# TVAR: Multivariate Threshold Autoregressive model In tsDyn: Nonlinear Time Series Models with Regime Switching

## Description

Estimate a multivariate Threshold VAR

## Usage

 1 2 3 4 5 TVAR(data, lag, include = c("const", "trend", "none", "both"), model = c("TAR", "MTAR"), commonInter = FALSE, nthresh = 1, thDelay = 1, mTh = 1, thVar, trim = 0.1, ngrid, gamma = NULL, around, plot = FALSE, dummyToBothRegimes = TRUE, trace = TRUE, trick = "for", max.iter = 2)

## Arguments

 data time series lag Number of lags to include in each regime include Type of deterministic regressors to include model Whether the transition variable is taken in levels (TAR) or difference (MTAR) commonInter Whether the deterministic regressors are regime specific (commonInter=FALSE) or not. nthresh Number of thresholds thDelay 'time delay' for the threshold variable (as multiple of embedding time delay d) PLEASE NOTE that the notation is currently different to univariate models in tsDyn. The left side variable is taken at time t, and not t+1 as in univariate cases. mTh combination of variables with same lag order for the transition variable. Either a single value (indicating which variable to take) or a combination thVar external transition variable trim trimming parameter indicating the minimal percentage of observations in each regime ngrid number of elements of the grid, especially for nthresh=3 gamma prespecified threshold values around The grid search is restricted to ngrid values around this point. Especially useful for nthresh=3. plot Whether a plot showing the results of the grid search should be printed dummyToBothRegimes Whether the dummy in the one threshold model is applied to each regime or not. trace should additional infos be printed out? trick type of R function called: for or mapply max.iter Number of iterations for the algorithm

## Details

For fixed th and threshold variable, the model is linear, so estimation can be done directly by CLS (Conditional Least Squares). The search of the parameters values is made upon a grid of potential values. So it is pretty slow.

nthresh=1: estimation of one threshold model (two regimes) upon a grid of ngrid values (default to ALL) possible thresholds and delays values.

nthresh=2: estimation of two thresholds model (three regimes) Conditional on the threshold found in model where nthresh=1, the second threshold is searched. When both are found, a second grid search is made with 30 values around each threshold.

nthresh=3: DOES NOT estimate a 3 thresholds model, but a 2 thresholds model with a whole grid over the thresholds parameters (so is really slow) with a given delay, is there rather to check the consistency of the method nthresh=2

## Value

An object of class TVAR, with standard methods.

Matthieu Stigler

## References

Lo and Zivot (2001) "Threshold Cointegration and Nonlinear Adjustment to the Law of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 533-76, September.