# Indicator Saturation

### Description

The `isat`

function undertakes multi-path indicator saturation to detect outliers and mean-shifts using impulses (IIS), step-shifts (SIS), or trend-indicators (TIS). Indicators are partitioned into blocks and selected over at a chosen level of significance (`t.pval`

) using the `getsm`

function.

### Usage

1 2 3 4 5 6 7 | ```
isat(y, mc=TRUE, ar=NULL, ewma=NULL, mxreg=NULL, iis=FALSE, sis=TRUE,
tis=FALSE, uis=FALSE, blocks=NULL, ratio.threshold=0.8, max.block.size=30,
vcov.type=c("ordinary", "white", "newey-west"), t.pval=0.001, do.pet=FALSE,
wald.pval=t.pval, ar.LjungB=NULL, arch.LjungB=NULL, normality.JarqueB=NULL,
info.method=c("sc", "aic", "hq"), include.gum=FALSE, include.empty=FALSE,
tol=1e-07, LAPACK=FALSE, max.regs=NULL, verbose=TRUE, print.searchinfo=TRUE,
alarm=FALSE, plot=TRUE)
``` |

### Arguments

`y` |
numeric vector, time-series or |

`mc` |
logical. TRUE (default) includes an intercept in the mean specification, whereas FALSE does not |

`ar` |
integer vector, say, c(2,4) or 1:4. The AR-lags to include in the mean specification |

`ewma` |
either NULL (default) or a list with arguments sent to the |

`mxreg` |
numeric vector or matrix, say, a |

`iis` |
logical. If TRUE, impulse indicator saturation is performed. |

`sis` |
logical. If TRUE, step indicator saturation is performed. |

`tis` |
logical. If TRUE, trend indicator saturation is performed. |

`uis` |
a matrix of regressors, or a list of matrices. |

`blocks` |
NULL (default), an integer (the number of blocks) or a user-specified list that indicates how blocks should be put together. If NULL, then the number of blocks is determined automatically |

`ratio.threshold` |
Minimum ratio of variables in each block to total observations to determine the block size, default=0.8. Block size used is the maximum of given by either the ratio.threshold and max.block.size. |

`max.block.size` |
Maximum size of block of variables to be selected over, default=30. Block size used is the maximum of given by either the ratio.threshold and max.block.size. |

`vcov.type` |
the type of variance-covariance matrix used. If NULL (default), then the type used is that of the 'arx' object. This can be overridden by either "ordinary" (i.e. the ordinary variance-covariance matrix) or "white" (i.e. the White (1980) heteroscedasticity robust variance-covariance matrix) |

`t.pval` |
numeric value between 0 and 1. The significance level used for the two-sided regressor significance t-tests |

`do.pet` |
logical. If TRUE, then a Parsimonious Encompassing Test (PET) against the GUM is undertaken at each regressor removal for the joint significance of all the deleted regressors along the current path. If FALSE (default), then a PET is not undertaken at each regressor removal. By default, the numeric value is the same as that of |

`wald.pval` |
numeric value between 0 and 1. The significance level used for the Parsimonious Encompassing Tests (PETs) |

`ar.LjungB` |
a two-item list with names |

`arch.LjungB` |
a two-item list with names |

`normality.JarqueB` |
a value between 0 and 1, or NULL. In the former case, a test for non-normality is conducted using a significance level equal to the numeric value. If |

`info.method` |
character string, "sc" (default), "aic" or "hq", which determines the information criterion to be used when selecting among terminal models. The abbreviations are short for the Schwarz or Bayesian information criterion (sc), the Akaike information criterion (aic) and the Hannan-Quinn (hq) information criterion |

`include.gum` |
logical. If TRUE, then the GUM (i.e. the starting model) is included among the terminal models. If FALSE (default), then the GUM is not included |

`include.empty` |
logical. If TRUE, then an empty model is included among the terminal models, if it passes the diagnostic tests, even if it is not equal to one of the terminals. If FALSE (default), then the empty model is not included (unless it is one of the terminals) |

`tol` |
numeric value (default = 1e-07). The tolerance for detecting linear dependencies in the columns of the regressors (see |

`LAPACK` |
logical. If TRUE, then use LAPACK. If FALSE (default), then use LINPACK (see |

`max.regs` |
integer. The maximum number of regressions along a deletion path. It is not recommended that this is altered |

`verbose` |
logical. TRUE (default) returns (slightly) more output than FALSE |

`print.searchinfo` |
logical. If TRUE (default), then a print is returned whenever simiplification along a new path is started, and whenever regressors are dropped due to exact multicolinearity |

`alarm` |
logical. If TRUE, then a sound is emitted (in order to alert the user) when the model selection ends |

`plot` |
logical. If TRUE, then the fitted values and the residuals of the final model are plotted after model selection |

### Details

Multi-path indicator saturation using impulses (IIS), step-shifts (SIS), or trend-indicators (TIS). Indicators are partitioned into sequential blocks (as of beta version 0.7) where the block intervals are defined by the ratio of variables to observations in each block and a specified maximum block size. Indicators are selected over using the `getsm`

function. Retained indicators in each block are combined and re-selected over. Fixed covariates that are not selected over can be included in the regression model either in the mxreg matrix, or for auto-regressive terms through the ar specification. See Hendry, Johansen and Santos (2007) and Castle, Doornik, Hendry, and Pretis (2015)

### Value

A list of class 'gets'

### Author(s)

Felix Pretis, http://www.felixpretis.org/

James Reade, https://sites.google.com/site/jjamesreade/

Genaro Sucarrat, http://www.sucarrat.net/

### References

Hendry, David, F., Johansen, Soren, and Santos, Carlos (2007): 'Automatic selection of indicators in a fully saturated regression'. Computational Statistics, vol 23:1, pp.317-335.

Castle, Jennifer, L., Doornik, Jurgen, A., Hendry, David F., and Pretis, Felix (2015): 'Detecting Location Shifts during Model Selection by Step-Indicator Saturation', Econometrics, vol 3:2, 240-264.

### See Also

Extraction functions for 'gets' objects: `coef.gets`

, `fitted.gets`

, `paths`

, `plot.gets`

, `print.gets`

,

`residuals.gets`

, `summary.gets`

, `terminals`

, `vcov.gets`

Related functions: `arx`

, `eqwma`

, `leqwma`

, `zoo`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | ```
##SIS using the Nile data
data(Nile)
isat(Nile, sis=TRUE, iis=FALSE, plot=TRUE, t.pval=0.005)
##SIS using the Nile data in an autoregressive model
#isat(Nile, ar=1:2, sis=TRUE, iis=FALSE, plot=TRUE, t.pval=0.005)
##HP Data
##load Hoover and Perez (1999) data:
#data(hpdata)
##make quarterly data-matrix of zoo type
##(GCQ = personal consumption expenditure):
#y <- zooreg(hpdata$GCQ, 1959, frequency=4)
##transform data to log-differences:
#dlogy <- diff(log(y))
##run isat with step impulse saturation on four
##lags and a constant 1 percent significance level:
#isat(dlogy, ar=1:4, sis=TRUE, t.pval =0.01)
##Example with additional covariates entering through mxreg:
##(GYDQ = disposable personal income):
#x <- zooreg(hpdata$GYDQ, 1959, frequency=4)
##transform data to log-differences:
#dlogx <- diff(log(x))
##run isat with step impulse saturation on four
##lags and a constant 1 percent significance level:
#isat(dlogy, mxreg=x, ar=1:4, sis=TRUE, t.pval =0.01)
``` |