# Srho.test: Entropy Test For Serial And Cross Dependence For Categorical... In tseriesEntropy: Entropy Based Analysis and Tests for Time Series

## Description

Bootstrap/permutation tests of serial and cross dependence for integer or categorical sequences.

## Usage

 ```1 2``` ```Srho.test(x, y, lag.max, B = 1000, stationary = TRUE, plot = TRUE, quant = c(0.95, 0.99), nor = FALSE) ```

## Arguments

 `x, y` integer or factor time series objects or vectors. (`y` is missing in the univariate case). `lag.max` maximum lag at which to calculate Srho; default is `trunc(N/4)` where N is the number of observations. `B` number of bootstrap/permutation replications. `stationary` logical. If `TRUE` assumes stationarity and computes marginal probabilities by using all the N observations. If `FALSE` uses N-k observations where k is the lag. `plot` logical. If `TRUE`(the default) produces a plot of Srho together with permutation confidence bands under the null hypothesis of independence. `quant` quantiles to be specified for the computation of the significant lags and the plot of confidence bands. Up to 2 quantiles can be specified. Defaults are 95% and 99%. `nor` logical. If `TRUE` normalizes Srho with respect to its attainable maximum. Defaults to `FALSE`.

## Details

Univariate version: test for serial dependence
```Srho.test(x, lag.max, B = 1000,
stationary = TRUE, plot = TRUE, quant = c(0.95, 0.99), nor = FALSE)```
Bivariate version: test for cross dependence
```Srho.test(x, y, lag.max, B = 1000,
stationary = TRUE, plot = TRUE, quant = c(0.95, 0.99), nor = FALSE)```

## Value

An object of class "Srho.test", which is a list with the following elements:

 `.Data` vector of `lag.max` elements containing Srho computed at each lag. `quantiles` Object of class `"matrix"`: contains the quantiles of the bootstrap/permutation distribution under the null hypothesis. `test.type` Object of class `"character"`: contains a description of the type of test performed. `significant.lags` Object of class `"list"`: contains the lags at which Srho exceeds the confidence bands at `quant`% under the null hypothesis. `p.value` Object of class `"numeric"`: contains the bootstrap p-value for each lag. `lags` integer vector that contains the lags at which Srho is computed. `stationary` Object of class `"logical"`: `TRUE` if the stationary version is computed. `data.type` Object of class `"character"`: contains the data type. `notes` Object of class `"character"`: additional notes.

## Warning

Unlike `ccf` the lag k value returned by `Srho.test(x,y)` estimates Srho between `x[t]` and `y[t+k]`. The result is returned invisibly if plot is TRUE.

## Author(s)

Simone Giannerini<[email protected]>

## References

Granger C. W. J., Maasoumi E., Racine J., (2004) A dependence metric for possibly nonlinear processes. Journal of Time Series Analysis, 25(5), 649–669.

Maasoumi E., (1993) A compendium to information theory in economics and econometrics. Econometric Reviews, 12(2), 137–181.

See also `Srho`, `Srho.ts`. The function `Srho.test.ts` implements the same test for numeric data.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```set.seed(12) x <- as.integer(rbinom(n=30,size=4,prob=0.5)) y <- as.integer(rbinom(n=30,size=4,prob=0.5)) z <- as.integer(c(4,abs(x[-30]*2-2))-rbinom(n=30,size=1,prob=1/2)) # no dependence Srho.test(x,lag.max=4) # univariate Srho.test(x,y,lag.max=4) # bivariate # lag 1 dependence Srho.test(x,z,lag.max=4) # bivariate ```

### Example output

```Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE