Smoothing techniques for market fluctuation signals/I lyginimo metodu taikymas rinkos svyravimams prognozuoti.

Dzikevicius, Audrius ; Saranda, Svetlana

1. Introduction

Investment decision-making is often based on the following three dimensions: value, time and risk. The main characteristic of the stock market is its dynamic condition, so value and risk are the measures which can only be forecasted but not known exactly in advance. Financial crisis in the beginning of the 21st century was caused by crashes in stock markets. Nowadays economists analyze the current financial crisis and try to find the main reasons why the world economy constantly suffers from booms and busts (Dzikevicius, Zamzickas 2009). Racickas and Vasiliauskaite (2010) identified one of the major financial crisis depth indicators. It is the country's stock market indexes. Stock market index observation allows determining current stock market situation. If Academia finds the appropriate way to forecast at least exact market trend or its fluctuation signals, the subsequence of such financial crisis as the world has seen in the 21st century can be more opportune for the further financial markets and national economic development. As the globalization processes are spread widely between different countries, the crash of one stock market causes the influence on other stock markets in other countries.

The events of the last two years indicated the principles of investors' behaviour: an inadequate risk assessment, the desire to obtain abnormal returns, the orientation of short-term investment horizons or the speculation. Such attitude skews stock market trends and its behavior. As the investment process is an important part of investment banks', insurance companies', etc. activity, it should involve more efficient and accurate forecasting methods. So the aim of this study is to find out more appropriate forecasting techniques suitable to indicate the fluctuations of the stock market. The previous study (Dzikevicius et al. 2010) was based on analysis of simple Technical Analysis (further TA) rules. The results implied that application of simple trading rules to forecast stock prices can generate significant forecasted value errors and deviations from real prices and it is not appropriate to generate price movement trends. The continuous research (Dzikevicius, Saranda 2010) was the first academia research of using TA to predict the values for OMX Baltic Benchmark Index and compare it with S&P 500 Index of US using an exponential smoothing method--the exponential moving average (further--the EMA). The results were affirmative: the exponential smoothing method was appropriate to indicate the future values of S&P 500 and OMX Baltic Benchmark indexes. With the reference to previous researches smoothing techniques will be tested again to decide whether it is a powerful tool to forecast stock market fluctuation signals. The OMX Baltic Benchmark PI Index and related sector indexes are the objects to be forecasted to find out the trend of the Baltic region stock markets.

2. The review of applied forecasting and risk evaluation methods

Investors' endeavor that the value of assets held steady improves. In addition they are interested in not just increase in the value but also the speed of value growth. Only initial asset price is known. Two dimensions such as final asset price and current profit are unknown (Rutkauskas, Martinkute 2007). Technical factors are related to the securities market which focuses on the evolution of prices and trade circulation, demand and supply factors. An important statistical tool which allows identifying the market conditions is an equity index (Norvaisiene 2005). In our case OMX Baltic Benchmark PI index is a statistical stock market price dynamics measure tool. Securities market is still relatively new for individual investors. As the new type of investors such as an individual investor appeared in the stock market, a huge flow of information on the investment management and assessment issue is needed (Jureviciene 2008). Growing stock market and rising activity of the investors attracts more growing attention (Dudzeviciute 2004).

TA researchers Edwards and Magee (1992), Myers (1989), Pring (1993) described this method as a technique which needs patterns of history prices of a financial instrument to be used. The Moving Average rule is one of the numerous methods with a common set of TA basic principles (Caginalp, Balenovich 2003). Klimaviciene and Jureviciene (2007) quizzed investors to determine their investment preferences. The survey showed that 17.3% of the respondents invested into securities, 14.3% of respondents invest directly into shares, and 15.4% of the surveyed investors speculated and invested. The survey made by Mizrach and Weerts (2007) showed that 52% of semi-professional traders used simple moving rules and 56% preferred chart patterns. The survey made among market participants by Taylor and Allen (1992) showed that 90% of respondents placed some weight in TA.

Brock et al. (1992) found that TA has a support in forecasting U.S. Dow Jones index. Lo, Mamaysky and Wang (2000) reviewed the literature and summarized that technical analysis rules can be effective to extract useful information from market prices. Technical analysis tests made by Academia provide slightly different results. Parisi and Vasquez (2000) have tested variable moving average (VMA) rules and concluded that VMA usage is profitable in Chile. On the other hand, Ratner and Leal (1999) found that these rules do not work in the same market. Bessembinder and Chan (1995) found that VMA short-term rules are profitable in Japan while later in 1999 Ratner and Leal (1999) made opposite conclusions. Ito (1999) test results imply that VMA rules add some value in Indonesia meantime Ratner and Leal (1999) state that they do not. Barkoulas et al. (2000) tested the model of an autoregressive fractionally integrated moving average in the Greek stock market and concluded that price movements are influenced by realizations from the recent past and the remote past. Bokhari et al. (2005) tested some smaller companies on UK indexes FTSE 100, FTSE 250 and FTSE Small Cap and concluded that in these markets the higher predictive ability of technical trading rules exists.

