasting, 128
Eigenvalue, 396Eigenvector, 396EM algorithm, 544Error-correction model, 380Estimation, extreme value parameter, 304Exact likelihood method, 53Exceedance, 318Exceeding times, 318Excess return, 5Extended autocorrelation function, 59Extreme value theory, 301
Factor analysis, 426Factor mimicking portfolio, 420Factor model
common factor, 406estimation, 428factor loading, 406specic factor, 406
Factor rotation, varimax, 429Filtering, 493Forecast
horizon, 47origin, 47
Forecast updating formula, 513Forecasting, see Markov chain Monte Carlo
methodForward ltering and backward sampling, 583Fractional differencing, 89
INDEX 603
GARCH model, 114Cholesky decomposition, 468diagonal multivariatemultivariate, 459time-varying correlation, 466
GARCH-M model, 123, 588Generalized least squares, 415Generalized Pareto distribution, 320Geometric ergodicity, 158Gibbs sampling, 545Global minimum variance portfolio, 411Griddy Gibbs, 553
Hazard function, 245Hh function, 281Hill estimator, 306Hyperparameter, 554
Identiability, 371IGARCH model, 122, 290Implied volatility, 98Impulse response function, 63, 362Innovation, 31Inverted yield curve, 82Invertibility, 52, 379Invertible ARMA model, 62Itos lemma, 258
multivariate, 273Ito process, 256
Joint distribution function, 7Jump diffusion, 275
Kalman lter, 496, 524Kalman gain, 495, 524Kernel, 168
bandwidth, 169Epanechnikov, 169Gaussian, 169
Kernel regression, 168Kurtosis, 9
excess, 9
Lag operator, 36Lead-lag relationship, 341Leptokurtic, 9Leverage effect, 99, 125, 579Likelihood function, 17Linear time series, 31Liquidity, 210LjungBox statistic, 27, 101
multivariate, 346
Local linear regression, 173Local trend model, 491Log return, 5Logit model, 239Long position, 6Long-memory
stochastic volatility, 135time series, 89
Marginal distribution, 7Market model, 408Markov chain Monte Carlo method (MCMC),
177, 594Markov process, 543Markov property, 32Markov switching model, 164, 588Martingale difference, 114Maximum likelihood estimate (MLE),
exact, 368Mean equation, 101Mean excess function, 321Mean excess plot, 321Mean reversion, 49, 63
half-life, 49Metropolis algorithm, 551MetropolisHasting algorithm, 552Missing value, 531, 558Model checking, 44Moment of a random variable, 8Moving-average model, 50
NadarayaWatson estimator, 169Neural network, 177
activation function, 178feed-forward, 177skip layer, 179
Neuron, see Neural networkNode, see Neural networkNonlinearity test, 183
Brock-Dechert-Scheinkman (BDS), 185bispectral, 184F-test, 188Keenan, 187RESET, 186Tar-F, 190
Nonstationarity, unit-root, 64Nonsynchronous trading, 207Nuisance parameter, 188
OptionsAmerican, 252at-the-money, 252European call, 97
604 INDEX
in-the-money, 252out-of-the-money, 252stock, 252strike price, 97, 252
Order statistics, 299Ordered probit model, 218Orthogonal factor model, 427Outlier
additive, 558detection, 561
Parametric bootstrap, 192Partial autoregressive function (PACF), 40Peaks over thresholds, 318 -weight, 62Pickands estimator, 306Platykurtic, 9Poisson process, 275
inhomogeneous, 329intensity function, 322
Portmanteau test, 27. See also LjungBoxstatistic
Positive denite matrix, 396Prediction, 493Present value, 4Price change and duration (PCD) model, 238Principal component analysis, 421, 478-weight, 31Put-call parity, 266
Quantile, 8denition, 289
R-square, 46adjusted, 47
Random coefcient (RCA) model, 133Random walk, 64
with drift, 65Realized volatility, 141, 492Reduced form model, 349Regression, with time series errors, 80Return level, 317
stress period, 317RiskMetrics, 290
Sample autocorrelation, 26Scree plot, 425Seasonal adjustment, 72Seasonal model, 72
multiplicative, 75
Shape parameter of a distribution, 302Shock, 31, 48, 101Short position, 6Simple return, 3Skewness, 9Smoothed disturbance, 528Smoothing, 167, 493Square root of time rule, 291Standard Brownian motion, 69State space model, 509
nonlinear, 176Stationarity, 25
weak, 340Steady state, 525Stochastic diffusion equation, 256Stochastic volatility model, 134, 565
multivariate, 571Structural equation, 350Structural form, 350Structural time series model (STSM), 491, 521Student-t distribution
standardized, 108Survival function, 322
Tail index, 302TGARCH model, 130
general form, 161Threshold, 159Threshold autoregressive model
multivariate, 392self-exciting, 159smooth, 163
Threshold co-integration, 392Time plot, 17Transactions data, 212Trend stationary model, 67
Unit-root test, 68Unit-root time series, 64Unobserved component model, 521
Value at Risk (VaR), 287, 480econometric approach, 294homogeneous Poisson process, 324inhomogeneous Poisson process, 328RiskMetrics, 290of a short position, 316traditional extreme value, 312
Vector autoregressive (VAR) model, 349Vector ARMA model, 371
marginal models, 375
INDEX 605
Vector moving average model, 365VIX Volatility Index, 98Volatility, 97Volatility equation, 101Volatility model
factor, 477Volatility smile, 274
Weighted least squares, 415White noise, 31Wiener process, 253
generalized, 255
YuleWalker equationmultivariate, 354