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Financial market crises predictionFinancial market crises prediction by multifractal and wavelet by multifractal and wavelet
analysis.analysis.
Russian Plekhanov Academy of EconomicsRussian Plekhanov Academy of Economics
Romanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.VRomanov 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..
The main aim of this research 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
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 of 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 introduced in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured".• A shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification.• 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
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
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 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
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 waves"
• Displays multiple chaotic,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
April 13, 2023 14
Dynamic systems fractals
Crisis prediction techniqueCrisis prediction technique
Because our goal is the prediction of crises, we are Because our goal is the prediction of crises, we are trying to first find out the best indicator, using trying to first find out the best indicator, using methodologies of fractal, multifractal and wavelet methodologies of fractal, multifractal and wavelet analysis.analysis.
First of all we looking for several different predictorsFirst of all we looking for several different predictors
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.
Definition the Fractal DimensionDefinition the Fractal Dimension
Fractal dimension :Fractal dimension :
wherewhere NNAA (1/(1/nn) –) – the number of blocks with length of the sided the number of blocks with length of the sided, ,
equalsequals 1/ 1/nn, , which necessary to coverwhich necessary to cover a set a set А.А. For S For S – – Serpinsky triangle:Serpinsky triangle: 58,1
)2ln(
)3ln(
)2ln(
)3ln(lim n
n
nsd
)ln(
))/1(ln(lim
n
nNd A
n
Hurst exponent (H) as one of predictorsHurst exponent (H) as one of predictors
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
Fractal Dimension Index(FDI = 2-H)Fractal Dimension Index(FDI = 2-H)
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
Stochastic process {x(t)} is called Multifractal, if it has stationary increments and satisfies the condition
,
when c(q) – predictor, E- operator of mathematical expectation, , – intervals on the real axis.
Scaling function , which takes into account the impact of the time on the moments q.
Multifractal spectrum of singularityMultifractal spectrum of singularityas the second predictoras the second predictor
)(q
Bt
1τ(q)qtΔt+t tΔc(q)(=)|xxE(| )
.Multifractal spectrum of singularity Multifractal spectrum of singularity is defined by Legendre transform:
)]([minarg)( qqfq
Multifractal spectrum of singularity Multifractal spectrum of singularity 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).
Five steps Five steps of multifractal spectrum of singularity of multifractal spectrum of singularity estimation: estimation: The First step: The First step: 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.
The second step:The second step:Time series Time series preprocessingpreprocessing
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
The third step: The third step: Partition functions Partition functions computingcomputing
For 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 ||),(
The fourth step: The fourth step: Scaling function Scaling function computingcomputing
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
The fifth step: The fifth step: Multifractal spectrum Multifractal spectrum of singularity of singularity estimationestimation
1. Lipshitz – Hoelder exponent estimation: :
where, i = 1, 2, 3, 4.2. Multifractal spectrum of singularity Multifractal spectrum of singularity estimation by Legendre
transform
qqqqqdq
d iiii
i
/)(/))1()((
)])()([min(arg)]([minarg)( qqqqqf iiq
iq
I
Scaling functionScaling function
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
Multifractal spectrum of singularity at period 09.07.96-
21.07.98
Multifractal spectrum of singularity at period 18.11.96-
30.11.98
Multifractal spectrum of singularityMultifractal spectrum of singularity
Dow Jones Industrial Index, pre-crisis situation
19.12.2006-06.10.2008
Scaling functionsScaling functions
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)
Scaling functionsScaling functions
Scaling functionsScaling functions
linear scaling-function (q) (monofractal process)
Multifractal spectrum of singularity RTSI at period 16.05.2000 -30.05.2002
Multifractal spectrum of singularity Multifractal spectrum of singularity for analyzed situationsfor analyzed situations
Multifractal spectrum of singularity DJI at period 19.12.2006-08.10.2008
Multifractal spectrum of singularity RTSI at period
16.12.2003-10.01.2006
Russian default 1998 and USA Black Monday 1987 analysis
Plot of the august 1998 Russian default currency exchanging data
Plot of width of fractal dimension spectrum (Δ(t)=αmax-αmin) for different time periods
0
5
10
15
20
25
30
0 100 200 300 400 500 600
Ряд1
US Dow Jones index for Black Monday 1987 for period 17.10.1986-31.12.1987
Plot of width of fractal dimension spectrum (Δ(t)=αmax-αmin) 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
Indexes DJI, RTS.RS, NASDAQ,S&P 500 falling at 2008 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
"Needles“, that determine the expansion of Multifractal "Needles“, that determine the expansion of Multifractal spectrum at hourly schedule spectrum at hourly schedule 5.2008-11.20085.2008-11.2008
Graph of Multifractal spectrum singularity width (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) atat
Russian index RTSI at periodRussian index RTSI at period 0707.10.19.10.199999--0707.1.111..20082008
interval Qmin Qmax
N ∆
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 (Graph of Multifractal spectrum singularity width (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 (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at at
American index Dow Jones IndustrialAmerican index Dow Jones Industrial at period 07at period 07.10.19.10.199999--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.
