check_weightfun_pars: Check the argument `weightfun_pars`

Description

check_weightfun_pars checks that the argument weightfun_pars. is correctly set, if not, tries to correct them.

Usage

check_weightfun_pars(
  data,
  p,
  M,
  d,
  weight_function = c("relative_dens", "logistic", "mlogit", "exponential", "threshold",
    "exogenous"),
  weightfun_pars = NULL,
  cond_dist = c("Gaussian", "Student", "ind_Student", "ind_skewed_t")
)

Value

Does checks the argument weightfun_pars and throws an error if something is wrong; returns a corrected version of the argument if possible.

Arguments

data

a matrix or class 'ts' object with d>1 columns. Each column is taken to represent a univariate time series. Missing values are not supported.

p

a positive integer specifying the autoregressive order

M

a positive integer specifying the number of regimes

weight_function

What type of transition weights $\alpha_{m,t}$ should be used?

"relative_dens":: $\alpha_{m,t}= \frac{\alpha_mf_{m,dp}(y_{t-1},...,y_{t-p+1})}{\sum_{n=1}^M\alpha_nf_{n,dp}(y_{t-1},...,y_{t-p+1})}$, where $\alpha_m\in (0,1)$ are weight parameters that satisfy $\sum_{m=1}^M\alpha_m=1$ and $f_{m,dp}(\cdot)$ is the $dp$-dimensional stationary density of the $m$th regime corresponding to $p$ consecutive observations. Available for Gaussian conditional distribution only.

"logistic":

$M=2$, $\alpha_{1,t}=1-\alpha_{2,t}$, and $\alpha_{2,t}=[1+\exp\lbrace -\gamma(y_{it-j}-c) \rbrace]^{-1}$, where $y_{it-j}$ is the lag $j$ observation of the $i$th variable, $c$ is a location parameter, and $\gamma > 0$ is a scale parameter.

"mlogit":

$\alpha_{m,t}=\frac{\exp\lbrace \gamma_m'z_{t-1} \rbrace} {\sum_{n=1}^M\exp\lbrace \gamma_n'z_{t-1} \rbrace}$, where $\gamma_m$ are coefficient vectors, $\gamma_M=0$, and $z_{t-1}$ $(k\times 1)$ is the vector containing a constant and the (lagged) switching variables.

"exponential":

$M=2$, $\alpha_{1,t}=1-\alpha_{2,t}$, and $\alpha_{2,t}=1-\exp\lbrace -\gamma(y_{it-j}-c) \rbrace$, where $y_{it-j}$ is the lag $j$ observation of the $i$th variable, $c$ is a location parameter, and $\gamma > 0$ is a scale parameter.

"threshold":

$\alpha_{m,t} = 1$ if $r_{m-1}<y_{it-j}\leq r_{m}$ and $0$ otherwise, where $-\infty\equiv r_0<r_1<\cdots <r_{M-1}<r_M\equiv\infty$ are thresholds $y_{it-j}$ is the lag $j$ observation of the $i$th variable.

"exogenous":

Exogenous nonrandom transition weights, specify the weight series in weightfun_pars.

See the vignette for more details about the weight functions.

weightfun_pars

If weight_function == "relative_dens":: Not used.

If weight_function %in% c("logistic", "exponential", "threshold"):

a numeric vector with the switching variable $i\in\lbrace 1,...,d \rbrace$ in the first and the lag $j\in\lbrace 1,...,p \rbrace$ in the second element.

If weight_function == "mlogit":

a list of two elements:

The first element $vars:: a numeric vector containing the variables that should used as switching variables in the weight function in an increasing order, i.e., a vector with unique elements in $\lbrace 1,...,d \rbrace$.

The second element $lags:

an integer in $\lbrace 1,...,p \rbrace$ specifying the number of lags to be used in the weight function.

If weight_function == "exogenous":

a size (nrow(data) - p x M) matrix containing the exogenous transition weights as [t, m] for time $t$ and regime $m$. Each row needs to sum to one and only weakly positive values are allowed.

cond_dist

specifies the conditional distribution of the model as "Gaussian", "Student", "ind_Student", or "ind_skewed_t", where "ind_Student" the Student's $t$ distribution with independent components, and "ind_skewed_t" is the skewed $t$ distribution with independent components (see Hansen, 1994).