# diss.AR.PIC: Model-based Dissimilarity Measure Proposed by Piccolo (1990) In TSclust: Time Series Clustering Utilities

## Description

Computes the distance between two time series as the Euclidean distance between the truncated AR operators approximating their ARMA structures.

## Usage

 `1` ```diss.AR.PIC(x, y, order.x=NULL, order.y=NULL, permissive=TRUE) ```

## Arguments

 `x` Numeric vector containing the first of the two time series. `y` Numeric vector containing the second of the two time series. `order.x` Specifies the ARIMA model to be fitted for the series x. When using `diss` wrapper, use `order` argument instead. See details. `order.y` Specifies the ARIMA model to be fitted for the series y. When using `diss` wrapper, use `order` argument instead. See details. `permissive` Specifies whether to force an AR order of 1 if no order is found. Ignored if neither order.x or order.y are NULL

## Details

If `order.x` or order.y are `NULL`, their respective series will be fitted automatically using a AR model. If `permissive` is `TRUE` and no AR order is found automatically, an AR order of 1 will be imposed, if this case fails, then no order can be found and the function produces an error. `order.x` and `order.y` contain the three components of the ARIMA model: the AR order, the degree of differencing and the MA order, specified as in the function `arima`.

If using `diss` function with "AR.PIC" `method`, the argument `order` must be used instead of `order.x` and `order.y`. `orders` is a matrix with one row per ARIMA, specified as in `arima`. If `order` is `NULL`, automatic fitting imposing a AR model is performed.

## Value

The computed distance.

## Author(s)

Pablo Montero Manso, Jos<c3><a9> Antonio Vilar.

## References

Piccolo, D. (1990) A distance measure for classifying arima models. J. Time Series Anal., 11(2), 153–164.

Montero, P and Vilar, J.A. (2014) TSclust: An R Package for Time Series Clustering. Journal of Statistical Software, 62(1), 1-43. http://www.jstatsoft.org/v62/i01/.

`diss.AR.MAH`, `diss.AR.LPC.CEPS`, `diss`, `arima`, `ar`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## Create three sample time series x <- arima.sim(model=list(ar=c(0.4,-0.1)), n =100, n.start=100) y <- arima.sim(model=list(ar=c(0.9)), n =100, n.start=100) z <- arima.sim(model=list(ar=c(0.5, 0.2)), n =100, n.start=100) ## Compute the distance and check for coherent results #ARIMA(2,0,0) for x and ARIMA(1,0,0) for y diss.AR.PIC( x, y, order.x = c(2,0,0), order.y = c(1,0,0) ) diss.AR.PIC( x, z, order.x = c(2,0,0), order.y = c(2,0,0) ) # AR for y (automatically selected) and ARIMA(2,0,0) for z diss.AR.PIC( y, z, order.x=NULL, order.y=c(2,0,0) ) #create a dist object for its use with clustering functions like pam or hclust diss( rbind(x,y,z), METHOD="AR.PIC", order=rbind(c(2,0,0), c(1,0,0), c(2,0,0)) ) ```