PATTERNS PRECEDING CRITICAL TRANSITIONS IN SOCIOECONOMIC SYSTEMS

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PATTERNS PRECEDING CRITICAL TRANSITIONS IN
SOCIO-ECONOMIC SYSTEMS

• V. Keilis-Borok (1,2), A. Soloviev (1)
• International Institute of Earthquake Prediction
  Theory and Mathematical Geophysics, Russian
  Academy of Sciences, Russia (soloviev_at_mitp.ru /
  Phone [phone]),
• (2) Institute of Geophysics and Planetary Physics
  and Department of Earth and Space Sciences,
  University of California, Los Angeles, USA
  (vkb_at_ess.ucla.edu / Phone [phone])

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CRITICAL TRANSITIONS

• One of the most important features of
  hierarchical dissipative complex systems
  persistent reoccurrence of abrupt overall changes
  critical transitions.
•  In economic systems
•     starts and ends of economic recessions
•     episodes of a sharp increase in the
  unemployment rate Fast Acceleration of
  Unemployment (FAU).
•  In socio-economic urban systems (megacities)
•     surge of the homicides in a megacity.

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OUTCOMES OF PREDICTION

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METHODOLOGY

• These studies belong to the so-called technical
  analysis, consisting of a heuristic search for
  phenomena preceding critical transitions.
• The methodology used for technical analysis is
  the pattern recognition of infrequent events. It
  was developed by the artificial intelligence
  school of the Russian mathematician I.M.Gelfand
  for the study of rare phenomena of highly complex
  origin.
• The pattern recognition approach has been
  successfully applied also to prediction of the
  outcome of American elections as well as in
  seismology and earthquake prediction, geological
  prospecting, and in many other fields.
• Our goal is to identify by an analysis of
  macroeconomic indicators (in the case of economic
  systems) or of statistics of several types of
  less severe crime (in the case of megacities) a
  robust and rigidly defined prediction algorithm
  of the yes or no variety indicating at any time
  moment, whether a critical transition should be
  expected or not within the subsequent months.

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V.Keilis-Borok, J.Stock, A.Soloviev, and
P.Mikhalev. Journal of Forecasting,
2000PREDICTION OF RECESSIONS

• INITIAL DATA
• American Economic Recessions, 1960 2003,
• the National Bureau of Economic Research (NBER)
• Peaks Troughs
• 1 196004 196102
• 2 196912 197011
• 3 197311 197503
• 4 198001 198007
• 5 198107 198211
• 6 199007 199103
• 200103 200111
• Peak is the last month before a recession, and
  through is the last month of a recession (a
  recession comes to the end in this month).
• The time series, consisting of monthly values of
  the economic indexes, which were known, as
  correlated with the approach of a recession have
  been considered.

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FUNCTIONALS AND DESCRETIZATION

• The local linear least-squares regression of an
  index f(m) within the sliding time window (q, p)
• W f(m/q,p) K f(q,p)m B f(q,p), q ? m ? p
• Functionals
• Growth rate K f(m/s) K f(m-s,m)
• Deviation from long-term trend R f(m) f(m) W
  f(m/t1,m-1),
• where t is the end (through) of the previous
  recession.
• Descretization
• To give a robust quantitative definition of a
  premonitory behavior of the indexes and the
  functionals, we consider their values on the
  lowest level of resolution, distinguishing only
  the values above and below a threshold T f(Q). It
  is defined as a percentile of a level Q, that is,
  by the condition that the index or the functional
  exceeds T f(Q) during Q of the months
  considered.

