FINANCIAL MARKET CRASH PREDICTION

Financial market crises prediction by Financial market crises prediction by multifractal and wavelet analysis.multifractal and wavelet analysis.

Russian Plekhanov Academy of EconomicsRussian Plekhanov Academy of Economics

Romanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.V.Romanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.V.

It is well known, that financial markets are essentially non-linear systems and financial time series are fractals.

That’s why prediction of crash situations at finance market is a very difficult task. It doesn’t allow us to use effectively such well-known methods as ARIMA or MACD in view of their sluggishness.

Multifractal and wavelets analysis methods are providing more deep insight into the nature of phenomena. Multiagent simulation makes it possible to explicate dynamic properties of the system.

The main aim is to find out the predictors or some kind of predicting signals which may warn as about forthcoming crisis

The aim of the researchThe aim of the research

a) Changing of ruble/dollar exchange rate at period 01.08.1997-01.11.1999 (Default in Russia)

b) American Index Dow Jones Industrial at “Black Monday” 1987 at period 17.10.1986-31.12.1987

с) Dow Jones Industrial Index

e) Nasdaq

d) RTSI

07.10.1999 -06.10.2008

07.10.1999 -06.10.2008

07.10.1999 -06.10.2008

Indexes DJI, RTS.RS, NASDAQ,S&P 500 falling at crisis period

1 monthSeptember 15,2008 – October 17, 2008

The collapse in the stock markets the analysts linked to the negative external background. U.S. indexes have completed a week 29.09 - 6.10 falling, despite the fact that the U.S. Congress approved a plan to rescue the economy.

Investors fear that the attempt to improve the situation by pouring in amount of $ 700 billion, which involves buying from banks illiquid assets will not be able to improve the situation in credit markets and prevent a decline in the economy.

3 months July 17,2008 – October 17, 2008

When Asian stock indices collapsed to a minimum for more than three years. The negative news had left the Russian market no choice – its began to decline rapidly.

6 months April 17,2008 – October 17, 2008

Efficient Market Hypothesis (EMH) asserts, that financial markets are "informationally efficient", or that prices on traded assets, e.g., stocks, bonds, or property, already reflect all known information. The efficient-market hypothesis states that it is impossible to consistently outperform the market by using any information that the market already knows, except through luck. Information or news in the EMH is defined as anything that may affect prices that is unknowable in the present and thus appears randomly in the future.

Capital Asset Pricing Model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

Arbitrage pricing theory (APT), in finance, is a general theory of asset pricing, that has become influential in the pricing of stocks. APT holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

Efficient Market HypothesisEfficient Market Hypothesis versusversus Fractal Market HypothesisFractal Market Hypothesis

Efficient market hypothesysEfficient market hypothesys ((EMHEMH))

Assumption of normal distribution of prices increments

The weak form EMH from a purely random distribution of prices has been criticized

Semi-strong form of EMH, in which all available information is reflected in the prices used by professionals

Changing prices in the long run does not show the presence of «memory»

Fractral market hypothesysFractral market hypothesys(FMH)

Prices shows leptoexcess effect for prices probability distribution(“fat tails”)

The prices plot looks similary for the period of time in the day, week, month (fractal pattern)

Reducing the reliability of predictions with the increase of its period

Prices shows short-term and long-term correlation and trends (the effect of feedback)

Chaotic activity of the market

FractalsFractals ––The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured".(colloquial) a shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification.(mathematics) a geometric object that has a Hausdorff dimension greater than its topological dimension.

The second feature that characterizes fractals is the fractional dimension.

The word fractal came from fractional values – partial values, which may take the fractal dimension of objects

Fractals may cause the application of Iterative Functions System

The image, which is the only fixed point of IFS is called attractor

Fractal definitionFractal definition

Chaos and dynamics of fractal marketChaos and dynamics of fractal market

Market prices tend to level the natural balance within the price range

These levels or ranges can be described as «attractors»

However, the data within those ranges remain casual

Point attractorsPoint attractors• The simplest form of the attractor. In theory, compatible

with the balance of supply and demand in the economy or the market equilibrium.

