How to understand switching w/o switches work by : , Podobnik, - PowerPoint PPT Presentation

"Quantifying Fluctuations on Time Scales from Milliseconds to Years, using concepts of critical phenomena" [HES@bu.edu] How to understand “switching w/o switches” work by : , Podobnik, Gabaix, Preis, Vodenska, Pammolli, Riccaboni, Mantegna, Havlin, Buldyrev, Schneider, Gopikrishnan, Plerou, Liu, Cizeau, Wang, Yamasaki, Rosenow, Amaral, Petersen, Levy, Ivanov, Matia, Weber, Chessa, Lee, Meyer, Carbone, Ben-Jacob, Kenett, Moat, Fu & YOU? Buldyrev, Pammolli, Riccaboni, & HES : “ Rise & Fall of Business Firms” (2016). • We fail to understand bubbles: Some think the few big bubbles are what we must understand & control (Isaac Newton) • INTERDEPENDENT (“COUPLED”) networks of traders • Microtrend switching and bubbles of **ALL** size/time scales • We cannot predict future value, but we can quantify risk -- like earthquakes, tornados, heart attacks, ... Take-Home Message = “Data Driven Discovery” (DDD) reveals 1 finance fluctuations exemplify “switching w/o switches” Thursday, August 13, 15 1

EXAMPLE: complex interacting Networks: S&P 500 index “Big switch” : 19 Oct. 1987 (25% worldwide “earthquake/tsunami”) Thursday, August 13, 15 2

units: Stan.Dev. your eye sees the power law: BY EYE (Mandelbrot)-- what do these data tell us? Returns non-Gaussian (known qualitatively, but under- appreciated!) Large events cluster (like earthquakes) (also known qualitatively ) “Aftershocks” Omori-correlated (Lillo/Mantegna 03; Petersen/Havlin/HES 07) “Aftershocks of each aftershock” Omori-correlated: long-range power law Thursday, August 13, 15 3

(BY EYE) WHAT DO THESE DATA TELL US? “Inverse cubic law” holds over 6 orders of magnitude on y-axis (8 for pdf: inverse quartic) events 8 orders of magnitude MORE RARE Mandelbrot: 1.7 than everyday values conform to the SAME pdf Gutenberg-Richter earthquake law: mag = 7 quake obeys same law as mag = 1 quake 200,000 data points per stock, 1000 stocks 4 = 200,000,000 data points Gopikrishnan, Plerou, HES Thursday, August 13, 15 4

TEST: if interacting system of subunits, should be “universality” DATA: power-law exponents are Universal (indep of time period, country, volatility (ex 1987,2008,.. same!). implies what?? Thursday, August 13, 15 5

Physicists look for Correlations in Complex Systems ((economists knew these results, qualitatively, as volatility clustering....so calculate autocorrelation function and get a “law”)) Volatility • Returns are UN-correlated after 4 min • Absolute value of returns (volatility) is long range correlated, so returns CAN NOT BE serially independent. Thursday, August 13, 15 6

“How?” “Models?”: Herd vs. News? (1) “ herd effect” (exchange int. J). (2) “ news effect” (external field H) (c) modified Edwards-Anderson Each stock is a unit, interacting “spin glass” with TIME-dependent with other stocks (units) and LONG-range interactions both signs bathed in a magnetic field H (news). J depends on the two stocks, and H depends on the stock. Both can change with time. Possible models: (a) Units can be in Q different DISCRETE states: “Potts Model” (Potts 1952). (b) n-dimensional units. Each can be in a CONTINUUM of states: 7 “n-Vector Model” (HES 1969) Thursday, August 13, 15 7

mist The case H=0 (no news): Ising model? Text Thursday, August 13, 15 8

mist The case H=0 (no news): Ising model? Text Thursday, August 13, 15 8

Can a law describe bubbles and crashes in ! ! financial markets? Goal: every trade---msec level... Tobias Preis 1,2 and H. Eugene Stanley 1 Physics World, May 2011 DETAILS IN: T. Preis, J. Schneider, HES``Switching Processes in Financial Markets,'' PNAS 108, 7674 Figure 1 | Scale-free behavior of financial market fluctua- tions. Financial market time series feature identical proper- ties on very different time scales. All four curves are sub- sets of a 14 million transactions dataset taken from a German DAX future time series. The price curves cover time periods of roughly 1 day (top curve), 1 hour, 10 minutes, and 1 minute (bottom curve). Local maximum and minimum values are marked as blue and red circles. 9 Thursday, August 13, 15 9

BIG QUESTION: How to analyze? A: Preis/Stanley PNAS 108,7674 (b) 1&+&.#56"+5,6',-'%,7"%'$.57&'&8+.&#"' ( � t=3 fi xed) 9&+:,0 � t � t Trend #2 � t � t Price � t � t � t � t Trend #1 Trend #3 Volume 10 Transaction by transaction Thursday, August 13, 15 10

11 Preis/HES/Schneider: PNAS 108,7674; Physics World May 2011 Thursday, August 13, 15 11

SCALE FREE SPECIFIC HEAT NEAR HELIUM SWITCH POINT Note: Same FUNCTION for 3 different scales: 6 orders of magnitude!!! 12 Thursday, August 13, 15 12

Q: Can we quantify this dip in intertrade waiting time? A: Evidence for a mathematical (power law) singularity (a) xxxx ε < 1 0.05 ε > 1 + = 0.12 β τ 0.00 * log 10 τ * − = 0.09 β τ − 0.05 − 0.10 − 0.15 − 1.6 − 1.4 − 1.2 − 1.0 − 0.8 − 0.6 − 0.4 log 10 ε − 1 13 PNAS 108, 7674 Thursday, August 13, 15 13

