Notation
- General notation
-
- ‘is defined as’
-
-
(or 
in Chapter 10) - Sets and spaces
-
- positive integers, integers, rational numbers, real numbers
-
- positive real line
-
-
‐dimensional Euclidean space -
- complement of the set
-
- half‐closed interval
- Matrices
-
-
‐dimensional identity matrix -
- the set of
real matrices - Processes
- iid
- independent and identically distributed
- iid (0,1)
- iid centered with unit variance
-
or 
- discrete‐time process
-
- GARCH process
-
- conditional variance or volatility
-
- strong white noise with unit variance
-
- kurtosis coefficient of
-
or 
- lag operator
-
or 
- sigma‐field generated by the past of
- Functions
-
- 1 if
, 0 otherwise -
- integer part of
-
- autocovariance and autocorrelation functions of
-
- sample autocovariance and autocorrelation
- Probability
-
- Gaussian law with mean
and covariance matrix 
-
- chi‐square distribution with
degrees of freedom -
- quantile of order
of the 
distribution -
- convergence in distribution
- a.s.
- almost surely
-
-
in probability -
-
equals 
up to the stochastic order 
- Estimation
-
- Fisher information matrix
-
- asymptotic variance of the QML
-
- true parameter value
-
- parameter set
-
- element of the parameter set
-
- estimators of
-
- volatility built with the value
-
- as
but with initial values -
-
-
- approximation of
, built with initial values -
- asymptotic variance and covariance
- Some abbreviations
- ES
- expected shortfall
- FGLS
- feasible generalized least squares
- OLS
- ordinary least squares
- QML
- quasi‐maximum likelihood
- RMSE
- root mean square error
- SACR
- sample autocorrelation
- SACV
- sample autocovariance
- SPAC
- sample partial autocorrelation
- VaR
- value at risk
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