Detecting Regime Shifts in Detecting Regime Shifts in the Mean and Variance: the Mean and Variance: Methods and Specific Methods and Specific

ExamplesExamples Sergei RodionovSergei Rodionov

JISAO, University of Washington, Seattle, JISAO, University of Washington, Seattle,

WA.WA.

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1900 1905 1910 1915 1920 1925 19301910

5% significance level

0

0.1

0.2

0.3

0.4

0.5

0.6

RSI

1910

Detecting Shifts in the Mean

January PDO

Searching for the first regime shift

RSI – Regime Shift Index

l = 10

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1900 1905 1910 1915 1920 1925 1930

5% significance level0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

RSI1910

1912

1914

1922

Searching for the next regime shift

January PDO

l = 10

www.BeringClimate.noaa.gov

Entry Form

-3

-2

-1

0

1

2

3

std

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 20000

0.2

0.4

0.6

0.8

l = 10

0.05p = 0.1

The North Pacific Index (Nov-Mar)1899-2003

RSI

1924

1948

1977

1924

1948

1977

19581989

2003

-3

-2

-1

0

1

2

3

1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001

p = 0.05

l =

Arctic Oscillation, 1951-2003

1075

1989

1994

1996

1972

1977

Effect of Outliers

0

0.05

0.1

0.15

0.2

0.25

0.3

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

RS

I

1943

1934 1989

1998

1976

1977

PDOaPDOwPDOs

PDOaPDOs

PDOaPDOs

PDOwALPINPINCAR

PNA

NPICPCNPINCAR

PDOwAO

EPI PDOsEPI

AI

NPICPC

Regime Shifts in Climatic Indices

p = 10l = 0.1

Shifts in the variance for var1, 1901-1960Probability = 0.1, cutoff length = 10

-4

-3

-2

-1

0

1

2

3

4

5

1901

1904

1907

1910

1913

1916

1919

1922

1925

1928

1931

1934

1937

1940

1943

1946

1949

1952

1955

1958

Regime index for the variance Probability = 0.1, cutoff length = 10

0

0.2

0.4

0.6

0.8

1

1.2

1901

1904

1907

1910

1913

1916

1919

1922

1925

1928

1931

1934

1937

1940

1943

1946

1949

1952

1955

1958

Std = 1 Std = 1Std = 2

Shifts in the mean for Icelandic SLP, 1951-2003Probability = 0.3, cutoff length = 6, Huber parameter = 1

9800

9850

9900

9950

10000

10050

10100

10150

1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003

Shifts in the mean for mean winter SAT in central England, 1951-2003Probability = 0.3, cutoff length = 6, Huber parameter = 1

0

1

2

3

4

5

6

7

8

1951 1955 1959 1963 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003

Shifts in the mean for spring SAT (MAM) in Odessa, 1881-2004Probability = 0.1, cutoff length = 10

0

2

4

6

8

10

12

1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001

1989

Shifts in the mean for annual Volga runoff, 1878-1994Probability = 0.2, cutoff length = 8, Huber parameter = 1

050

100150200250300350400450500

1878 1888 1898 1908 1918 1928 1938 1948 1958 1968 1978 1988

19781990

ConclusionsConclusions

• Characteristics of the sequential method:Characteristics of the sequential method:– Automatic detection of regime shifts,Automatic detection of regime shifts,– Improved performance at the ends of time series,Improved performance at the ends of time series,– Can be tuned up to detect regimes of different Can be tuned up to detect regimes of different

scales,scales,– Can handle the incoming data regardless of Can handle the incoming data regardless of

whether they are presented in the form of whether they are presented in the form of anomalies or absolute values,anomalies or absolute values,

– Works well with the time series containing a trend,Works well with the time series containing a trend,– Can be applied to a large set of variables.Can be applied to a large set of variables.