GombayCPA_test {funtimes}

Change Point Detection in Autoregressive Time Series

Description

The function detects change points in autoregressive (AR) models for time series. Changes can be detected in any of p + 2 (mean, var, phi) autoregressive parameters where p is the order of the AR model. The test statistic is based on the efficient score vector (Gombay 2008).

Usage

GombayCPA_test(
  y,
  a.order,
  alternatives = c("two-sided", "greater", "lesser", "temporary"),
  crit.type = c("asymptotic", "bootstrap"),
  num.bootstrap = 1000
)

Arguments

y

a vector that contains univariate time-series observations. Missing values are not allowed.

a.order

order of the autoregressive model which must be a non-negative integer number.

alternatives

a string parameter that specifies a type of the test (i.e., "two-sided", "greater", "lesser", and "temporary"). The option "temporary" examines the temporary change in one of the parameters (Gombay 2008).

crit.type

method of obtaining critical values: "asymptotic" (default) or "bootstrap".

num.bootstrap

number of bootstrap replications if crit.type = "bootstrap". The default number is 1000.

Details

The function tests for a temporary change and a change in specific model parameters. Critical values can be estimated via asymptotic distribution "asymptotic" (i.e., the default option) or sieve bootstrap "bootstrap". The function employs internal function change.point and sieve bootstrap change.point.sieve function.

Value

A list with the following components:

index

points of change for each parameter. The value of the "alternatives" determines the return: "temporary" – returns max, min, and abs.max points; "greater" – returns max points; "lesser" – returns min points; "two-sided" – returns abs.max.

stats

test statistic values for change points in mean, var, phi.

p.values

p-value of the change point test.

Author(s)

Palina Niamkova, Dorcas Ofori-Boateng, Yulia R. Gel

References

Gombay E (2008). “Change detection in autoregressive time series.” Journal of Multivariate Analysis, 99(3), 451–464. doi:10.1016/j.jmva.2007.01.003.

See Also

mcusum.test change point test for regression and terrorism dataset used in the Example 2

Examples

## Not run: 
#Example 1:

#Simulate some time series:
series_1 = arima.sim(n = 100, list(order = c(2,0,0), ar = c(-0.7, -0.1)))
series_2 = arima.sim(n = 200, list(order = c(2,0,0), ar = c(0.1, -0.6)))
main_series = c(series_1, series_2)

result11 = GombayCPA_test(series_1, 2, "two-sided")
result11 #== No change point ===#

result12 = GombayCPA_test(main_series, 2, "two-sided")
result12  #=== One change at phi values ===#

result13 = GombayCPA_test(main_series, 2, "two-sided", "bootstrap")
result13  #=== One change at phi values ===#



#Example 2:

#From the package 'Ecdat' consider a time series with annual world number of victims of
#terrorism in the US from 1970 till 2016:
c.data = Ecdat::terrorism['nkill.us']
nkill.us.ts <- ts(c.data, start = 1970, end = 2016)

#Now perform a change point detection with one sided tests:
GombayCPA_test(nkill.us.ts, 0, "lesser")
GombayCPA_test(nkill.us.ts, 0, "greater")
nkill.us.ts[32]
year = 1970 + 31
print(year)
plot(nkill.us.ts)

#In both cases we find that the change point is located at the position 31 or 32. We can
# examine it further by checking the value of this position (using: nkill.us.ts[32]) as well as
# by plotting the graph (using: plot(nkill.us.ts)). The detected change point corresponds to
#the year of 2001, when the 9/11 attack happened.

## End(Not run)