Metghalchi et al. (2007) concluded that technical trading rules have power to predict and they can be used to design a trading strategy in the Austrian stock market. Lonnbark and Soultanaeva (2009) were interested in studying whether technical trading rules are profitable on the Baltic stock markets and evaluated different VMA rules on index data from Vilnius, Riga and Tallinn markets and found that VMA rules exhibit no profitability when testing method accounts for dependence structure in the data. As the analysis of the literature on TA was made, it can be concluded that most authors make researches of the methods setting a goal of getting a profit by forecasting stock markets but not to predict their fluctuations. They place a lot of attention to the stock returns but not stock or index trends. Marshall et al. (2008) tested whether the relationship between a firm's industry and the profitability of TA exists and they have not found any substantiation. Kannan et al. (2010) implied that most common averages are 20, 30, 50, 100, and 200 days.

This study will find out whether these common averages are predictive in the Baltic stock market. Girdzijauskas et al. (2009) have found out that the exponential growth models are more suitable for the modeling processes in the near future. Exponential smoothing method is a part of both the quantitative decision making methods and TA and it can be described as the forecast method when the estimates are used in the weighted average of the values of the time series (Pabedinskaite 2007). Tillson (1998) advised to use specific smoothing Constant [alpha]:

[alpha] = 2/n + 1, (1)

where n is EMA number of days. For the markets signal forecast exponential smoothing is used:

[F.sub.t+1] = [alpha][Y.sub.t] + (1 - [alpha]) [F.sub.t], (2)

where [alpha] is smoothing Constant (0 < [alpha] < 1). In our case we modify (2) formula to calculate n day EMA:

[F.sub.t+1] = [alpha][Y.sub.t] + (1 - [alpha])[F.sub.t] = [F.sub.t] + [alpha]([Y.sub.t] - [F.sub.t]) = Ft + ([Y.sub.t] - [F.sub.t]). (3)

With the limitation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In this research we test particular case when n [member of] (2;100).

The selected forecast method--the EMA--efficiency is based on the forecast's accuracy level (Pilinkiene 2008). Makridakis et al. (1983) advised to use the following forecast accuracy measures: Mean Error (ME), Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Standard Deviation of Errors (SDE), Mean Percent Error (MPE), Mean Absolute, Percent Error (MAPE), etc. In our study we use MSE, MAD, MFE, MAPE and Tracking signal measures to evaluate the accuracy of the forecast trend (Table 1).

Every forecasting process is related to risk and is relevant to all stock market participants. Aniunas et al. (2009) emphasized that investors need to evaluate acceptable risk level during analysis of investment models and before making decisions. Different mathematical--statistical models are used to evaluate risk. Market risk evaluation needs to quantify the risk of losses and its volume due to movements in financial market variables (Jorion 2003). The investor can not precisely determine the real value of the investment. Higher risks mean the greater potential dispersion of the profitability. By 1960, the portfolio of management performance was measured mainly in accordance with the profitability achieved.

The concept of the risk has been known but investors did not know how to measure it quantitatively. Modern portfolio theory has shown investors how the risk can be quantified by the standard deviation of profitability. At the same time no quantitative measures related both profitability and risk. These factors were considered separately, i.e. investors are grouped into similar risk investment classes, according to the profitability of the standard deviation and then alternative investment return for only certain classes of risk is evaluated (Dzikevicius 2004). Smaller standard deviation means lower investment risk level and vice versa. Risk cannot be fully appreciated by standard deviation of returns (Peciulis, Siaudinis 1997). Risk is defined as the probability that the actual profit or return on investment will deviate from the expected size (Norvaisiene 2005). With the purpose to minimize risk, researchers use modern methods of statistics and probability theory. One of them is the Stock price correlation method described by Rutkauskas, Damasiene (2002). Correlation can be described as a parameter of some stochastic processes which are used to model variations in financial asset price. Financial asset prices exist now and are observed in the past but it is not possible to determine exactly what prices will be in the future. Correlation is a measure of co-movements between two return series (Alexander 2001). This method is relevant to indexes because if the correlation ratio is negative (R<0), the trend of total stocks (indexes) is linked to decrease compared to another (main) index. To select an appropriate investment tool, modern portfolio theory suggests using the Capital Assessment Pricing Model (further--the CAPM). The CAPM is one of the methods to calculate the profitability or the risks. The CAPM provides the link between each security and risk profitability. When in the market the equilibrium exists, the expected stock returns are proportional to systematic risk, which is inevitable even diversifying the portfolio. The relationship between the proposed securities and profitable systematic risk can be evaluated by the CAPM, proposed by William Sharpe in 1960.