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 (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at at
American index Dow Jones IndustrialAmerican index Dow Jones Industrial at period 07at period 07.10.19.10.199999--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.
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 (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at at
American index NASDAQ Composite at period 07American index NASDAQ Composite at period 07.10.19.10.199999--0909.1.122..20082008
Wavelet analysis and crisis predictionWavelet analysis and crisis prediction
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 experiment-1 of our study we usedIn experiment-1 of our study we used Daubechies wavelet functions decomposition (db-4 wavelet functions 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
-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
Changes difference of maximum values of decomposition of Dobeshi-12 for the period 19.09.1997 -12.02.1999.
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
The difference of maximum coefficientsThe difference of maximum coefficients of of Daubechies -12-12 (17.10.1986- (17.10.1986-
31.12.1987) 31.12.1987)
Here 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, if we use the average of the indicator is the intervals difference, then we can find that the sharp increase occurring 18.09.1998, that is 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 of this indicator in the starting time was 74.5 times (initial value = 0.15; following value = 11.23)
Wavelet Analysis for Crisis Wavelet Analysis for Crisis Detection ( experiment Detection ( experiment – – 2)2)
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
April 13, 202356
Financial market model FIMASIM
The main functional modules are: FMSWorld, which contains virtual world classes and relationships, FMSStandardRoles, which contains financial market classes, and others.
Standard classes of the system are: Trader (TFMTrader) Broker (TFMSBroker) Company (TFMCompany) Market, stock exchange (TFMSMarket) Strategy (TFMSStrategy) Plan (TFMSPlan) Order, transaction request (TFMSShareTransactionRequest) Transaction (TFMSShareTransactiont)
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Virtual market program interface
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The experiments were made with aim to find out at which values of parameters the market instability arises.
Experiment 1:Overall parameters: MARKET_MAKER_TRADER_COUNT = 2; RANDOM_TRADER_COUNT = 0; FUNDAMENTAL_TRADER_COUNT = 500; BROKER_COUNT = 5; MARKET_COUNT = 1; COMPANY_COUNT = 10; CLASSIFICATORS_COUNT = 31;
Companies: COMPANY_MAX_ASSETS = 50000000; // 50Mbyte COMPANY_MIN_ASSETS = 1000000; // 1Mbyte
Brokers: MIN_BROKER_MARKET_ACCOUNT_MONEY =
100000; // 100k. MAX_BROKER_MARKET_ACCOUNT_MONEY =
150000; // 300k. BROKER_MONEY = 10000; // 10k.
