- a
- ACD (autoregressive conditional duration), 115
- Adaptive GARCH estimator, 254
- Aggregation, 275
- APARCH (asymmetric power ARCH), 96
- ARCH effect test, 147, 227, 230
- ARCH(∞), 36–41
- ARIMA, ,
- ARMA, , , 12
- autocorrelation,
- for squares of GARCH, 18
- identification, 132
- multivariate, 274
- Asymmetries, see Leverage effect, 73
- Autocorrelation
- Autocovariance
- empirical, ,
- for squares of GARCH, 46–49
- multivariate, 274
- theoretical,
- Autoregressive moving average model, see ARMA,
- b
- Bahadur's approach, 232, 247
- Bartlett's formula, , 13, 404
- BEKK GARCH, 281
- Beta‐t‐GARCH, 113
- Black–Scholes formula, 326
- c
- CARR(conditional autoregressive range), 116
- Causal, see Nonanticipative solution, 40
- CCC (constant conditional correlations) GARCH
- estimation, 297
- stationarity, 289
- Cholesky GARCH, 286
- CLT (central limit theorem)
- for α‐mixing processes, 375
- for martingale increments, 127, 158, 164, 167, 199, 202, 210, 369, 371, 429
- Coefficient of determination, 159
- Corner method, 138
- d
- DCC GARCH, 280
- Diagonal GARCH, 276
- Diffusions, 317–324
- e
- EbE (equation‐by‐equation) estimator of multivariate GARCH, 300
- EGARCH (exponential GARCH), 77
- invertibility, 80
- moments, 79
- stationarity, 78
- EM algorithm, 359
- Ergodicity of stationary processes, 13, 22, 367
- f
- Factor GARCH, 284, 315
- FF (full‐factor) GARCH, 285
- FGLS, 165–168
- Forward–Backward algorithm, 358
- Functional GARCH, 118
- g
- GARCH(p, q)
- definitions, 17
- identification, 140
- kurtosis, 45
- moments, 42–43
- prediction of the squares, 50–54
- second‐order stationarity, 25, 34
- strict stationarity, 22, 27–34, 28
- vector representation, 27
- GARCH‐X, 109
- GAS (generalized autoregressive score), 113
- GARCH‐M, 320
- Geometric ergodicity, see Markov chain, 63
- GJR‐GARCH, 91
- h
- HEAVY (high‐frequency‐based volatility), 111
- HAC (heteroscedasticity and autocorrelation consistent), 137, 146, 158
- Heteroscedasticity,
- Hamilton filter, 358
- HMM (hidden Markov model), 353–362
- l
- Lagrange multiplier test, 143–148, 159
- LAN (local asymptotic normality), 256
- Least absolute deviations, 267
- Leptokurticity,
- Leverage effect, , 74, 104, 121
- Likelihood ratio test, 226–234
- Linearly regular,
- Log‐GARCH, 82
- Long‐Memory ARCH,40
- Long‐run variance, 137, 146, 158
- Lyapunov exponent, 27, 28, 31, 33, 55, 69, 94, 178, 298
- m
- Markov chain, 59–64, 319, 353, 387–392
- Markov switching models, 353–363
- Martingale difference, 368
- Martingale increments, see Martingale difference, 368
- MIDAS (mixed data sampling), 113
- Mixing coefficients, 371
- ARCH(q), 69
- ARCH(1), 64
- GARCH(1,1), 66
- ML for GARCH, 249–260
- asymptotic behavior, 250
- comparison with the QML, 251
- misspecification, 260
- one step estimator, 252
- n
- News impact curve, 91
- Nonanticipative solution, 22
- o
- O‐GARCH (orthogonal GARCH), 284
- OLS, 161–165
- asymptotic properties, 163–165
- constrained OLS, 169–170
- for GARCH(p, q), 212
- Options, 324
- p
- PC‐GARCH, see O‐GARCH, 284
- PCA (principal components analysis), 284, 315
- Persistence of shocks,22
- Pitman's approach, 233, 247
- Portmanteau test, 128–129, 149
- Purely non‐deterministic,
- q
- QGARCH (quadratic GARCH), 98
- QML for ARCH
- QML for ARMA‐GARCH, 183
- asymptotic normality, 186, 187
- consistency, 185
- QML for GARCH, 175–177
- asymptotic law at the boundary, 222, 226
- non‐Gaussian, 261, 262
- optimality condition, 251
- QML for general multivariate GARCH, 292–294
- Quasi‐likelihood, 176
- r
- Random walk, 26
- Realised‐GARCH, 112
- Realised volatility measures, 111–112, 341
- RiskMetrics, 57, 332
- s
- Score test, see Lagrange multiplier test, 143, 226–234
- Self‐weighted QMLE, 266
- Semi‐parametric GARCH model, 254
- SRE (Stochastic Recurrence Equation), 74–77, 81, 99
- Stationarity
- Stochastic discount factor, 325
- Stochastic volatility model, 11, 112, 324, 345–353
- Student's t test, 227, 229
- t
- TGARCH (threshold GARCH), 90
- v
- Variance targeting estimation, 299
- VaR (value at risk), 331–336
- Vector GARCH, 276
- Volatility, , 10, 336
- Volatility clustering, , 19
- w
- Wald test, 226‐234
- Weighted least squares, 265
- White noise, 12
- multivariate, 274
- strong, , 12
- weak, , 12
- Whittle estimator, 268
- Wold's representation,
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