Variable [beta] determines price changes of a stock or other security in the portfolio in comparison with the stock market prices. B coefficient indicates a systematic risk. In market countries [beta] is calculated on the assumption that the total financial asset portfolio is described by the various markets indexes (Gaidiene 1995). Using this methodology, the required yield is calculated on the basis of a risk indicator expressed in [beta]:

[k.sub.r(j)] = [k.sub.rf] + [[beta].sub.(j)] ([k.sub.M] - [k.sub.rf]), (9)

where [k.sub.r(j)] is preferred return rate of the j security, [k.sub.rf] is risk-free profit level, [[brta].sub.(j)] is beta coefficient representing the j security risk, [k.sub.M] is market return rate, [k.sub.M] - [k.sub.rf] is market risk premium.

According to this model, the desired rate of return is calculated as the risk-free rate of profit and risk premium, systematic assessment of security risk (Norvaisiene 2005). According to the CAPM, risk level of each index will be calculated using (3) formula and it will describe the systematic risk as OMXBBPI includes the same companies' stocks as industry indexes do and involves a part or each index risk.

The other method which is more complicated to identify the level of risk is the analysis of the distribution of index returns using Chi-Squared Test technique (Pukenas 2005):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

where: [O.sub.i]--current frequencies, [E.sub.i]--expected frequencies, k--the range of variables.

Calculated theoretical frequencies coincide with a number of empirical frequencies. From here there is a necessity to compare empirical frequencies and calculated or expected frequencies so that they would establish reliability or contingency of a divergence observed between them.

3. Description of the index and industries

Benchmark index (OMX Baltic Benchmark) is one of indexes of OMX Baltic index family. It is available in the Baltic region. The index consists of a portfolio of the largest in the capitalization and most liquid companies of shares traded on the OMX Baltic Stock exchanges. Company stock weight in the index depends on the company's stock market value and number of stock in the market, i.e. the index includes only the share capital, which circulates freely in the market. So it will be particularly useful for OMXBB investment products as controllers and comparative index for investors. For the Price index (PI) such as mentioned in the article, dividends are not evaluated (not deducted). Thus, the price index only reflects the constituent stock price movements.

[FIGURE 1 OMITTED]

The industry indexes cover the entire Baltic securities market. They are based on the GICS classification standard. GICS is an international classification created to meet investors' demand for more accurate, more comprehensive, standardized classification. Industry indexes indicate trends in the sector and allow comparing the same industry companies. The indexes include all Baltic Stock exchanges and the Official Secondary trading list of the companies. They are counted separately for each GICS sector.

In this research we use daily data and our sample includes stock market close prices of 11 indexes: OMX Baltic Benchmark PI (Baltic States) and all industry indexes (Table 2).

Information on local daily prices was found on the stock market's respective websites. We source data for the same periods. The data is for the 01/01/2000-30/12/2009 period.

In this stage of the research the hypothesis No. 1 (H1) arises: whether the industry index share of the basic composition of the index affects the strength of the relationship between industry index and index OMXBBPI.

For this purpose the share of each industry index was calculated (Fig. 1).

As it is seen in Fig. 1, Lithuanian companies predominate (51.61%) in OMXBBPI composition. Major part of the index consists of OMXB20PI Industrials (19.35%), OMXB25PI Consumer Discretionary (16.13%), OMXB10PI Energy (12.90%), OMXB15PI Financials and OMXB30PI Consumer Staples (each 12.90%). OMXBBPI is the most diversified by Lithuanian companies, and least by Latvian and Estonian.

Evaluated correlation ratio determines the relationship strength among all indexes (Table 3) and rejects the H1.

80% of the industry indexes have a link with the main OMXBBPI index (R > 0.9). A rather weak form of the relationship is with telecommunications sector index which is 0.6762, while the Information Technology index has opposite direction trend and the effect is very low in the basic index -0.2816. H1 must be rejected because the investigation revealed that different indexes, representing part of the same index OMXBBPI have different degrees of impact on the main index. For example, OMXPBI35, OMXB40PI and OMXB50PI each makes 6.45% of the OMXBBPI composition, but their correlation coefficients are -0.2816 and 0.9825 respectively. The relationship among index returns (Table 4) once again determines that H1 should be rejected.