• Represent market volatility on balance, or "market noise"

• Displays Multiple varying the amplitude fluctuation, which are contained within the set limit cycle attractor, called «phase space».

Limit cycle attractorsLimit cycle attractors

Strange or fractal attractorsStrange or fractal attractors

Attractors typesAttractors types

Serpinsky TriangleSerpinsky Triangle

Fractals examplesFractals examples

Another fractals examplesAnother fractals examples

Fractal attractors andFractal attractors and financial markets financial markets

Stocks and futures - classic examples of securities. Profit from buying and selling comparable with fluctuations in the pendulum

Each bearer security or futures contract are located in its own phase space

Long-term forecasting is heavily dependent on accurate measurement of initial conditions of the market

Fractals on capital marketFractals on capital market Financial markets describes a

nonlinear function of active traders

Traditional methods of technical analysis based on linear equations and Euclidean geometry are inadequate

Market jumps growth and recession are nonlinear

Technical analysis methods are poor indicators of the relationship trend and trading decisions

Fractals can describe the phenomena that are not described in Euclidean geometry

Stochastic process {x(t)} is called Multifractal, if it has fixed increments and satisfies the condition

,

when c(q) – predictor, E- operator of mathematical expectation, , – intervals on the real axis.

Scaling function taking into account the impact of time on points q.

MultifractalMultifractal

Qq

)(q

Bt

1τ(q)qtΔt+t tΔc(q)(=)|xxE(| )

Definiting the Fractal Dimension IndexDefiniting the Fractal Dimension Index Fractal dimension indedx Fractal dimension indedx ((FDIFDI))::

NS(1/2NS(1/2nn))––the number of blocks with a length of handthe number of blocks with a length of hand

1/21/2nn, , which necessarywhich necessary,, to cover S to cover S – – Serpinsky triangleSerpinsky triangle..

Где Где NNAA (1/(1/nn) –) – the number of blocks with length of hand the number of blocks with length of hand, , equalequal

1/1/nn, , which necessary to coverwhich necessary to cover variety variety А.А.

Фрактальное Множество

А

58,1)2ln(

)3ln(

)2ln(

)3ln(lim n

n

nsd

)ln(

))/1(ln(lim

n

nNd A

n

Fractal Dimension IndexFractal Dimension Index

Defines the persistence or antipersistence of Defines the persistence or antipersistence of market. Persistent market weakly fluctuated market. Persistent market weakly fluctuated around the market trend around the market trend

antipersistent market shows considerable volatility antipersistent market shows considerable volatility on the trend on the trend

antipersistent market is more rugged pricing antipersistent market is more rugged pricing schedule and more frequently show a change schedule and more frequently show a change trendstrends

Crisis prediction techniqueCrisis prediction technique

Because our goal is the prediction of crises, we Because our goal is the prediction of crises, we are trying to first find out the best indicator, using are trying to first find out the best indicator, using methodology Multifractal and wavelet analysis.methodology Multifractal and wavelet analysis.

Then we test various types of pre-processing the Then we test various types of pre-processing the original time series to find the best indicator.original time series to find the best indicator.

Hurst exponentHurst exponent

Depending on the value of Heurst Depending on the value of Heurst exponent the properties of the exponent the properties of the process are distinguished as follows:process are distinguished as follows: When H = 0.5, there is a process of When H = 0.5, there is a process of random walks, which confirms the random walks, which confirms the hypothesis EMH. hypothesis EMH.

When H > 0.5, the process has long-When H > 0.5, the process has long-term memory and is persistent, that term memory and is persistent, that is it has a positive correlation for is it has a positive correlation for different time scales. different time scales.

When H < 0.5, time-series is anti-When H < 0.5, time-series is anti-persistent with average switching persistent with average switching from time to time.from time to time.

Ttzzx ttt ,...,1,lnln 1

11

1,),(

t

t

uu xxxxtx

),(min),(max)(11

txtxRtt

1

21)(

uu xxS

log)(

)(log SR

H

Time series partitioningTime series partitioning Time series: {xt}; t [0, T].

