trend.test {aTSA} | R Documentation |

## Trend Test

### Description

Performs an approximate Cox-Stuart or Difference-Sign trend test.

### Usage

```
trend.test(x, method = c("cox.stuart", "diff.sign"), plot = FALSE)
```

### Arguments

`x` |
a numeric vector or univariate time series. |

`method` |
test method. The default is |

`plot` |
a logical value indicating to display the plot of data.
The default is |

### Details

Cox-Stuart or Difference-Sign test is used to test whether the data have a
increasing or decreasing trend. They are useful to detect the linear or nonlinear trend.
The Cox-Stuart test is constructed as follows.
For the given data `x[1],...,x[t]`

, one can divide them into two sequences with
equal number of observations cutted in the midpoint and then take the paired difference,
i.e., `D = x[i] - x[i+c], i = 1, ..., floor(n/2)`

, where `c`

is the index of
midpoint. Let `S`

be the number of positive or negative values in `D`

. Under the
null hypothesis that data have no trend, for large `n`

= length(x), `S`

is
approximately distributed as `N(n/2,n/4)`

, such that one can immediately obtain
the p value. The exact Cox-Stuart trend test can be seen in `cs.test`

of
`snpar`

package.

The Difference-Sign test is constructed as the similar way as Cox-Stuart test. We first
let `D = x[i] - x[i - 1]`

for `i = 2, ..., n`

and then
count the number of positive or negative values in `D`

, defined as `S`

.
Under the null hypothesis, `S`

is approximately distributed as
`N((n-1)/2,(n+1)/12)`

. Thus, p-value can be calculated based on the null distribution.

### Value

A list with class "`htest`

" containing the following components:

`data.name` |
a character string giving the names of the data. |

`method` |
the type of test applied. |

`alternative` |
a character string describing the alternative hypothesis. |

`p.value` |
the p-value for the test. |

`statistic` |
the value of the test statistic with a name describing it. |

### Note

Missing values are removed.

### Author(s)

Debin Qiu

### References

D.R. Cox and A. Stuart (1955). Some quick sign tests for trend in location
and dispersion. *Biometrika*, Vol. 42, pp. 80-95.

P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods, second ed., Springer, New York, 1991. (p. 37)

### Examples

```
x <- rnorm(100)
trend.test(x,plot = TRUE) # no trend
x <- 5*(1:100)/100
x <- x + arima.sim(list(order = c(1,0,0),ar = 0.4),n = 100)
trend.test(x,plot = TRUE) # increasing trend
```

*aTSA*version 3.1.2.1 Index]