diag_std_et_cnd: Standardized Series e_t for Diagnostics
In sebinum/baqgarchutil: Analyse a Fitted baqGARCH Model

Description Usage Arguments Value Details References See Also Examples

Transform a (multivariate) k-dimensional series a_t and its corresponding conditional variance to a standardized univariate series e_t and a standardized multivariate series e_t^k.

1	diag_std_et_cnd(eps, cnd_h)

`eps`	A `matrix` / `data.frame` / `numeric vector` of (multivariate) financial time series. Each column contains a series, each row an observation of the series.
`cnd_h`	A `matrix` / `data.frame` with the conditional variance of eps. The dimensions of `cnd_h` need to fulfil the following conditions: `nrow(cnd_h) == nrow(eps)` and `ncol(cnd_h) == ncol(eps)^2`.

A list containing the standardized univariate conditional series e_t and the (marginally) standardized multivariate conditional series e_t.

Ling & Li (1997) proposed model diagnostics based on a standardized scalar series ê_t.

The residuals of a k-dimensional financial time series a_t = z_t - μ (where z_t stands for the return series and μ for the return series conditional mean) and it's time conditional covariance matrices can be transformed to a quadratic standardized residual series ê_t:

ê_t = â'_t * ∑_t^-1 * â_t

where ∑_t denotes the estimated conditional covariance matrices of the k-dimensional series a_t. The lag-l autocorrelation of ê_t is denoted by

ρ_l = (∑_{t=l+1}^T * (ê_t - k) * (ê_{t-l} - k)) / (∑_{t=1}^T (ê_t - k)²

where E(â'_t ∑_t^{-1} â_t) = k (for more details see the references). The series returned is ê_t - k and thus can be used to compute the autocorrelation.

An approach focusing on the squared elements of a (marginally) multivariate standardized series was proposed by Tse (2002), where the ith standardized residual is denoted by

η_{it} = â_{it} / √{σ_{ii,t}}, i = 1, ..., k

σ_{ii,t} stands for the (i,i)th element of the time dependent conditional covariance matrices sum_t and a_t = z_t - μ (where again z_t stands for the return series and μ for the return series conditional mean).

Ling, S. & Li, W. K. (1997). Diagnostic checking of nonlinear multivariate time series with multivariate ARCH errors. Journal of Time Series Analysis, 18: 447–464.

Tse, Y. K. (2002). Residual-based diagnostics for conditional heteroscedasticity models. Econometric Journal, 5: 358–373.

Tsay, R. S. (2014). Multivariate Time Series Analysis with R and Financial Applications. John Wiley. Hoboken, NJ.

Tsay, R. S (2015). MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models. R package version 0.33.

diag_dufour_roy, diag_ljung_box, diag_mv_ch_model for Test Statistics which can be used on the series diag_std_et_cnd

# create data
eps <- mgarchBEKK::simulateBEKK(2, 150)

# fit the model
gjr <- mgarchBEKK::mGJR(eps$eps[[1]], eps$eps[[2]])

# apply the news impact function to the model
nif <- baq_nifunction(gjr)

# get the standardized series
et_cnd <- diag_std_et_cnd(eps = nif$eps, cnd_h = nif$baq_h)