M |
a positive integer specifying the number of regimes
|
weight_pars |
a vector containing transition weight parameter values.
- If
weight_function == "relative_dens" : a length M-1 vector (\alpha_1,...,\alpha_{M-1}) .
- If
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.
- If
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 .
- If
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.
- If
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.
- If
weight_function == "exogenous" : of length zero.
|
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.
|
weight_constraints |
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).
|
accuracy |
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.
|
Returns a numeric vector ...
- If
weight_function == "relative_dens"
: a length M-1
vector (\alpha_1,...,\alpha_{M-1})
.
- If
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.
- If
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
.
- If
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.
- If
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.
- If
weight_function == "exogenous"
: of length zero.