# runs: Runs test In TSA: Time Series Analysis

## Description

Test the independence of a sequence of random variables by checking whether there are too many or too few runs above (or below) the median.

## Usage

 `1` ```runs(x,k=0) ```

## Arguments

 `x` time series `k` the value above or below which runs are counted; default is zero, so data is assumed to have zero median

## Details

The runs test examines the data in sequence to look for patterns that would give evidence against independence. Runs above or below k are counted. A small number of runs would indicate that neighboring values are positively dependent and tend to hang together over time. On the other hand, too many runs would indicate that the data oscillate back and forth across their median of zero. Then neighboring residuals are negatively dependent. So either too few or too many runs lead us to reject independence. When applied to residuals, the runs test is useful for model diagnostics.

## Value

 `pvalue` p-value of the test `observed.runs` observed number of runs `expected.runs` expected number of runs `n1` number of data less than or equal to k `n2` number of data above k

Kung-Sik Chan

## Examples

 ```1 2 3 4 5 6``` ```data(tempdub) month.=season(tempdub) # the period sign is included to make the printout from # the following command clearer. model3=lm(tempdub~month.) # intercept is automatically included so one month (Jan) is dropped summary(model3) runs(rstudent(model3)) ```

### Example output

```Attaching package: 'TSA'

The following objects are masked from 'package:stats':

acf, arima

The following object is masked from 'package:utils':

tar

Call:
lm(formula = tempdub ~ month.)

Residuals:
Min      1Q  Median      3Q     Max
-8.2750 -2.2479  0.1125  1.8896  9.8250

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)       16.608      0.987  16.828  < 2e-16 ***
month.February     4.042      1.396   2.896  0.00443 **
month.March       15.867      1.396  11.368  < 2e-16 ***
month.April       29.917      1.396  21.434  < 2e-16 ***
month.May         41.483      1.396  29.721  < 2e-16 ***
month.June        50.892      1.396  36.461  < 2e-16 ***
month.July        55.108      1.396  39.482  < 2e-16 ***
month.August      52.725      1.396  37.775  < 2e-16 ***
month.September   44.417      1.396  31.822  < 2e-16 ***
month.October     34.367      1.396  24.622  < 2e-16 ***
month.November    20.042      1.396  14.359  < 2e-16 ***
month.December     7.033      1.396   5.039 1.51e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.419 on 132 degrees of freedom
Multiple R-squared:  0.9712,	Adjusted R-squared:  0.9688
F-statistic: 405.1 on 11 and 132 DF,  p-value: < 2.2e-16

\$pvalue
[1] 0.216

\$observed.runs
[1] 65

\$expected.runs
[1] 72.875

\$n1
[1] 69

\$n2
[1] 75

\$k
[1] 0
```

TSA documentation built on July 2, 2018, 1:04 a.m.