# diss.ACF

##### Autocorrelation-based Dissimilarity

Computes the dissimilarity between two time series as the distance between their estimated simple (ACF) or partial (PACF) autocorrelation coefficients.

##### Usage

```
diss.ACF(x, y, p = NULL, omega=NULL, lag.max=50)
diss.PACF(x, y, p = NULL, omega=NULL, lag.max=50)
```

##### Arguments

- x
Numeric vector containing the first of the two time series.

- y
Numeric vector containing the second of the two time series.

- p
If not NULL, sets the weight for the geometric decaying of the autocorrelation coefficients. Ranging from

`0`

to`1`

.- lag.max
Maximum number of simple or partial autocorrelation coefficients to be considered.

- omega
If not NULL, completely specifies the weighting matrix for the autocorrelation coefficients.

`p`

is ignored if`omega`

is used.

##### Details

Performs the weighted Euclidean distance between the simple autocorrelation ( `dist.ACF`

) or partial autocorrelation ( `dist.PACF`

) coefficients.
If neither `p`

nor `omega`

are specified, uniform weighting is used. If `p`

is specified, geometric wights decaying with the lag in the form \( p(1-p)^i\) are applied. If `omega`

(\(\Omega\)) is specified, $$ d(x,y) = {\{ ( \hat{\rho}_{x} - \hat{\rho}_{y} )^t \bm{\Omega} (\hat{\rho}_{x} - \hat{\rho}_{y} ) \}}^\frac{1}{2} $$ with \(\hat{\rho}_{x}\) and \(\hat{\rho}_{y}\) the respective (partial) autocorrelation coefficient vectors.

##### Value

The computed distance.

##### References

Galeano, P. and Pe<U+00F1>a, D. (2000). Multivariate analysis in vector time series. *Resenhas*, **4 (4)**, 383--403.

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 <- cumsum(rnorm(100))
y <- cumsum(rnorm(100))
z <- sin(seq(0, pi, length.out=100))
## Compute the distance and check for coherent results
diss.PACF(x, y)
diss.ACF(x, z)
diss.PACF(y, z)
#create a dist object for its use with clustering functions like pam or hclust
diss( rbind(x,y,z), "ACF", p=0.05)
# }
```

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