1. Financial market crises prediction by multifractal and wavelet analysis. Russian Plekhanov Academy of Economics Romanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.V .
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3. 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 Examples of analyzed financial market crisis situations(1)
4. 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 Examples of analyzed financial market current crisis
17. Hurst exponent (H) as one of predictors Depending on the value of Heurst exponent the properties of the process are distinguished as follows: When H = 0.5, there is a process of random walks, which confirms the hypothesis EMH. When H > 0.5, the process has long-term memory and is persistent, that is it has a positive correlation for different time scales. When H < 0.5, time-series is anti-persistent with average switching from time to time.
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19. 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 singularity as the second predictor . Multifractal spectrum of singularity is defined by Legendre transform :
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23. The third step: Partition functions computing For each preprocessed time series compute partition function for different N and q values :
25. The fifth step: Multifractal spectrum of singularity estimation 1. Lipshitz – Hoelder exponent estimation : : where, i = 1, 2, 3, 4. 2 . Multifractal spectrum of singularity estimation by Legendre transform
26. Scaling function Non-linear scaling function (q) ( Multifractal process ) Changes in currency for the Russian default of 1998
27. 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 singularity
28. Dow Jones Industrial Index, pre-crisis situation 19.12.2006-06.10.2008 Scaling functions Non-linear scaling-function (q) ( multifractal process )
30. Scaling functions linear scaling-function (q) (monofractal process ) Multifractal spectrum of singularity RTSI at period 16.05.2000 - 30.05.2002
31. Multifractal spectrum of singularity for 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
32. 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)= α max - α min ) for different time periods 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)= α max - α min ) the Black Monday
33. Indexes DJI , RTS.RS , NASDAQ , S&P 500 falling at 2008 crisis period 1 month S eptember 15,2008 – O ctober 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 1 7 ,2008 – O ctober 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 1 7 ,2008 – O ctober 17, 2008
36. Experimental results (RTSI) Graph of Multifractal spectrum singularity width assessment ( Δ (t)= α max - α min ) at russian index RTSI at period 07 .10.19 99 - 07 .1 1 . 2008 Over 4 years outstanding mortgage loans in Russia rose 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 78,603 in 2005. Why mortgage evolving so rapidly? Many factors. This increase in real incomes and the decline of distrust towards mortgage, as from potential 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 Moscow banks in the regions, and intensifying in the market of small and medium-sized banks. Pre-crisis situation: July 2008 - the beginning of september 2008
37. Graph of Multifractal spectrum singularity width ( Δ (t)= α max - α min ) at Russian index RTSI at period 07 .10.19 99 - 09 .1 2 . 2008
39. There was a sharp drop in the index and 9 october 2002 DJIA reached an interim minimum with a value of 7286,27. 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 Presse. World stock markets experienced a sharp decline in major indexes in connection with the bankruptcy Investbank Lehman Brothers. Graph of Multifractal spectrum singularity width assessment ( Δ (t)= α max - α min ) at american index Dow Jones Industrial at period 07 .10.19 99 - 07 .1 1 . 2008 Experimental results(DJI) 3 May, 1999, the index reached a value of 11014.70. Its maximum - mark 11722.98 - Dow-Jones index reached at 14 January 2000. Pre-crisis situation: July 2008 - the beginning of september 2008
40. Graph of Multifractal spectrum singularity width ( Δ (t)= α max - α min ) at American index Dow Jones Industrial at period 07 .10.19 99 - 09 .1 2 . 2008
42. Experimental results(NASDAQ) Graph of Multifractal spectrum singularity width assessment ( Δ (t)= α max - α min ) at american index NASDAQ Composite at period 07 .10.19 99 - 07 .1 1 . 2008 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 for two years, the number of companies whose shares are traded on the exchange fell from 60 to 38. 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 area of up to two thousand points. The index of technology companies NASDAQ Composite reached its peak in March 2000. Pre-crisis situation: July 2008 - the beginning of september 2008
43. Graph of Multifractal spectrum singularity width ( Δ (t)= α max - α min ) at American index NASDAQ Composite at period 07 .10.19 99 - 09 .1 2 . 2008
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45. Time series f(t) representation as linear combination of wavelet functions where j o – a constant, representing the highest level of resolution for which the most acute details are extracted .
49. Predicting the crisis with the help of wavelet analysis Changes difference of maximum values of decomposition of Dobeshi-12 for the period 19.09.1997 -12.02.1999.
54. Change the values of Hurst exponent said that the market in anticipation of becoming antipersistent crisis: H <0,5 Changing detailing factors wavelet decomposition of db-4 show conversion market (antipersistent)
55. Changing detailing factors wavelet decomposition of db-4 suggest crossing a market for the period 07.07.2005 - 24.11.2008
66. Fundamental analysis technology 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.
67. Analysis 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.
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69. The intensity of the flow of news data The 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: 20 Mb / day
70. Idea of system Past articles with news Past data pricing securities market Building model Model New arcticles with news Prediction results System exit
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