detectAO: Additive Outlier Detection In TSA: Time Series Analysis

Description

This function serves to detect whether there are any additive outliers (AO). It implements the test statistic lambda_{2,t} proposed by Chang, Chen and Tiao (1988).

Usage

 `1` ```detectAO(object, alpha = 0.05, robust = TRUE) ```

Arguments

 `object` a fitted ARIMA model `alpha` family significance level (5% is the default) Bonferroni rule is used to control the family error rate. `robust` if true, the noise standard deviation is estimated by mean absolute residuals times sqrt(pi/2). Otherwise, it is the estimated by sqrt(sigma2) from the arima fit.

Value

A list containing the following components:

 `ind` the time indices of potential AO `lambda2` the corresponding test statistics

Kung-Sik Chan

References

Chang, I.H., Tiao, G.C. and C. Chen (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.

`detectIO`

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```set.seed(12345) y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100) y[10] y[10]=10 y=ts(y,freq=1,start=1) plot(y,type='o') acf(y) pacf(y) eacf(y) m1=arima(y,order=c(1,0,0)) m1 detectAO(m1) detectAO(m1, robust=FALSE) detectIO(m1) ```

Example output

```Loading required package: leaps
locfit 1.5-9.1 	 2013-03-22
This is mgcv 1.8-20. For overview type 'help("mgcv-package")'.

Attaching package: 'TSA'

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

acf, arima

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

tar

[1] -2.126153
AR/MA
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 x x o o o o o o o o o  o  o  o
1 o o o o o o o o o o o  o  o  o
2 o o o o o o o o o o o  o  o  o
3 o x o o o o o o o o o  o  o  o
4 o x o o o o o o o o o  o  o  o
5 x x o o o o o o o o o  o  o  o
6 x o o o o o o o o o o  o  o  o
7 o x o o o o o o o o o  o  o  o

Call:
arima(x = y, order = c(1, 0, 0))

Coefficients:
ar1  intercept
0.5419     0.7096
s.e.  0.0831     0.3603

sigma^2 estimated as 2.788:  log likelihood = -193.33,  aic = 390.65
[,1]      [,2]      [,3]
ind      9.000000 10.000000 11.000000
lambda2 -4.018412  9.068982 -4.247367
[,1]
ind     10.000000
lambda2  7.321709
[,1]     [,2]
ind     10.000000 11.00000
lambda1  7.782013 -4.67421
```

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