Compute: Z={zt}, zt= lnxt+1-lnxt; t [0,T];

Divide interval [0, T] into N subintervals, 1 ≤ N ≤ Nmax.

Each subinterval contains int (T/N)=A values Z;

For each subinterval K; 1 ≤ K ≤ N current reading number lK;1 ≤ lK ≤ A; t = (K-1) А+ lK

As soon as we are looking for the best indicator of a coming default, we will use several variants of a preliminary processing.

Time series preprocessingTime series preprocessing

1. The original time series itself: Z={zt};

2. Preprocessed time series Z1={ }, K=1,2,…N,

where

3. Preprocessed time series

where

4. Preprocessed time series Z3={ }

ZK

A

llK

K

Kz

AZ

10

1

K

KlAK

S

ZZZ K

10

2

A

lKlK

K

KZZ

AS

1

2

0

1

KlAK ZZK

10

Partition functionsPartition functionsFor each preprocessed time series compute partition function for

different N and q values :

N

K

q

AKKAN ZTZqZ1

)1(0)(00 |)(|),(

N

K

qKKN ZTZqZ

11

1 |)(|),(

N

K

qAKN ZKAZqZ

1

)1(222 |)(|),(

N

K

q

AKKAN ZZqZ1

)1(3)(33 ||),(

Scaling functionsScaling functions

A

NAqZq

NN log

loglog),(log)(

00

A

NAqZq

NN log

loglog),(log)(

11

A

NAqZq

NN log

loglog),(log)(

22

A

NAqZq

NN log

loglog),(log)(

33

Fractal dimension spectrum Fractal dimension spectrum estimationestimation

1. Lipshitz – Hoelder exponent estimation: :

when, i = 1, 2, 3, 4.

2. Fractal dimension spectrum estimation by Legendre transform

qqqqqdq

d iiii

i

/)(/))1()((

)])()([min(arg)]([minarg)( qqqqqf iiq

iq

I

Fractal dimension spectrum Fractal dimension spectrum width as crash indicatorwidth as crash indicator

Multifractal may be composed of two or infinite number of monofractals with continuous varying α values. Width of α spectrum may be estimated as difference between maximum and minimum values of α:

Δ = max - min , By carrying out Legendre transform we are trying

using our program by estimating Δ to find differences in its values before and after crash.

Roughly speaking f() gives us number of time moments, for which degree of polynomial, needed for approximation f() equals (according to Lipshitz condition).


Non-linear scaling functionNon-linear scaling function(q) (q) ((Multifractal processMultifractal process))

Changes in currency for the Changes in currency for the Russian default of 1998Russian default of 1998

Assesment of multifractal spectrum of singularity at period 09.07.96-21.07.98

Assesment of multifractal spectrum of singularity at period 18.11.96-30.11.98

Screenshots assessment of Screenshots assessment of Multifractal spectrum of singularityMultifractal spectrum of singularity

Dow Jones Industrial Index, pre-crisis situation

19.12.2006-06.10.2008


Non-linear scaling-function (q) (multifractal process)

RTSI index, pre-crisis situation

19.12.2006-06.10.2008

Non-linear scaling-function (q) (multifractal process)



linear scaling-function (q) (monofractal process)

Assesment of multifractal spectrum of singularity RTSI at

period 16.05.2000 -30.05.2002

Screenshots assesment of Screenshots assesment of Multifractal spectrum of singularityMultifractal spectrum of singularity

Assesment of multifractal spectrum of singularity DJI at period 19.12.2006-08.10.2008

Assesment of multifractal spectrum of singularity RTSI at

period 16.12.2003-10.01.2006

"Needles" that determine the expansion of Multifractal "Needles" that determine the expansion of Multifractal spectrum on an hourly schedule spectrum on an hourly schedule 5.2008-11.20085.2008-11.2008

Experimental resultsExperimental results

Schedule assessment of the width of the spectrum of fractal singularity (Δ(t)=αmax-αmin) for different periods of time

