smart_weightpars generates random transition weight parameter values
relatively close to the ones given in weight_pars
smart_weightpars(
M,
weight_pars,
weight_function = c("relative_dens", "logistic", "mlogit", "exponential", "threshold",
"exogenous"),
weight_constraints = NULL,
accuracy
)Returns a numeric vector ...
weight_function == "relative_dens":a length M-1 vector \((\alpha_1,...,\alpha_{M-1})\).
weight_function == "logistic":a length two vector \((c,\gamma)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function == "mlogit":a length \(((M-1)k\times 1)\) vector \((\gamma_1,...,\gamma_{M-1})\), where \(\gamma_m\) \((k\times 1)\), \(m=1,...,M-1\) contains the mlogit-regression coefficients of the \(m\)th regime. Specifically, for switching variables with indices in \(I\subset\lbrace 1,...,d\rbrace\), and with \(\tilde{p}\in\lbrace 1,...,p\rbrace\) lags included, \(\gamma_m\) contains the coefficients for the vector \(z_{t-1} = (1,\tilde{z}_{\min\lbrace I\rbrace},...,\tilde{z}_{\max\lbrace I\rbrace})\), where \(\tilde{z}_{i} =(y_{it-1},...,y_{it-\tilde{p}})\), \(i\in I\). So \(k=1+|I|\tilde{p}\) where \(|I|\) denotes the number of elements in \(I\).
weight_function == "exponential":a length two vector \((c,\gamma)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function == "threshold":a length \(M-1\) vector \((r_1,...,r_{M-1})\), where \(r_1,...,r_{M-1}\) are the threshold values in an increasing order.
weight_function == "exogenous":of length zero.
a positive integer specifying the number of regimes
a vector containing transition weight parameter values.
weight_function == "relative_dens":a length M-1 vector \((\alpha_1,...,\alpha_{M-1})\).
weight_function == "logistic":a length two vector \((c,\gamma)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function == "mlogit":a length \(((M-1)k\times 1)\) vector \((\gamma_1,...,\gamma_{M-1})\), where \(\gamma_m\) \((k\times 1)\), \(m=1,...,M-1\) contains the mlogit-regression coefficients of the \(m\)th regime. Specifically, for switching variables with indices in \(I\subset\lbrace 1,...,d\rbrace\), and with \(\tilde{p}\in\lbrace 1,...,p\rbrace\) lags included, \(\gamma_m\) contains the coefficients for the vector \(z_{t-1} = (1,\tilde{z}_{\min\lbrace I\rbrace},...,\tilde{z}_{\max\lbrace I\rbrace})\), where \(\tilde{z}_{i} =(y_{it-1},...,y_{it-\tilde{p}})\), \(i\in I\). So \(k=1+|I|\tilde{p}\) where \(|I|\) denotes the number of elements in \(I\).
weight_function == "exponential":a length two vector \((c,\gamma)\), where \(c\in\mathbb{R}\) is the location parameter and \(\gamma >0\) is the scale parameter.
weight_function == "threshold":a length \(M-1\) vector \((r_1,...,r_{M-1})\), where \(r_1,...,r_{M-1}\) are the threshold values in an increasing order.
weight_function == "exogenous":of length zero.
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.
a list of two elements, \(R\) in the first element and \(r\) in the second element, specifying linear constraints on the transition weight parameters \(\alpha\). The constraints are of the form \(\alpha = R\xi + r\), where \(R\) is a known \((a\times l)\) constraint matrix of full column rank (\(a\) is the dimension of \(\alpha\)), \(r\) is a known \((a\times 1)\) constant, and \(\xi\) is an unknown \((l\times 1)\) parameter. Alternatively, set \(R=0\) to constrain the weight parameters to the constant \(r\) (in this case, \(\alpha\) is dropped from the constrained parameter vector).
a positive real number adjusting how close to the given parameter vector the returned individual should be. Larger number means larger accuracy. Read the source code for details.