# Two-phase or three-phase (penalized) maximum likelihood estimation of a reduced form smooth transition VAR model `fitSTVAR` estimates a reduced form smooth transition VAR model in two phases or three phases. In additional ML estimation, also penalized ML estimation is available. ```r fitSTVAR( data, p, M, weight_function = c("relative_dens", "logistic", "mlogit", "exponential", "threshold", "exogenous"), weightfun_pars = NULL, cond_dist = c("Gaussian", "Student", "ind_Student", "ind_skewed_t"), parametrization = c("intercept", "mean"), AR_constraints = NULL, mean_constraints = NULL, weight_constraints = NULL, estim_method, penalized, penalty_params = c(0.05, 0.2), allow_unstab, min_obs_coef = 3, sparse_grid = FALSE, h = 0.001, nrounds, ncores = 2, maxit = 2000, seeds = NULL, print_res = TRUE, use_parallel = TRUE, calc_std_errors = TRUE, ... ) ``` ## 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"`:**: c("$\\alpha_{m,t}=\n$", "$ \\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"`:**: c("$\\alpha_{m,t}=\\frac{\\exp\\lbrace \\gamma_m'z_{t-1} \\rbrace}\n$", "$ {\\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}

fitSTVAR function