Broker and market: MAX_COMMISION_PLANS = 3;
Market maker trader parameters: MIN_MM_TRADER_CHANGE_PERCENT = 0.1; MAX_MM_TRADER_CHANGE_PERCENT = 0.5;
Random Trader parameters: MIN_RANDOM_TRADER_PORTFOLIOS = 0; MAX_RANDOM_TRADER_PORTFOLIOS = 5; MIN_RANDOM_TRADER_MONEY = 50; MAX_RANDOM_TRADER_MONEY = 2000; MIN_RANDOM_TRADER_ACCOUNT_MONEY = 200; MAX_RANDOM_TRADER_ACCOUNT_MONEY = 1000; MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 20; MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 3000; MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01; MAX_RANDOM_TRADER_RISK_AMOUNT = 0.25;
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Program realization
Real price and fundamental price
distributionsMinimum, maximum and average price
distributions
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Experiment 2:Overall parameters:
MARKET_MAKER_TRADER_COUNT = 2;
RANDOM_TRADER_COUNT = 0;
FUNDAMENTAL_TRADER_COUNT = 500;
BROKER_COUNT = 20;
MARKET_COUNT = 1;
COMPANY_COUNT = 10;
CLASSIFICATORS_COUNT = 31;
Companies:
COMPANY_MAX_ASSETS = 15000; // 50Mbyte
COMPANY_MIN_ASSETS = 10000; // 1Mbyte
Brokers:
MIN_BROKER_MARKET_ACCOUNT_MONEY = 100000; // 100k.
MAX_BROKER_MARKET_ACCOUNT_MONEY = 150000; // 300k.
BROKER_MONEY = 10000; // 10k.
Broker and market:
MAX_COMMISION_PLANS = 5;
Market maker trader parameters: MIN_MM_TRADER_CHANGE_PERCENT = 0.5; MAX_MM_TRADER_CHANGE_PERCENT = 0.7;
Random Trader parameters: MIN_RANDOM_TRADER_PORTFOLIOS = 0; MAX_RANDOM_TRADER_PORTFOLIOS = 3; MIN_RANDOM_TRADER_MONEY = 10; MAX_RANDOM_TRADER_MONEY = 200000;
MIN_RANDOM_TRADER_ACCOUNT_MONEY = 200; MAX_RANDOM_TRADER_ACCOUNT_MONEY = 1000;
MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 20; MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 3000;
MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01; MAX_RANDOM_TRADER_RISK_AMOUNT = 0.5;
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Price time series. Experiment 2
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Experiment 3:Overall parameters:FUNDAMENTAL_TRADER_ MARKET_MAKER_TRADER_COUNT = 2; RANDOM_TRADER_COUNT = 250;COUNT = 250;
BROKER_COUNT = 5; MARKET_COUNT = 1; COMPANY_COUNT = 10; CLASSIFICATORS_COUNT = 31;
Companies: COMPANY_MAX_ASSETS = 50000000; // 50Mbyte COMPANY_MIN_ASSETS = 1000000; // 1Mbyte Brokers:MIN_BROKER_MARKET_ACCOUNT_MONEY = 100000; // 100k. MAX_BROKER_MARKET_ACCOUNT_MONEY = 300000; // 300k. BROKER_MONEY = 10000; // 10k.
Broker and market: MAX_COMMISION_PLANS = 3;
Market maker trader parameters:
MIN_MM_TRADER_CHANGE_PERCENT = 0.1;
MAX_MM_TRADER_CHANGE_PERCENT = 0.5;
Random Trader parameters:
MIN_RANDOM_TRADER_PORTFOLIOS = 0;
MAX_RANDOM_TRADER_PORTFOLIOS = 2;
MIN_RANDOM_TRADER_MONEY = 500;
MAX_RANDOM_TRADER_MONEY = 5000;
MIN_RANDOM_TRADER_ACCOUNT_MONEY = 2000;
MAX_RANDOM_TRADER_ACCOUNT_MONEY = 7000;
MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 2000;
MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 4000;
MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01;
MAX_RANDOM_TRADER_RISK_AMOUNT = 0.10;
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Price time series. Experiment 3
April 13, 202364
THANK YOU
ANY QUESTIONS?
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