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PRECURSORS OF RECESSIONS

• 1. Difference between interest rate on 10 year
  U.S. Treasury bond, and federal funds interest
  rate, on annual basis (G10FF). Low value of G10FF
  (Q 90).
• 2. Stock-Watson index of overall monthly economic
  activity defined by Stock and Watson (1989). It
  is a weighted average of four measures, depicting
  employment, manufacturing output, and retail
  sales which emphasise services (XCI). Low value
  of R XCI(m) (Q 75).
• 3. Index of help wanted advertising. This is
  put together by a private publishing company that
  measures the amount of job advertising
  (column-inches) in a number of major newspapers
  (LHELL). Low value of K LHELL(m/5) (Q 67).
• 4. Average weekly number of people claiming
  unemployment insurance (LUINC). Large value of K
  LUINC(m/10) (Q 17).
• 5. Total inventories in manufacturing and trade,
  in real dollars. Includes intermediate
  inventories (for example held by manufacturers,
  ready to be sent to retailers) and final goods
  inventories (goods on shelves in stores).
  (INVMTQ).
• Low value of R INVMTQ(m) (Q 25).
• 6. Interest rate on 90 day U.S. treasury bills at
  an annual rate, in (FYGM3).
• Large value of R FYGM3(m) (Q 25).

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BEHAVIOR OF G10FF

• The threshold of discretization is shown by a
  horizontal line, shaded vertical bars indicate
  recessions.

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HYPOTHETICAL PREDICTION ALGORITHM

• It happens that four or more precursors appear
  simultaneously within 6 to 14 months before each
  recession and at no other time. This allows to
  formulate a hypothetical prediction algorithm to
  be tested by advance prediction an alarm is
  declared for three months after each month with ?
  ? 4 (regardless of whether this month belongs or
  not to an alarm which has been already declared),
  where ? is the number of precursors.

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PRECURSORS OF THE END OF A RECESSION

• 1. Large value of G10FF (Q 33).
• 2. Low value of R XCI(m) (Q 75).
• 3. Low value of K LHELL(m/5) (Q 75).
• 4. Large value of K LUINC(m/10) (Q 50).
• 5. Low value of R INVMTQ(m) (Q 50).
• 6. Low value of R FYGM3(m) (Q 50).
• PREDICTION ALGORITHM
• An alarm is declared for three months after three
  consecutive months with ? ? 3 (regardless of
  whether these months belong or not to an alarm,
  which has been already declared), where ? is the
  number of precursors.

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V.Keilis-Borok, A.Soloviev, C.B.Allègre,
A.Sobolevskii, and M.Intriligator. Pattern
Recognition, 2005PREDICTION OF THE UNEMPLOYMENT
RISE

• Fast Acceleration of Unemployment (FAU)
• The local linear least-squares regression of an
  index f(m) within the sliding time window (q, p)
• W f(m/q,p) K f(q,p)m B f(q,p), q ? m ? p
• u(m) the number of unemployed in a month m.
• Smoothing out the seasonal variation of u U(m)
  W u(m/m-6,m6).
• Coarse measure of unemployment acceleration
• F(m/s) K U(m,m24) - K U(m-24,m).
• The FAUs are defined by the local maxima of F(m)
  exceeding a certain threshold F. The time m and
  the height F F(m) of such a maximum are,
  respectively, the time and the magnitude of a
  FAU. Acceleration ends in a month me of the
  subsequent local minimum of F(m).

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UNEMPLOYMENT IN FRANCE
Top Monthly unemployment, thousands of people.
Thin line u(m), data from the OECD database
note the seasonal variations. Thick line U(m),
data smoothed over one year. Bottom
Determination of FAUs. F(m) shows the change in
the linear trend of unemployment U(m). FAUs are
attributed to the local maxima of F(m) exceeding
threshold F 4.0 shown by solid horizontal line.
The thick vertical lines show moments of the
FAUs.
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PRECURSORS OF FAU

• 1. Industrial production index, composed of
  weighted production levels in numerous sectors of
  the economy, in relative to the index for 1990
  (IP). Large value of K IP(m/12) (Q 50).
• 2. Long-term interest rate on 10-year government
  bonds, in (L).
• Large value of K L(m/12) (Q 33).
• 3. Short-term interest rate on 3-month bills, in
  (S).
• Large value of K S(m/12) (Q 25).
• HYPOTHETICAL PREDICTION ALGORITHM
• An alarm is declared for 6 months after each
  month with ? 3 (regardless of whether this
  month belongs or not to an already determined
  alarm), where ? is the number of precursors.