In all cases the relationship is quite weak and indexes do not influence each other.

OMXB45PI and OMB55PI markets are more profitable but the risk level is high (Table 5). This proposition is based on standard deviation--0.0277 and 0.0222 respectively, while investment into OMXBBPI and OMB30PI index stocks generates less losses and lower profitability level--respectively 0.0110 and 0.0114 evaluating the return standard deviation. We have tested all indexes described in Section 2. In all cases p-value is higher than the significance level is, so there is no significant difference between the two methodologies for analysis: theoretical and empirical. [beta] parameter is the main indicator of the CAPM, it shows the systematic risk level. All tested indexes include systematic risk, only its level is different (Fig. 2). Non-systematic risk level varies from -0.005 to 0.0007, so it is nearly equal to zero. This means that nonsystematic risk does not exist. Investors take a greater level of the risk investing into B40PI (1.1783), B50PI (0.8745), B25PI (0.8008). The lower risk level is related to the investments into B30PI (0.3750), B45PI (0.3286) and B15PI (0.4225). So the research results imply that systematic risk exists in all industry stock markets, only the degree of risk varies. If to choose standard deviation as a risk measure, then using the highest level of the investment risk is taken in such markets as B40PI ([sigma] = 293940.02), B35PI ([sigma] = 188877.4195), B55PI ([sigma] = 121693.2415). The lowest value of the deviation which reflects the risk level are B15PI ([sigma] = 3438.9633), B50PI (415.7623). This difference can be explained by standard deviation and [beta] evaluation methodological difference because the first describes the fluctuation of index or return trend and it shows the common risk trends.

4. The results of forecasting using the EMA

This paper is focused on one of TA indicators--the exponential moving average rule (further--the EMA) and the possibility to use this method for market fluctuation signals. The methodology disassociates from particular buy-and-sell strategies and specific rules of application. It excludes transaction costs and fees, dividends are not paid (D = 0). In this stage of the research hypothesis No. 2 arises: whether the EMA has a predictable power on market fluctuation signals. Longer period of the EMA means higher bias level and less accurate forecast of prices but it does not mean that the EMA is not suitable to predict stock market fluctuations. All applied accuracy measures differ for forecasting industry indexes (Table 6). For specific indexes separate EMA lengths differ by forecasting accuracy level. This demonstrates MSE values. In particular markets this indicator provides lower or higher bias level.

MSE of forecasted values of B35PI and B40PI indexes are characterized by large swings. Wherewith the EMA is longer, MSE value is ipso facto higher. This tendency dominates in all markets. So it means that the Exponential Moving Average, which covers a longer period, generates more inaccurate value [F.sub.t]. The EMA provides the best results in B50PI market: [min.sub.MSE] = 0.1799, [max.sub.MSE] = 46.9391. This means that forecasted values are the closest to the actual ones and bias level is quite low in comparison with the other forecasted indexes.

MAD as a forecast accuracy measure implies that the EMA is suitable to forecast B50PI prices. Minimum and maximum values of MAD are the lowest compared to the other indexes.

MFE for P50PI is nearly equal to zero with the higher constant level and is equal to 1.0234 when n = 100. Although telecommunication industry stocks have the smallest share in OMBBPI structure, this index forecasts were the most accurate.

Trying to determine whether the selected forecasting method has a systematic bias, the Mean Forecasting Error was evaluated. Inasmuch as the MSE value of B15PI index forecast is 0.0013 and nearly zero, then the systematic bias does not exist. There are some negative average values of MSE in tested markets which indicate that in OMBBPI index stock market the forecasted values are being overvalued. This fact can be explained by correlation ratio among OMXBBPI and industry indexes. In all cases the relationship strength between n parameter and forecast accuracy measures such as MSE, MAD, MFE, MAPE is strong (R>0.97) (Table 7). If R>0.9 then values of related indexes are overvalued. The least overvalued (or not overvalued) are such indexes as OMXB15PI (R = 0.8782), OMXB45PI (R = -0.2816) and OMXB50PI (R = 0.6762). It leads to a conclusion that in all markets except OMXB15PI, OMXB45PI and OMXB50PI systematic errors exist in forecasting the stock prices using the EMA.

Since the time series values are quite high, the MAPE was assessed. This method highlights a part of systematic error comparing with the whole time series. In all cases MAPE is [member of] (0;1). The longer period influences the EMA is covering, the higher MAPE is. This trend is confirmed in all markets, only the degree of precision varies from 97.94% to 99.83%.