American Dow Jones at the «Black Monday» 1987 period 17.10.1986-

31.12.1987

Schedule assessment of the width of the spectrum of fractal singularity (Δ(t)=αmax-αmin) at the «Black Monday»

0

0,10,2

0,30,4

0,50,6

one yearbeforedefolt

11.07.96-23.07.98

19.07.96-31.07.98

29.07.96-10.08.98

06.08.96-18.08.98

14.08.96-26.08.98

00,050,1

0,150,2

0,250,3

Graph of Multifractal spectrum singularity width assessment Graph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) atat russian index RTSI at periodrussian index RTSI at period

0707.10.19.10.199999--0707.1.111..20082008interval Qmin Qma

xN ∆

1-51207.10.1999 –18.10.2001

-2 6 47 0,964151-662

16.05.2000 -30.05.2002-2 6 103 0,495

301-81215.12.2000 -31.12.2002

-2 6 129 1,62451-962

25.07.2001 -11.08.2003-2 5 31 0,81

601-111228.02.2002 -17.03.2004

-2 6 170 1,77751-1262

03.10.2002 -19.10.2004-2 6 129 2,17

901- 141215.05.2003 -02.06.2005

-2 6 129 1,9271051-1562

16.12.2003 -10.01.2006-2 5 43 0,952

1201-171226.07.2004 -15.08.2006

-2 5 21 0,8681351-1862

04.03.2005 -26.03.2007-2 5 22 0,89

1501-201206.10.2005 -25.10.2007

-2 5 23 0,8481651-2162

19.05.2006 -07.06.2008-2 5 40 0,927

1801-224619.12.2006 -06.10.2008

-2 7 145 2,1331765-2277

25.09.2006 -07.11.2008-2 7 161 2,177

Experimental resultsExperimental results(RTSI)(RTSI)

Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at russian index RTSI at period 07.10.1999-07.11.2008

Over 4 years outstanding mortgage loans in Russia rose Over 4 years outstanding mortgage loans in Russia rose more than 16 times - from 3.6 billion rubles. in 2002 to 58.0 billion more than 16 times - from 3.6 billion rubles. in 2002 to 58.0 billion rubles. in 2005. In quantitative terms - from 9,000 loans in 2002 to rubles. in 2005. In quantitative terms - from 9,000 loans in 2002 to

78,603 in 2005.78,603 in 2005.

Why mortgage evolving so rapidly? Many factors. This increase in real Why mortgage evolving so rapidly? Many factors. This increase in real incomes and the decline of distrust towards mortgage, as from potential incomes and the decline of distrust towards mortgage, as from potential buyers, and from the sellers, and a general reduction in the average interest buyers, and from the sellers, and a general reduction in the average interest rate for mortgage loans from 14 to 11% per annum, and the advent of rate for mortgage loans from 14 to 11% per annum, and the advent of Moscow banks in the regions, and intensifying in the market of small and Moscow banks in the regions, and intensifying in the market of small and medium-sized banks.medium-sized banks.

Pre-crisis situation: Pre-crisis situation: July 2008 - the beginning of september 2008 July 2008 - the beginning of september 2008

Graph of Multifractal spectrum singularity width assessment Graph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) atat Russian index RTSI at periodRussian index RTSI at period

0707.10.19.10.199999--0909.1.122..20082008

interval Qmin Qmax N ∆

1-51207.10.1999 –18.10.2001

-2 5 164 1,84151-662

16.05.2000 -30.05.2002-2 4 5 0,717

301-81215.12.2000 -31.12.2002

-2 5 134 1,77451-962

25.07.2001 -11.08.2003-2 5 65 1,01

601-111228.02.2002 -17.03.2004

-2 5 74 1,108751-1262

03.10.2002 -19.10.2004-2 4 11 0,791

901- 141215.05.2003 -02.06.2005

-2 4 38 0,8031051-1562

16.12.2003 -10.01.2006-2 4 50 0,815

1201-171226.07.2004 -15.08.2006

-2 4 53 0,8841351-1862

04.03.2005 -26.03.2007-2 4 57 0,973

1501-201206.10.2005 -25.10.2007

-2 4 29 0,8641651-2162

19.05.2006 -07.06.2008-2 4 11 0,836

1801-226319.12.2006 -06.10.2008

-2 5 151 2,324

Graph of Multifractal spectrum singularity width assessmentGraph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at american index Dow Jones Industrialat american index Dow Jones Industrial at period at period

