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 mth 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 ith 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 ith 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 ith variable.
"exogenous":Exogenous nonrandom transition weights, specify the weight series in weightfun_pars.
See the vignette for more details about the weight functions.
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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.
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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).
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