The graphical and bias analysis showed that the EMA is suitable to predict market fluctuations so H2 is accepted.

The hypothesis No. 3 arises after H2 is accepted: which period EMA helps to generate market fluctuations signals? Tracking signal (further TS) is a suitable method to control forecast accuracy and to find out exclusive EMA periods to predict market fluctuations. Using this method it was noticed that TS changes its trend when a specific EMA is applied (Table 7).

During the research it appeared that only certain period EMA can forecast the stock market fluctuations. There are common periods of EMA for each index: 48, 49, 50 days; 92, 93, 94 days. Every index needs some groups of additional period EMA.

To determine whether these EMAs work it is necessary to perform graphical analysis (Fig. 3). The analysis shows that when EMA value is higher than the real index value, index has a trend to fall down and vice versa, lower EMA value is related to the market growth. The largest OMX stock market fluctuations such as financial crisis of 2008-2009 are as a result of all forecasted the majority of different periods of EMA intersections. In this context a new problem arises: whether a mix of technical and functional analysis is a powerful tool to predict financial market bubbles. The research of the issue will be provided in a new study based on fundamental analysis issues and its further comparison with previous studies.

The EMA forecast results of the Baltic States stock market show the main trends of market development and investors' activity.

5. Empirical results and conclusions

This study is the first academia research of technical analysis usage to predict the stock market fluctuations for OMX Baltic Benchmark Index and Industrial indexes using exponential smoothing method. A significant part of semiprofessional traders use technical analysis as a method to forecast stock prices, but no researches in the Baltic States confirmed or refused the statistical validity of this method usage for predicting strong stock market fluctuations too.

EMA method is relevant to forecast stock market fluctuations of OMX index in the Baltic States. The research claims that for each index an appropriate EMA length should be found. So, it is 48-50, 48-70, 72-74, 92-94 days. The length differs from the EMA length mentioned in previous researches made by Academia on the global level. The correlation analysis showed that all industrial indexes mentioned in this study except OMXBPI45 have a strong dependence on the main OMX index.

As Lithuanian companies are predominant (51.61%) in OMXBBPI composition, in-depth analysis of Lithuanian companies' performance should be involved in evaluating the stock market conditions and predicting trends and fluctuations. 80% of the industrial indexes have a link with the main OMXBBPI index (R > 0.9) so industry analysis should be also involved in the analysis trying to predict further stock market development scenario. OMXB45PI and OMB55PI markets are most risky and this proposition is based on standard deviation--0.0277 and 0.0222 while OMXBBPI and OMB30PI are the least risky--0.0110 and 0.0114 respectively, evaluating the return standard deviation. Due to the risk level all forces which had an impact on these indexes should be identified. In all cases p-value is higher than the significance level is, so there is no significant difference between the two methodologies for analysis: theoretical and empirical.

[beta] parameter is the main indicator of CAPM and displays the systematic risk level. All tested indexes include systematic risk, only its level is different. Non-systematic risk level varies from -0.005 to 0.0007 and it is about zero. This means that non-systematic risk does not exist.

[FIGURE 3 OMITTED]

The most risky indexes are B40PI (1.1783), B50PI (0.8745), B25PI (0.8008). The least risky indexes are (B30PI), B45PI (0.3286) and B15PI (0.4225). So the research result is simply that systematic risk exists in all industry stock markets, only the degree of risk is various.

In all cases the relationship strength between n parameter and forecast accuracy measures such as MSE, MAD, MFE, MAPE is strong (R>0.97). The longer EMA means higher bias level and less accurate forecast to predict prices, but it does not mean that EMA is not suitable to predict stock market fluctuations.

The suggestion to use EMA method instead of SMA method (see previous studies of Dzikevicius, Saranda, Kravcionok 2010) was confirmed once again by descriptive statistics in each case. If the standard deviation reflects the risk of the index, it means that EMA method is less risky to use for estimating absolute error level.

It seems that EMA method is more suitable to predict stock market fluctuations rather than short moving average.

Summarizing the study, exponential smoothing method is appropriate to indicate the fluctuations of stock markets in OMX Baltic Benchmark index market. It should be noted that during the research it provided the closest forecast values to the real index values because the higher weight is ensured to real historical prices of the previous day.

Received 23 August 2010; accepted 26 October 2010

References

Alexander, C. 2001. Market Models: A Guide to Financial Data Analysis. New York: John Wiley & Sons.

Aniunas, P.; Nedzveckas, J.; Krusinskas, R. 2009. Variance--covariance risk value model for currency market, Inzinerine Ekonomika--Engineering Economics 1(161): 18-27.