0707.10.19.10.199999--0707.1.111..20082008

1765-228425.09.2006 -07.11.2008

-2 5 174 1,984

There was a sharp drop in the index and 9 october 2002 DJIA reached an interim There was a sharp drop in the index and 9 october 2002 DJIA reached an interim minimum with a value of 7286,27.minimum with a value of 7286,27.

Dow Jones Industrial index of 15 september 2008, fell to 4.42 per cent to 10,917 Dow Jones Industrial index of 15 september 2008, fell to 4.42 per cent to 10,917 points - is the largest of its fall in a single day since 9 october 2002, reported France points - is the largest of its fall in a single day since 9 october 2002, reported France Presse. World stock markets experienced a sharp decline in major indexes in Presse. World stock markets experienced a sharp decline in major indexes in connection with the bankruptcy Investbank Lehman Brothers.connection with the bankruptcy Investbank Lehman Brothers.

Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at american index Dow Jones Industrial at period 07.10.1999-07.11.2008

Experimental results(DJI)Experimental results(DJI)

3 May, 1999, the index reached a value of 3 May, 1999, the index reached a value of 11014.70. Its maximum - mark 11722.98 - 11014.70. Its maximum - mark 11722.98 -

Dow-Jones indexDow-Jones index reached at 14 January 2000.reached at 14 January 2000.


Graph of Multifractal spectrum singularity width assessmentGraph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at american index Dow Jones Industrialat american index Dow Jones Industrial at period at period

0707.10.19.10.199999--0909.1.122..20082008

interval Qmin

Qmax N ∆

1-51207.10.1999 –18.10.2001

-2 6 47 0,91151-662

16.05.2000 -30.05.2002-2 6 57 0,935

301-81215.12.2000 -31.12.2002

-2 6 86 1,092451-962

25.07.2001 -11.08.2003-2 5 25 0,74

601-111228.02.2002 -17.03.2004

-2 5 31 0,821751-1262

03.10.2002 -19.10.2004-2 5 129 1,385

901- 141215.05.2003 -02.06.2005

-2 4 9 0,7261051-1562

16.12.2003 -10.01.2006-2 4 13 0,765

1201-171226.07.2004 -15.08.2006

-2 4 19 0,781351-1862

04.03.2005 -26.03.2007-2 4 19 0,792

1501-201206.10.2005 -25.10.2007

-2 4 15 0,7781651-2162

19.05.2006 -07.06.2008-2 4 5 0,772

1801-226319.12.2006 -06.10.2008

-2 5 77 1,185

Graph of Multifractal spectrum singularity width assessmentGraph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at american index NASDAQ Composite at period at american index NASDAQ Composite at period

0707.10.19.10.199999--0707.1.111..20082008

1765-228425.09.2006 -07.11.2008

-2 6 207 1,067

Experimental results(NASDAQ)Experimental results(NASDAQ) Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at american index NASDAQ Composite at period 07.10.1999-07.11.2008

In August 2002 the first NASDAQ closes its branch in Japan, as well as In August 2002 the first NASDAQ closes its branch in Japan, as well as closing branches in Europe, and now it was turn European office, where closing branches in Europe, and now it was turn European office, where for two years, the number of companies whose shares are traded on the for two years, the number of companies whose shares are traded on the exchange fell from 60 to 38.exchange fell from 60 to 38.

After that happened result in a vast dropIn 2000, he reached even five thousandth mark, but After that happened result in a vast dropIn 2000, he reached even five thousandth mark, but after the general collapse of the market of computer and information technology is now in an after the general collapse of the market of computer and information technology is now in an area of up to two thousand points.area of up to two thousand points.

The index of technology companies The index of technology companies NASDAQ Composite reached its peak in NASDAQ Composite reached its peak in

March 2000.March 2000.


