Report of the Regime Shift Detection Group
Leader and lecturer: Sergei Rodionov, Rapporteur: Abigail Mcquatters-Gollop and
Violeta Velikova, Participants: Nesho Chipev, Snejana Moncheva, Galina Shtereva,
Georgiy Daskalov, Vesselina Mihneva, Sonia Ouzunova, Violin Raikov, Elisaveta
Peneva, Viktor Nikolsky, Laura Boicenko, Radka Mavrodieva, Svetla Bratanova,
Alexandra Uzunova.
Theme: Overview of Regime Shift Detection Methods, regime shift detection
software (author Sergei Rodionov), practical exercises.
Table of methods for detecting regime shifts and regime shift detection software are
downloadable from www.beringclimate.noaa.gov .
Regime shift detection methods:
(http://www.beringclimate.noaa.gov/regimes/Regime_shift_methods_list.htm
for
a
complete list of methods, contact person Sergei Rodionov).

Methods for detecting shifts in the mean:
o Students T test
 Most common, robust, well established but you need to test for a
regime shift by picking a year manually which violates the
assumption that the change point should not be pre-assigned (ie
each year should be given equal weight) and is not automatic.
o Bayesian analysis
 Accounts for uncertainty of estimating change points and can be
used for predictions but requires a mathematical model of the
data and works best with a single change point scenario.
o Mann-Whitney U test
 Non parametric and easy to use but the data needs to be
detrended.
o Lepage test
 Non parametric and similar to Mann-Whitney U and Pettitt tests.
Can be used to detect different shaped trends as well as regime
shifts but is a single change point scenario. Not automatic and a
single change point scenario.
o Wilcoxon rank sum
 Non parametric and similar to Mann-Whitney U test.
o Pettitt test
 Non parametric and similar to Mann-Whitney U test. Can be used
to detect different shaped trends as well as regime shifts but is a
single change point scenario.
o Mann-Kendall test
 Also non parametric but not automatic and data must be
detrended.
o Standard normal homogeneity test (SNHT)
 Very popular and mostly used for meterological time series. Not
good when change points are close together in time, there are
o
o
o
o
o
o
o
more than 4 change points, or methodology of sampling or
analysis has changed over time.
 Free package available on net: OnClim. Contains the standard
normal homogeneity test.
Regression based approach
 Better than SNHT when multiple change points exist but not
sensitive to small shifts or shifts that occur within 10 points of
one another.
CUSUM test
 Cumulative deviation test. Easy to use but works with anomalies
and using different base periods may affect results.
Oerlemans method
 Based on comparison of an a priori described typical change with
an interval of a given time series. Can be applied to any time
series and results are easy to compare but a statistical significance
test can’t be constructed and requires the best fitting of a curve
that represents an idealized break in the data. No longer used.
Signal-to-Noise ratio
 A regime shift is defined when the signal to noise ration exceeds
1. Simple and easy to use but only works for a single change
point.
Intervention analysis
 Extension of ARIMA method. Allows for quantitative estimate
for statistical significance of step interventions while accounting
for autocorrelation in the time series but, like with t test, the time
and type of intervention should be specified in advance.
Markov chain Monte Carlo
 Strong basis on Bayesian approach. Must find best model to
describe your data which makes method complex and difficult to
use.
Lanzante method
 Designed to determine a shift from a trend. Can find shifts where
none exist and doesn’t work with big trends or when change
points are within 25 points of one another.
o STARS
 A sequential version of the partial CUSUM method combined
with the t-test (Rodionov, 2004). Automatic detection of multiple
change-points. Signals a possibility of a regime shift in real time.
Outperforms the Lanzante method if the shifts occur on a
background of a trend. Requires some experimentation when
choosing the probability level and cutoff length. Does not
explicitly take into account the autocorrelation.

Methods for finding shifts in the variance:
o Downton-Katz method
 More theoretical than practical. No assumptions are required
about the frequency distribution but it needs a reference time
series with no potential change shifts. The change shifts must be
separated by at least 25 points.
o Rodionov method
 Similar to STARS, but based on the F-test. It is included in the
regime shift detection calculator. Automatic detection of multiple
change-points. Signals a possibility of a regime shift in real time.
The method is not documented yet. It is still in the experimental
phase.

Methods for finding shifts in the spectrum (frequency structure):
o Nikiforov method
 Use ARIMA models of time series before and after potential shift
and combined with the likelihood ratio test. Strong theoretical
basis but only works with singe change point scenarios.

