Change Point Detection
A change point is an abrupt shift or a temporal pattern switch (e.g.,
beginning of a trend) in a time series. In FFA, change points indicate
inhomogeneous periods, meaning a single model may not represent the
entire record adequately. Instead, piecewise analysis should be applied
to each homogeneous sub-period. The FFA framework provides two
statistical tests for change point detection:
- The Pettitt test, for sudden changes in the mean.
- The Mann-Kendall-Sneyers (MKS) test, for detecting changes in
trend.
This vignette will demonstrate how these statistical tests can be
used together to robustly identify change points.
Case Study
This vignette will explore the Kootenai River at Porthill (08NH021)
station, located on the border of British Columbia and Idaho. The
station is located downstream of the Libby Dam, which finished
construction in 1972. Data for this station is provided as
CAN-08NH021.csv in the ffaframework
package.
library(ffaframework)
df <- data_local("CAN-08NH021.csv")
head(df)
#> year max
#> 1 1928 2350
#> 2 1929 1680
#> 3 1930 1730
#> 4 1931 1470
#> 5 1932 2190
#> 6 1933 2640
plot_ams_data(df$max, df$year, title = "Kootenai River at Porthill (08NH021)")
The Pettitt Test
This rank-based test detects a single abrupt change in the median of
a time series. The null hypothesis assumes no change point. Use the
eda_pettitt_test function to perform the test. It requires
two arguments:
data: the annual maximum series (AMS)years: corresponding numeric vector of years
pettitt_test <- eda_pettitt_test(df$max, df$year)
print(pettitt_test$p_value)
#> [1] 0
print(pettitt_test$change_year)
#> NULL
plot_pettitt_test(pettitt_test)
Conclusion: A p-value of <0.001 provides strong
evidence of a change point in the year 1972.
The MKS Test
The Mann-Kendall-Sneyers (MKS) test identifies trend changes in the
data.
Use eda_mks_test with the same arguments as above.
mks_test <- eda_mks_test(df$max, df$year)
print(mks_test$p_value)
#> [1] 0.01495225
print(mks_test$change_df$year)
#> NULL
plot_mks_test(mks_test)
Conclusion: At a p-value of 0.015, there is evidence
of trend changes in 1960 and 1985.
Note: Since the MKS test can identify multiple
change points, the reported p-value is determined using the most
significant change point.
Interpreting and Selecting Change Points
In this example, the Pettitt and MKS tests both suggest structural
changes in the time series.
Consider the following guidelines when choosing where to split the
data:
- Incorporate domain knowledge and case-specific
understanding. In this example, we know that a water regulation
structure was built in 1972 (the Libby dam). This supports the results
of the Pettitt test.
- Avoid overpartitioning. The Pettitt and MKS tests
operate independently and may detect multiple change points. To minimize
sample size issues and reduce uncertainty, retain only significant
change points with physical justification.
- Prioritize based on p-value. Lower p-values
indicate stronger evidence and should be given more weight.