# Multivariate Threshold Autoregressive model

### Description

Estimate a multivariate Threshold VAR

### Usage

1 2 3 4 5 |

### 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 |

`gamma` |
prespecified threshold values |

`around` |
The grid search is restricted to |

`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: |

`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.

### Author(s)

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.

### See Also

`lineVar`

for the linear VAR/VECM,
`TVAR.LRtest`

to test for TVAR, `TVAR.sim`

to
simulate/bootstrap a TVAR.

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
data(zeroyld)
data<-zeroyld
TVAR(data, lag=2, nthresh=2, thDelay=1, trim=0.1, mTh=1, plot=TRUE)
##The one threshold (two regimes) gives a value of 10.698 for the threshold and 1 for the delay.
#Conditional on this values, the search for a second threshold (three regimes) gives 8.129.
#Starting from this values, a full grid search finds the same values and confims
#the first step estimation.
``` |

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