Barkoulas, J. T.; Baum, C. F.; Travlos, N. 2000. Long Memory in the Greek Stock Market, Applied Financial Economics 2(10): 177-184. doi:10.1080/096031000331815

Bessembinder, H.; Chan, K. 1995. The profitability of technical trading rules in the Asian stock markets, Pacific-Basin Finance Journal 3: 257-284. doi:10.1016/0927-538X(95)00002-3

Bokhari, J.; Cai, C.; Hudson, R.; Keasey, K. 2005. The predictive ability and profitability of technical trading rules: does company size matter?, Economics Letters 86: 21-27. doi:10.1016/j.econlet.2004.03.037

Brock, W.; Lakonishock, J.; LeBaron, B. 1992. Simple technical trading rules and the stochastic properties of stock returns, Journal of Finance 47: 1731-1764. doi:10.2307/2328994

Caginalp, G.; Balenovich, D. 2003. A theoretical foundation for technical analysis, Journal of Technical Analysis 59: 5-22.

Dudzeviciute, G. 2004. Vertybiniu popieriu portfelio sudarymas ir vertinimas [Securities portfolio construction and evaluation], Verslas: teorija ir praktika [Business: Theory and Practice] 5(3): 116-124.

Dzikevicius, A. 2004. Vertinimo, koreguoto pagal rizika, metodiku palyginamoji analize, Vagos 64(17): 97-103.

Dzikevicius, A.; Zamzickas, M. 2009. An Overview of Financial Crisis in U.S., Economics and Management 14: 166-172.

Dzikevicius, A.; Saranda, S.; Kravcionok, A. 2010. The accuracy of simple trading rules in stock markets, Economics and Management 15: 910-916.

Edwards, R.; Magee, J. 1992. Technical Analysis of Stock Trends. New York: New York Institute of Finance.

Gaidiene, Z. 1995. Finansu valdymas [Finance management]. Kaunas: Pasaulio lietuviu kulturos, mokslo ir svietimo centras.

Girdzijauskas, S., et al. 2009. Ekonominiu burbulu susidarymas ir galimybes ju isvengti [Formation of economic bubbles: causes and possible preventions], Technological and Economic Development of Economy 15(2): 267-280. doi:10.3846/1392-8619.2009.15.267-280

Ito, A. 1999. Profits on technical trading rules and time-varying expected returns: Evidence from Pacific-Basin equity markets, Pacific-Basin Finance Journal 7(3/4): 283-330. doi:10.1016/S0927-538X(99)00008-6

Jorion, P. 2003. Financial risk management. New York: John Wiley & Sons.

Juozaitiene, L. 2007. Imones finansai: analize ir valdymas [Corporate finance: analysis and management]. Siauliai: Siauliu universiteto leidykla.

Jureviciene, D. 2008. Asmeniniu finansu pagrindai [Personal finance basics]. Vilnius: Technika.

Kannan, K. S.; Sekar, P. S.; Sathik, M. M.; Arumugam, P. 2010. Financial Stock Market Forecast using Data Mining Techniques, International Multi Conference of Engineers and Computer Scientists 1: 555-559.

Klimaviciene, A.; Jureviciene, D. 2007. Asmens investiciju i finansines priemones pletros galimybes Lietuvoje [Personal investment in the financial arrangements for the development possibilities in Lithuania], Verslas: teorija ir praktika [Business: Theory and Practice] 8(1): 33-43.

Lo, A. W.; Mamaysky, H.; Wang, J. 2000. Foundations of technical analysis: computational algorithms, statistical inference, and empirical implementation, Journal of Finance 55(4): 1705-1765. doi:10.1111/0022-1082.00265

Lonnbark, C.; Soultanaeva, A. 2009. Profitability of technical trading rules on the Baltic stock markets, Umea Economic Studies 761: 1-5.

Marshall, B. R.; Qian, S.; Young, M. 2008. Is Technical Analysis Profitable On U.S. Stocks With Certain Size, Liquidity Or Industry Characteristics?, Applied Financial Economics 19(15): 1213-1221. doi:10.1080/09603100802446591

Makridakis, S. G.; Wheelwright, S. C.; Hyndman, R. J. 1998. Forecasting: Methods and Application. 3rd ed. New York: John Wiley & Sons.

Metghalchi, M.; Glasure, Y.; Garza-Gomez, X.; Chen, C. 2007. Profitable technical trading rules for the Austrian stock market, International Business & Economics Research Journal 9(6): 49-58.

