# diss.AR.LPC.CEPS

##### Dissimilarity Based on LPC Cepstral Coefficients

Computes the dissimilarity between two time series in terms of their Linear Predicitive Coding (LPC) ARIMA processes.

##### Usage

```
diss.AR.LPC.CEPS(x, y, k = 50, order.x=NULL, order.y=NULL,
seasonal.x=list(order=c(0, 0, 0), period=NA),
seasonal.y=list(order=c(0, 0, 0), period=NA),
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.

- k
Number of cepstral coefficients to be considered.

- order.x
Numeric matrix. Specifies the ARIMA models to be fitted for the series x. When using

`diss`

wrapper, use`order`

argument instead. See details.- order.y
Numeric matrix. Specifies the ARIMA ARIMA models to be fitted for the series y. When using

`diss`

wrapper, use`order`

argument instead. See details.- seasonal.x
A list of

`arima`

seasonal elements for series x. When using`diss`

wrapper, use`seasonal`

argument instead. See details.- seasonal.y
A list of

`arima`

seasonal elements for series x. When using`diss`

wrapper, use`seasonal`

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.
`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`

.

`seasonal.x`

and `seasonal.y`

are lists with two components: 'order' and 'period'. See `seasonal`

parameter of `arima`

, except that specification using a numeric `vector`

of length 3 is not allowed.

If using `diss`

function with "AR.LPC.CEPS" `method`

, the argument `order`

must be used instead of `order.x`

and `order.y`

. `order`

is a matrix with one row per series, specified as in `arima`

. If `order`

is `NULL`

, automatic fitting imposing a AR model is performed. The argument `seasonal`

is used instead of `seasonal.x`

and `seasonal.y`

. `seasonal`

is a list of elements, one per series in the same order that the series are input. Each element of `seasonal`

must have the same format as the one in `arima`

.

##### Value

The computed distance.

##### References

Kalpakis, K., Gada D. and Puttagunta, V. (2001) Distance measures for effective clustering of arima time-series. *Proceedings 2001 IEEE International Conference on Data Mining*, 273--280.

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/.

##### See Also

##### Examples

```
# NOT RUN {
## 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
diss.AR.LPC.CEPS(x, y, 25) #impose an AR automatically selected for both series
#impose an ARIMA(2,0,0) for series x and an AR automatically selected for z
diss.AR.LPC.CEPS(x, z, 25, order.x = c(2,0,0), order.y = NULL )
diss.AR.LPC.CEPS(y, z, 25)
#create a dist object for its use with clustering functions like pam or hclust
diss( rbind(x,y,z), METHOD="AR.LPC.CEPS", k=20, order=rbind(c(2,0,0), c(1,0,0), c(2,0,0)),
seasonal=list( list(order=c(1,0,0), period=1), list(order=c(2,0,0), period=3),
list(order=c(1,0,0), period=1)) )
# }
```

*Documentation reproduced from package TSclust, version 1.2.4, License: GPL-2*