Index

Adaptive GARCH estimator

Aggregation

contemporaneous

stability by

temporal

APARCH (asymmetric power ARCH)

ARCH effect test

ARCH(∞)

ARIMA

ARMA

autocorrelation

for squares of GARCH

identification

multivariate

identifiability

Asymmetries, see Leverage effect

Autocorrelation

empirical

partial

theoretical

Autocovariance

empirical

for squares of GARCH

multivariate

theoretical

Autoregressive moving average model, see

ARMA

Bahadur’s approach

Bartlett’s formula

generalized

BEKK GARCH

Black-Scholes formula

Causal, see Nonanticipative solution

CCC (constant conditional correlations) GARCH

estimation

stationarity

CLT (central limit theorem)

forα-mixing processes

for martingale differences

for martingale increments

for stationary martingale differences

Coefficient of determination

Corner method

DCC GARCH

Diagonal GARCH

Diffusions

EGARCH (exponential GARCH)

moments

stationarity

Ergodicity of stationary processes

Factor GARCH

BEKK representation

FF (full-factor) GARCH

FGLS

GARCH

semi-strong

strong

weak

GARCH(p, q)

definitions

identification

kurtosis

moments

prediction of the squares

second-order stationarity

strict stationarity

vector representation

GARCH-M

Geometric ergodicity, see Markov chain

GJR-GARCH

HAC (heteroscedasticity and autocorrelation consistent)

Heteroscedasticity

conditional

IGARCH(p, q)

Irreducibility, see Markov chain

Itô’s lemma

Kurtosis

Lagrange multiplier test

optimal

LAN (local asymptotic normality)

Least absolute deviations

weighted

Leptokurticity

Leverage effect

Likelihood ratio test

optimal

Linearly regular

Long-run variance

Lyapunov exponent

Markov chain

Martingale difference

Martingale increments, see Martingale difference

Mixing coefficients

ARCH(q)

ARCH(l)

GARCH(1,1)

ML for GARCH

asymptotic behavior

comparison with the QML

missspecification

one step estimator

News impact curve

Nonanticipative solution

O-GARCH (orthogonal GARCH)

OLS

asymptotic properties

constrained OLS

for GARCH(p, q)

Options

PC-GARCH, see O-GARCH

PC A (principal components analysis)

Persistence of shocks

Pitman’s approach

Portmanteau test

Purely nondeterministic

QGARCH (quadratic GARCH)

QML for ARCH nonstationarity

QML for ARMA-GARCH

asymptotic normality

consistency

QML for GARCH

asymptotic law at the boundary

asymptotic normality

consistency

non-Gaussian

optimality condition

Quasi-likelihood

Random walk

RiskMetrics

Score test, see Lagrange multiplier test

Self-weighted QMLE

Semi-parametric GARCH model

Stationarity

second order

multivariate

strict

Stochastic discount factor

Stochastic volatility model

Student’s t test

TGARCH (threshold GARCH)

stationarity

VaR (value at risk)

estimation

Vector GARCH

stationarity

Volatility

historical

implied

realized

Volatility clustering

Waldtest

optimal

Weighted least squares

White noise

multivariate

strong

weak

Whittle estimator

Wold’s representation

multivariate

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