Mizrach, B.; Weerts, S. 2007. Highs and lows: a behavioural and technical analysis, Applied Economics 19: 767-777.

Myers, T. 1989. The Technical Analysis Course. Chicago: Probus.

Norvaisiene, R. 2005. Imones investiciju valdymas [Enterprise investment management]. Kaunas: Technologija.

Pabedinskaite, A. 2006. Kiekybiniai sprendimu metodai. Koreliacine regresine analize. Prognozavimas [Quantitative decision making methods. Forecasting]. Vilnius: Technika.

Parisi, F.; Vasquez, A. 2000. Simple technical trading rules of stock returns: Evidence from 1987 to 1998 in Chile, Emerging Markets Review 1: 152-164. doi:10.1016/S1566-0141(00)00006-6

Peciulis, S.; Siaudinis, S. 1997. Ivadas i vertybiniu popieriu rinka [Introduction to the stock market]. Vilnius: Lietuvos bankininkystes, draudimo ir finansu institutas.

Pilinkiene, V. 2008. Selection of Market Demand Forecast Methods: Criteria and Application, Inzinerine Ekonomika--Engineering Economics 3(58): 19-25.

Pring, M. 1993. Martin Pring on Market Momentum. Gloucester: Probus Professional Pub.

Pukenas, K. 2005. Sport research data analysis with SPSS program. Kaunas: Lietuvos kuno kulturos akademija.

Racickas, E.; Vasiliauskaite, A. 2010. Global financial crisis and its impact on Lithuanian economy, Management and Economics 15: 1006-1017.

Ratner, M.; Leal, R. 1999. Tests of technical trading strategies in the emerging equity markets of Latin America and Asia, Journal of Banking and Finance 23(12): 1887-1905. doi:10.1016/S0378-4266(99)00042-4

Rutkauskas, A. V.; Damasiene, V. 2002. Finansu valdymas [Finance management]. Siauliai: Siauliu universiteto leidykla.

Rutkauskas, A. V.; Martinkute, R. 2007. Investiciju portfelio anatomija ir valdymas [Investment portfolio anatomy and management]. Vilnius: Technika. doi:10.3846/1371-M

Taylor, M. P.; Allen, H. 1992. The use of technical analysis in the foreign exchange market, Journal of International Money and Finance 11: 304-314. doi:10.1016/0261-5606(92)90048-3

Tillson, T. 1998. Smoothing techniques for more accurate signals, Stocks & Commodities 16(1): 33-37.

Audrius Dzikevicius (1), Svetlana Saranda (2)

Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223 Vilnius, Lithuania E-mails: (1) Audrius.Dzikevicius@vgtu.lt; (2) 20055868@vgtu.lt

Audrius Dzikevicius (1), Svetlana Saranda (2)

Vilniaus Gedimino technikos universitetas, Sauletekio al. 11, LT-10223 Vilnius, Lietuva El. pastas: (1)Audrius.Dzikevicius@vgtu.lt; (2)20055868@vgtu.lt

Iteikta 2010-08-23; priimta 2010-10-26

AUDRIUS DZIKEVICIUS. Associate Professor at the Department of Finance Engineering of VGTU, defended a doctoral Dissertation "Trading Portfolio Risk Management in Banking" (2006) and was awarded the degree of Doctor in Social Sciences (Economics). In 2007 he started to work as an associate professor at the Department of Finance Engineering of VGTU. His research interests cover the following items: portfolio risk management, forecasting and modelling of financial markets, valuing a business using quantitative techniques.

SVETLANA SARANDA was awarded Office Financial Management (the branch of study program) Bachelor's degree in 2009. Final Thesis on the investment issue "Optimal Investment Portfolio Formation in OMX Stock Exchange" was awarded the highest mark. At the moment Saranda continues the research on market forecasting possibilities issue. The research interests cover the following items: investments, forecasting and modelling of financial markets, securities portfolio formation and management.

Table 1. Forecast Accuracy Measures

Forecast Accuracy Measure   Formula

Mean Square       MSE       MSE = [SIGMA] ([F.sub.t] -
Error                       [Y.sub.t]).sup.2]/n (4)

Mean Absolute     MAD       MAD = [SIGMA] [F.sub.t] -
Deviation                   [Y.sub.t]/n (4)

Mean Forecast     MFE       MAD = [SIGMA] [F.sub.t] -
Error                       [Y.sub.t]/n (5)

Mean Absolute     MAPE      MFE = [SIGMA] [F.sub.t] -
Percentage Error            [Y.sub.t]/n (6)

Tracking Signal   TS        MAPE = 1/n [SIGMA]|[F.sub.t] -
                            [Y.sub.t]/[Y.sub.t]|

Forecast Accuracy        Description
Measure

Mean Square              For as much any error is being raised with
Error                    the square. So this way highlights the
                         significant error values. This feature is
                         quite significant because forecasting methods
                         with approximations of bias are frequently
                         more suitable than the method which gives not
                         only negligible errors but significant.