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UNEMPLOYMENT IN THE USA
Thin line r(m), original data. Thick line R(m),
data after smoothing out the seasonal variations.
The thick vertical lines show the moments when
unemployment started to rise (local minima of
smoothed unemployment rate).
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EQUIVALENTS OF PRECURSORS FOR THE USA

• 1. For IP - "industrial production, total". This
  is index of real (constant dollars) output in the
  entire economy (dimensionless) (IP).
• Large value of K IP(m/12) (Q 50).
• 2. For L - interest rate on 10-year U.S. treasury
  bonds, at an annual rate, in (FYGT10). Large
  value of K FYGT10(m/12) (Q 33).
• 3. For S - Interest rate on 90 day U.S. treasury
  bills at an annual rate, in (FYGM3). Large
  value of K FYGM3(m/12) (Q 25).
• APPLICATION OF THE ALGORITHM

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V.Keilis-Borok, D.Gascon, A.Soloviev,
M.Intriligator, R.Pichardo, and F.Vinberg. In
T.Beer and A.Ismail-Zadeh (eds), Risk Science and
Sustainability, 2003PREDICTION OF THE HOMICIDE
SURGE

• Target of prediction the Start of the Homicide
  Surge (SHS)

The gray bar marks the period of the homicide
surge.
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THE DATA

• Sources
• (i) The National Archive of Criminal Justice Data
  (NACJD), placed on the web site
  (http//www.icpsr.umich.edu/NACJD/index.html).
• (ii) Data bank of the Los Angeles Police
  Department (LAPD Information Technology
  Division) it contains similar data for the years
  1990 May 2001.
• Types of crime considered (monthly time series)
• Homicide Robberies Assaults Burglaries
• All (H) All (Rob) All (A) Unlawful not
  forcible
•     With firearms With firearms (FA) entry
  (UNFE)
• (FRob) With knife or Attempted forcible
  With knife or cutting instrument entry
  (AFE)
• cutting instrument (KCIA)
• (KCIR) With other
•      With other dangerous weapon
• dangerous weapon (ODWA)
• (ODWR) Aggravated injury
•       Strong-arm assaults (AIA)
• robberies (SAR)

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HOMICIDE SURGES IN LOS ANGELES, 1975-1993

• Thin curve original time series, H(m), per
  3,000,000 inhabitants.
• Thick curve smoothed series H(m).
• Vertical lines the targets of prediction (SHS).
• Gray bars the periods of homicide surge.

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PRECURSORS OF SHS 1. ALL robberies (Rob). Low
value of K Rob(m/12) (Q 66.7). 2. Robberies
with firearms (FRob). Low value of K FRob(m/12)
(Q 66.7). 3. Robberies with knife or cutting
instrument (KCIR). Low value of K KCIR(m/12) (Q
50). 4. Robberies with other dangerous weapon
(ODWR). Low value of K ODWR(m/12) (Q 87.5). 5.
Assaults with firearms (FA). Large value of K
FA(m/12) (Q 50). 6. Assaults knife or cutting
instrument (KCIA). Large value of K KCIA(m/12)
(Q 50). 7. Unlawful not forcible entry (UNFE).
Large value of K UNFE(m/12) (Q 50).  
HYPOTHETICAL PREDICTION ALGORITHM An alarm is
declared for 9 months each time when ? ? 6 for
two consecutive months (regardless of whether
these two months belong or not to an already
declared alarm), where ? is the number of
precursors.  
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SCHEME OF PREMONITORY CHANGES IN CRIME STATISTICS

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PERFORMANCE OF THE PREDICTION ALGORITHM FOR LOS
ANGELES,1975-2002

• Thin curve original time series, H(m), per
  3,000,000 inhabitants.
• Thick curve smoothed series H(m).
• Vertical lines the targets of prediction (SHS).
• Gray bars the periods of homicide surge.
• Red bars the alarms declared by the
  hypothetical prediction algorithm.

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APPLICATION OF THE PREDICTION ALGORITHM TO NEW
YORK CITY, 1975-1994

• Thin curve original time series, H(m), per
  7,000,000 inhabitants.
• Thick curve smoothed series H(m).
• Vertical lines the targets of prediction (SHS).
• Gray bars the periods of homicide surge.
• Red bars the alarms declared by the
  hypothetical prediction algorithm.