Methods for finding shifts in the system (multi dimensional):
o Principle component analysis
 Not just meant for regime shift detection but reduces the
dimensionality of the system. Requires no a priori assumption
about candidate regime shift years.
o Average standard deviates
 Creates a regime index consisting of average standard deviates.
Easy to use but requires an a priori specification of a regime shift
date and a sign reversal of some time series which leads to
spurious amplification of the shift. Need harmony between types
of information you are analyzing. Doesn’t work for short time
series with steep trends.
o Fisher information
 Ratio of system acceleration and speed along the state space
trajectory. Requires a careful choice of input variables and their
weighting. Result difficult to interpret and no way to assess
statistical significance.
o Vector autoregressive method
 Formal approach for regime shift detection. Regime shift is
identified as point at which the system changes from one steady
state to another. Requires a large number of observations for the
model and the results are sensitive to the selection of variables.
Software demonstration (S. Rodionov):
As mentioned above, there are a number of methods designed for a detection of
regime shifts in both the individual series and entire systems. The overwhelming
majority of these methods, however, experience deterioration in their performance
toward the ends of time series. Rodionov (2004) developed a new method based on a
sequential algorithm that can signal a possibility of a regime shift in real time. The code
for the method is written in Visual Basic for Application (Excel). The program can
detect regime shifts both in the mean level of fluctuation and in the variance. How to
work with this software:
o Download
Shift
Detection
Excel
Add-in
from
website
http://www.beringclimate.noaa.gov.
o Copy into add-in folder in Excel directory.
o Double click the icon and choose ‘enable macros’. If your computer says
that macros are not allowed, change your security level from high to
medium (Tools menu).
o You will see a new menu item in Excel. For this to show up every time
you run Excel, go to Tools-->Templates and add-ins-->Add. Navigate to
detection exe file and click OK to add it to the add-ins menu and check
the option for the detection software.
o To generate a time series: choose length, mean, and variance options.
o From time series data worksheet, choose ‘shift detection’ and chose to
look for shifts in either the mean or variance. It is a good idea to run the
software for the mean, which also calculates the residuals. You can then
work with the residuals which are created in a new worksheet.
o Experiment with different options (sig. level, etc). When shift is well
defined, options won’t matter as much as when the shift is subtle.
o Residual creation removes trends. Use this to look for shifts in the
variance.
o If you have monthly data, you can work with the monthly anomalies.
o Software assumes there is no missing data – this problem is for the user
to deal with (for example by replacing missing values with the mean).
o What about samples of different sizes?
 It is up to the user how to weight these samples; it is the user’s
task to prepare the time series for analysis.
o If you have a steep trend in your data? The software might fail to show a
good result. You could perform the analyses for the time derivative of
the variable. Or you can detrend the time series, it is according to your
preferences.
Definitions of regime shifts:
o A regime shift occurs when a statistically significant difference exists
between the mean value of the variable before and after a certain point
based on the t-test.
o Shifts can sometimes be ‘seen’ in red noise when there actually is no
regime shift.
Xt = Xt-1 + Et (red noise)
o The regime shifts appear as a quasi-stationary states in measured
parameters, separated by periods of rapid transition.
o True regime shifts are not random features of the time series, but
are formally associated with the ideas of nonlinear amplification,
alternative basins of attraction, multiple stable states, hysteresis and
fold catastrophe, all of which require the underlying dynamics to be
nonlinear in origin.
o See Nature paper in Vol 435/19 May 2005:
“Distinguishing random environmental fluctuations from ecological
catastrophes for the North Pacific Ocean.” Chih-hao Hsieh, Sarah M. Glaser,
Andrew J. Lucas and George Sugihara, Scripps Institution of Oceanography.
This paper states that biological time series have actual regime shifts being
non-linear while climatic don’t, at least not according to the tested data from
the North Pacific Ocean, showing the hallmarks of linear stochastic
generating mechanisms.
o The only way to tell if there actually is a regime shift is to either model
the whole system or get more data.

What technique can you use to find different states in a system?
o Cluster analysis, tree structure techniques, fuzzy stat techniques but these
only give you the number of states and don’t tell anything about the
dynamics between states. There is no one technique that is good for all
systems.
Practical exercises, examples:
Shifts in the mean for summer biomass (Galata) , 1967-2004
Probability = 0.01, cutoff length = 10, Huber parameter = 1
A
600
500
400
300
200
100
Shifts in the mean for summer biomass (Emine), 1973-2003
Probability = 0.05, cutoff length = 10, Huber parameter = 1
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
0
B
250
200
150
100
50
Figure 1, A and B. Software demonstration of Shifts in the fodder
mesozooplankton community off the Bulgarian coast – Cape Galata and Cape
Emine*:
2003
2001
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
0
Shifts in the mean for Northwest, 1965-2001
Probability = 0.05, cutoff length = 10, Huber parameter = 1
A
700
600
500
400
300
200
100
1999
2001
2001
Regime index for the mean value
Probability = 0.05, cutoff length = 10
1999
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
1965
0
B
0,6
0,4
0,2
1997
1995
1993
1991
1989
1987
1985
1983
1981
1979
1977
1975
1973
1971
1969
1967
-0,2
1965
0
-0,4
-0,6
-0,8
Figure 2, A and B. Software demonstration of Shifts in the Aurelia aurita biomass
in the North-Western part of the Black Sea*.
* Comments on the Figures will be included in the paper “High and low energy
ecosystem structure in terms of regime shifts: examples from the Black Sea”, V.
Velikova, V. Mihneva, 2005, Workshop Proceedings (in press).
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