FROM THE VERY SMALL TO THE VERY LARGE ~1/100 SECOND !"""#$%%"&'() ! ! $ ! ! $ /012/&30/245/546 ! " $ ! " $ ./01.&2/.134.435 789!!:;<&=";;>?!:&<>8:&;@9!: - # ! %)*' $ # ' %)* .67#8&9:;8&<=6!8&>&$%%&?6@< %)* &A&$B$%%&;:@"CD !"# $% & # '( !"# $% & # '( - # ! %)*+ %)' %)' $ # ' ! # ! %)%, $ # ' %)% %)% ! # %)%. $ # ' GERMAN MARKET US MARKET ! ')+ ! '), ! ')* ! ')' ! ')% ! $)+ ! $), ! $)* ! $)' ! $)% ! $)+ ! $)* ! $)' ! $)% ! %), ! %)+ ! %)* ! %)' TICK BY TICK DATA SET DAILY DATA SETS !"# $% & ! " $ !"# $% & ! " $ DAX FUTURE ALL 500 S&P500 STOCKS 2007—2008 1962 — 2009 14m records ! ! $ 2.6m records ! ! $ %)+% ! " $ ! " $ %)$% 012345&6578 / # ! %)$* # ' %)$* 123456&7689 29:#;&<=>;&?@9!;&A&$%%&B9C? :;<!!=>?&@">>AB!=&?A;=&>C<!= !"# $% &' ( !"# $% &' ( / # ! %)$$ # ' %)%* %)$% &D&$E$%%&>=C"FG ! # ! %)%0 # ' %)%* %)%% ! # ! %)%* # ' %)%% ! +), ! +)- ! +). ! +)+ ! +)% ! $), ! $)- ! $). ! $)+ ! $)+ ! $), ! $)- ! $)% ! %). ! %)+ ! %), ! %)- !"# $% & ! " $ !"# $% & ! " $ T. Preis 100x60x60x24x100 = 1,000,000,000....9 orders of magnitude ! 14 Preis/HES (2011 PNAS, May 2011 Physics World) Thursday, August 13, 15 14

A BIG BIG SURPRISE: “Critical-point-like” phenomena near the “switch point” [like helium?] WHY? WHY? WHY? Preis/HES/Schneider (PNAS, Physics World) (a) Network of traders---watching the identical screen??? (b) “Scale-free PANIC” as trader worries to miss the switch??? (c) Other reason??? (a) (b) Volume Inter-trade times 1.1 1.4 Averaged over 1.0 all t slices Δ 1.3 v * ( ε ) τ * ( ε ) 0.9 1.2 Averaged over 1.1 all t slices Δ 0.8 0.8 1.0 Each slice shows the color-coded behavior 0.7 0.7 1.10 for a fixed t (here t=72). Δ Δ 1.5 1.5 90 1.05 1.00 1.4 1.4 80 0.95 70 70 1.3 Order Δ t of extrema Order Δ t of extrema 0.90 60 60 1.2 0.85 50 50 0.80 1.1 40 40 0.75 1.0 30 30 0.70 0.65 15 0.9 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Renormalized time between successive extrema Renormalized time between successive extrema Thursday, August 13, 15 15

......... ......... + 240 a ) b ) N= 216 N= 343 350 ¡State ¡Points ¡ 235 . N= 729 N= 512 analyzed 230 4 ¡system ¡sizes T g 225 both ¡sides ¡of ¡Widom ¡ 220 line P [MPa] ........... ........... ��� t ����� ����� t ��������� min 215 both ¡sides ¡of ¡LLPT ¡line .......... .......... 210 . . . . . . xt CP 205 Kesselring,Lascaris, ¡ ........ ...... 200 Franzese, ¡Buldyrev, ¡ Herrmann,HES: 195 Nature ¡Sci. ¡Rep.2012; ¡ ... ........... ��������� 190 J. ¡Chem. ¡Phys. ¡ 2013 230 235 240 245 250 255 260 T [K] 16 Thursday, August 13, 15 16

Test 21: time dep. for 1 state point near ph. trans. line: Kesselring,Lascaris, Franzese, Buldyrev, Herrmann,HES : ¡Nature ¡Sci.Rep.2012; ¡ ¡JCP ¡2013 1.1 1.1 1.05 1.05 3 ] 1.0 1.0 [g/cm 0.95 0.95 0.9 0.9 0.85 0.85 0 20 40 60 80 100 120 140 160 180 200 0.0 0.2 0.4 0.6 0.8 1.0 t [ns] histogram Thursday, August 13, 15 17

+ 18 Thursday, August 13, 15 18

+ 18 Thursday, August 13, 15 18

Question: How to recognize true from apparent return-return correlations? Answer (Wigner): Eigenvalue distribution of covariance matrix VERSUS that of a random distribution. 1000 TAQ stocks (hence 1000 eigenvalues) Question: Which stocks dominate the eigenvectors corresponding truly random matrix to the 20 (matrix whose deviating entries are random eigenvalues? numbers) Laloux et al; Plerou et al 19 [PRL & PRE] Thursday, August 13, 15 19

Question: Which stocks dominate the eigenvector corresponding to a “deviating” eigenvalue? V. Plerou et al. , PRL and 20 PRE Thursday, August 13, 15 20