Graph of Multifractal spectrum singularity width assessmentGraph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at american index NASDAQ Composite at period at american index NASDAQ Composite at period

0707.10.19.10.199999--0909.1.122..20082008

Default’s Default’s 19981998 indicator. indicator.

Данные min max

11.08.98 2,837 3,337 0,5

12.08.98 2,837 3,335 0,498

13.08.98 2,838 3,325 0,487

14.08.98 2,839 3,344 0,505

17.08.98 1,8 3,36 1,56

18.08.98 1,97 3,3 1,33

19.08.98 1,355 3,26 1,905

20.08.98 1,499 3,264 1,765

21.08.98 1,499 3,4 1,901

24.08.98 1,5 3,249 1,749

a)

b)

Part Multifractal spectrum of data related to graph b)

The red line shows that the width multifraktalnogo spectrum begins to grow at the same time as changing the exchange rate, but more clearly.

Wavelet-analysisWavelet-analysis

где ,(t)– where ,(t)– function with zero mean centered

around zero with time scale and time horizon . Family of wavelet vectors is created from mother function

by displacement and scaling

,)()(),( , dtttxW

)(1

)(

tt

Time series f(t) representation as linear Time series f(t) representation as linear combinationcombination of wavelet functionsof wavelet functions

where jo – a constant, representing the highest level of resolution for which the most acute details are extracted .

),()()( ,,,

0

00tttf kj

kkj

jjkj

kj

dtttf kjkj )()( ,, 00

dtttf kjkj )()( ,,

WA crisis detectionWA crisis detection experiment experiment - 1- 1

In our study we usedIn our study we used Daubechies wavelet functions wavelet functions decomposition (db-4 decomposition (db-4 ии db-12). db-12).

The goal was the detection of the signal, which could The goal was the detection of the signal, which could predict the sudden changes. Data on exchange rates predict the sudden changes. Data on exchange rates (USD) to the ruble were taken from the site www.rts.ru (USD) to the ruble were taken from the site www.rts.ru for the period 1.09.1995 - 12.02.1999for the period 1.09.1995 - 12.02.1999

The total number of numbered in the order several times The total number of numbered in the order several times in the interim for the period 1.09.1995 - 12.02.1999 was in the interim for the period 1.09.1995 - 12.02.1999 was 862 value.862 value.

Graph of changingGraph of changing RTS indexes at period RTS indexes at period 1.09.1995 – 12.02.19991.09.1995 – 12.02.1999

0

5

10

15

20

25

01.0

9.1

995

04.1

1.1

995

22.0

1.1

996

27.0

3.1

996

04.0

6.1

996

09.0

8.1

996

14.1

0.1

996

18.1

2.1

996

25.0

2.1

997

05.0

5.1

997

10.0

7.1

997

12.0

9.1

997

18.1

1.1

997

27.0

1.1

998

02.0

4.1

998

10.0

6.1

998

14.0

8.1

998

19.1

0.1

998

24.1

2.1

998

The division time series on the rangesThe division time series on the ranges

To achieve the goal of this time series was divided into 7 To achieve the goal of this time series was divided into 7 overlapping intervals located unevenly, so that the overlapping intervals located unevenly, so that the interval 4 (242-753) immediately preceding the time of interval 4 (242-753) immediately preceding the time of default and subsequent intervals captured the moment of default and subsequent intervals captured the moment of default. default.

Each interval consisted of 512 values: 1-512, 101-612, Each interval consisted of 512 values: 1-512, 101-612, 201-712, 242-753, 251-762, 301-812, 351-862.201-712, 242-753, 251-762, 301-812, 351-862.

