egu 2005rep MITPAN

PATTERNS PRECEDING CRITICAL TRANSITIONS IN SOCIO-ECONOMIC SYSTEMS : 

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@mitp.ru / Phone: +70951104678), (2) Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California, Los Angeles, USA (vkb@ess.ucla.edu / Phone: +13102065667)

CRITICAL TRANSITIONS : 

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.

OUTCOMES OF PREDICTION : 

OUTCOMES OF PREDICTION

METHODOLOGY : 

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.

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

V.Keilis-Borok, J.Stock, A.Soloviev, and P.Mikhalev. Journal of Forecasting, 2000 PREDICTION OF RECESSIONS INITIAL DATA American Economic Recessions, 1960 – 2003, the National Bureau of Economic Research (NBER) # Peaks Troughs 1 1960:04 1961:02 2 1969:12 1970:11 3 1973:11 1975:03 4 1980:01 1980:07 5 1981:07 1982:11 6 1990:07 1991:03 2001:03 2001:11 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.

FUNCTIONALS AND DESCRETIZATION : 

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/t+1,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.

PRECURSORS OF RECESSIONS : 

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%).

BEHAVIOR OF G10FF : 

BEHAVIOR OF G10FF The threshold of discretization is shown by a horizontal line, shaded vertical bars indicate recessions.

HYPOTHETICAL PREDICTION ALGORITHM : 

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.

PRECURSORS OF THE END OF A RECESSION : 

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.

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

V.Keilis-Borok, A.Soloviev, C.B.Allègre, A.Sobolevskii, and M.Intriligator. Pattern Recognition, 2005 PREDICTION 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,m+6). Coarse measure of unemployment acceleration: F(m/s) = K U(m,m+24) - 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).

UNEMPLOYMENT IN FRANCE : 

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.

PRECURSORS OF FAU: 

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.

UNEMPLOYMENT IN THE USA: 

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).

EQUIVALENTS OF PRECURSORS FOR THE USA : 

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

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: 

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, 2003 PREDICTION OF THE HOMICIDE SURGE Target of prediction – the Start of the Homicide Surge (SHS) The gray bar marks the period of the homicide surge.

THE DATA: 

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)

HOMICIDE SURGES IN LOS ANGELES, 1975-1993 : 

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.

Slide19: 

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.  

SCHEME OF PREMONITORY CHANGES IN CRIME STATISTICS : 

SCHEME OF PREMONITORY CHANGES IN CRIME STATISTICS

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

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.

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

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.