Predicting the crisis with the help of wavelet analysisPredicting the crisis with the help of wavelet analysis

# Interval Maximum for all levels

Difference maximum ratios

1 1-512 0,068796 -

2 101-612 0,140859 0,072062

3 201-712 0,150173 0,009314

4 242-753 11,234599 11,084426

5 251-762 11,850877 0,616278

6 301-812 7,944381 -3,906496

7 351-862 9,802439 1,858058

-6

-4

-2

0

2

4

6

8

10

12

13.02.1998 10.07.1998 07.09.1998 18.09.1998 30.11.1998 12.02.1999

# interval Average value

Difference averages

1 1-512 5,249121 -

2 101-612 5,518002 0,268881

3 201-712 5,759273 0,241271

4 242-753 5,926961 0,167688

5 251-762 6,077492 0,150531

6 301-812 7,124922 1,047431

7 351-862 8,672407 1,547484

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

1,8

13.02.1998 10.07.1998 07.09.1998 18.09.1998 30.11.1998 12.02.1999

The schedule change ratios of difference from the average value of currencies this intervala to the value of the previous intervala for the period 19.09.1997-12.02.1999 (dates are taken on the right border, ie 512 value).

The schedule changes difference ratios of maximum ratios of decomposition of Dobeshi-12 for the period 19.09.1997-12.02.1999 (dates are taken on the right border, ie 512 value)

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000№

interval Maximum for all levels

Difference maximum

ratios

1 1-128 13083,070 --------------

2 64-192 223,834 -12859,235

3 96-224 262,039 38,204

4 106-234 258,122 -3,916

5 111-239 262,371 3,917

6 114-242 14785,540 14523,169

7 124-252 789,933 -13995,607

8 126-254 1298,050 508,117

9 177-305 475,376 -822,673

The schedule changes difference maximum The schedule changes difference maximum coefficients of expansion in the Dobeshi-12 coefficients of expansion in the Dobeshi-12 (17.10.1986-31.12.1987).(17.10.1986-31.12.1987).

The difference coefficientsThe difference coefficients of of Daubechies -12-12

«Black Monday» Detector«Black Monday» Detector

At the previous slide we can see the positive peak earlier 01.10.87 and negative peak before 15.10.87.

This is more than 4 days before the «Black Monday».

Sharp line connects the two peaks. Obviously, this information can serve as a detector impending crisis.

42 days prior to the default Of the figure shows that the start of trading, the corresponding spike in the

dollar may be adopted point 742 (21.08.1998), a peak corresponds to 754 points (07.09.1998).

As we can see from the previous slide in the event of data processing by the Russian default by default, if we use the average of the indicator is the intervals difference, then we can find that the sharp increase occurring 18.09.1998, ie delayed by at least 11 days. At the same time schedule for the coefficients of wavelet functions shows us that the beginning of dramatic changes difference wavelet coefficients of expansions is a point 712 (10.07.1998).

We can, apparently, to predict the onset of default at least 42 days (10.07.1998 - 21.08.1998). At the same time increase the maximum value (Fig. 4) of this indicator in the starting time was 74.5 times (initial value = 0.15; following value = 11.23)

WA crisis detectionWA crisis detection experiment experiment - - 22

In our experiment, number 2, we used Daubechies wavelet functions decomposition (db-4).

The goal was the detecting the signal, which could predict the sudden changes in the index DJI (Dow Jones Index - Dow Jones). Data on DJI were taken from the site http://finance.yahoo.com for the period 7.10.1999 - 24.11.2008

The total number of numbered in the order several times in the interim for the period 7.10.1999 - 24.11.2008 at 2299 values.

Graph Graph DJIDJI change 7.10.1999- change 7.10.1999-88.1.111.2008.2008

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Change the values of Hurst exponent said that the market in anticipation Change the values of Hurst exponent said that the market in anticipation of becoming antipersistent crisis: H <0,5of becoming antipersistent crisis: H <0,5

Changing detailing factors wavelet decomposition of db-4 showChanging detailing factors wavelet decomposition of db-4 show conversion market (antipersistent)conversion market (antipersistent)

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Changing detailing factors wavelet decomposition of Changing detailing factors wavelet decomposition of db-4 suggest crossing a market for the period db-4 suggest crossing a market for the period

07.07.2005 - 24.11.200807.07.2005 - 24.11.2008

Fundamental analysisFundamental analysis Fundamental analysis is based on an assessment of market

conditions in general and assessing the future development of a single issuer.

Fundamental analysis is a fairly laborious and a special funding agencies.

Fundamental analysis depends on the news of factors. By random and unexpected news include political and natural, as well as war.

How to conduct a fundamental analysis can be divided into four separate units, correlating with each other.

Fundamental analysis Fundamental analysis technologytechnology

The first unit - is a macroeconomic analysis of the economy as a whole.

The second unit - is an industrial analysis of a particular industry.

A third unit - a financial analysis of a particular enterprise.

A fourth unit - analyzing the qualities of investment securities issuer.

Fundamental analysis technology includes an analysis of news published in the media, and comparing them with the securities markets.

Analysis MethodAnalysis Method

Keyword extraction, characterizing the market: boost or cut, the increase / decrease.

Automatic analysis using the terminology the ontology.

Processing time series (filtering, providing trends, the seasonal components).

Using neural networks to classify the flow of news and processing time series.

•Examine what news articles relevant to the company, Yahoo uses

profiling to establish consistency between articles and companies.

•For each trend formed a temporary window to explore how art

relates to the trend.

•It is believed that there is a match, if the article appeared a few

hours before the trend.

News analysis targetNews analysis target

The intensity of the flow of news dataThe intensity of the flow of news dataThe joint processing of digital and text dataThe joint processing of digital and text data

Digital data Time series

The movement of financial instruments (price / volume)

Flow intensity:

5Mb/day, on the tool

Text data

Text flows

Various types:

News, financial reports, company brochures, government documents

Flow intensity:

20Mb/day

Idea of systemIdea of system

Past articles with newsPast articles

with news

Past data pricing

securities market

Past data pricing

securities market

Building modelBuilding model

ModelModel

New arcticles

with news

New arcticles

with news

Prediction results

Prediction results

System exit

System exit

Real system architectureReal system architecture

SYSTEM QUIRK

Reuters News Feed

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Down

Time Series of Up and Down

Financial instrument (Reuters) e.g. FTSE

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Generate Signal (Buy / Sell)

Comparsion time and stocks by timeComparsion time and stocks by time

Text analysis should apply:Text analysis should apply:Recognition of the named entity. The discovery of those (people), organizations, Recognition of the named entity. The discovery of those (people), organizations,

currencies.currencies.

Extracting key information related to organizations, persons, facts, evidence from Extracting key information related to organizations, persons, facts, evidence from documents.documents.

The establishment of relations between the patterns.The establishment of relations between the patterns.

Creating a template to scripting events, organizations, regions.Creating a template to scripting events, organizations, regions.

The formation of coherence - to collect information on sovstrechaemosti The formation of coherence - to collect information on sovstrechaemosti expressions. The result of the system is the text as a set of the following expressions. The result of the system is the text as a set of the following components:components:

<AGENT> <CONCERN> <GOAL> <AGENT><AGENT> <CONCERN> <GOAL> <AGENT> <CONCERN, THE IMPORTANCE> <GOAL, the value><CONCERN, THE IMPORTANCE> <GOAL, the value>

Between formed in such a description of news and current prices of assets in the Between formed in such a description of news and current prices of assets in the securities market established statistical connection to predict price changes securities market established statistical connection to predict price changes depending on the nature of news.depending on the nature of news.

Fundamental analysis ontologyFundamental analysis ontology

News, alterNews, alter securities coursesecurities course

Automatic 3-side Automatic 3-side integrationintegration

Competetive Competetive researchesresearches, , discovered discovered

automaticallyautomatically

Concentrated content, Concentrated content, organised with organised with

semantic categoriessemantic categories

Relevant content, Relevant content, not expressed not expressed

evidentlyevidently

(semantic (semantic associations)associations)

Automatic content Automatic content integration from sources integration from sources

and other providersand other providers

Fundamental analysis results with Fundamental analysis results with ontology usingontology using

Price graphs and charts Price graphs and charts

Pricing modelscalls figures or creatings, which appers on price graphs

These figures, or education (chart pattern), divided into some groups and can be used to predict the market dynamics

FINANCIAL MARKET CRASH PREDICTION

Economy & Finance

Transcript of FINANCIAL MARKET CRASH PREDICTION