Mean Absolute            It is similar to standard deviation but the
Deviation                formula of estimation is less difficult to
                         apply for time series. The usage is advisable
                         when the forecast bias must be estimated using
                         the same evaluation units as forecast factor
                         is evaluated.

Mean Forecast            Very often it is very important to estimate
Error                    whether the forecast method has a systematic
                         error i.e. the present forecast value is
                         always major (or minor) than time series
                         value. In this case the mean forecast error
                         is being used. If the systematic bias does
                         not exist the MFE value will be equal to zero.
                         If the forecast value is signally negative the
                         forecast method overestimates trend series.
                         If the systematic bias is signally positive
                         the forecast method generates major values
                         than time series.

Mean Absolute            The Mean Absolute Percentage Error is useful
Percentage Error         when assessing the forecast error an important
                         factor is the estimated value. MAPE estimates
                         the size of bias comparing with time series
                         values. This fact is very important when the
                         times series value is quite large.

Tracking Signal          Tracking signal is the method to control the
                         forecast accuracy. New data is compared with
                         forecast time series and adequacy is
                         evaluated.

Table 2. Forecast objects

OMX Baltic Index Group

OMX Baltic Benchmark    OMX Baltic Energy       OMX Baltic Materials
PI

OMXBBPI                 OMXB10PI                OMXB15PI

OMX Baltic Benchmark    OMX Baltic Health       OMX Baltic Financials
PI                      Care

OMXBBPI                 OMXB35PI                OMXB40PI

OMX Baltic Industrials  OMX Baltic Consumer     OMX Baltic Consumer
                        Discretionary           Staples

OMXB20PI                OMXB25PI                OMXB30PI

OMX Baltic Informa-     OMX Baltic Telecommu-   OMX Baltic
tion Technology         nication Services       Utilities

OMXB45PI                OMXB50PI                OMXB55PI

Table 3. The relationship between OMXBBPI and industry indexes and
their share (%)

                       OMXBBPI correlation    % share in the index
                              ratio

OMXB10PI                      0.9680                 12.90%
OMXB15PI                      0.8782                 12.90%
OMXB20PI                      0.9754                 19.35%
OMXB25PI                      0.9737                  3.23%
OMXB30PI                      0.9706                 12.90%
OMXB35PI                      0.9155                  6.45%
OMXB40PI                      0.9825                  6.45%
OMXB45PI                     -0.2816                  6.45%
OMXB50PI                      0.6762                  3.23%
OMXB55PI                      0.9186                 16.13%
Correlation ratio             0.3074                     --

Table 4. Index returns' correlation ratios

          OMX       B10PI     B15PI     B20PI

OMX       1.0000
B10PI     0.4011    1.0000
B15PI     0.2520    0.2046    1.0000
B20PI     0.6004    0.2359    0.1932    1.0000
B25PI     0.6336    0.2604    0.2180    0.4781
B30PI     0.3617    0.2093    0.2202    0.2828
B35PI     0.2612    0.1826    0.1440    0.1760
B40PI     0.7262    0.3074    0.2221    0.3616
B45PI     0.1305    0.1102    0.1056    0.1312
B50PI     0.6613    0.1767    0.1256    0.3131
B55PI     0.2789    0.1794    0.1227    0.1713

          B25PI     B30PI     B35PI     B40PI

OMX
B10PI
B15PI
B20PI
B25PI     1.0000
B30PI     0.3446    1.0000
B35PI     0.2162    0.1960    1.0000
B40PI     0.4468    0.2733    0.2477    1.0000
B45PI     0.1002    0.1277    0.0856    0.1227
B50PI     0.3356    0.1761    0.1092    0.3205
B55PI     0.1998    0.1841    0.1207    0.1876

          B45PI     B50PI     B55PI

OMX
B10PI
B15PI
B20PI
B25PI
B30PI
B35PI
B40PI
B45PI     1.0000
B50PI     0.0523    1.0000
B55PI     0.0561    0.1894    1.0000

Table 5. Index returns' descriptive statistics

Statistics                 x           min           max            CT

OMX                    0.04%        -8.44%         9.38%        0.0110
B10PI                  0.05%       -16.56%        12.22%        0.0160
B15PI                  0.01%       -12.68%        16.37%        0.0185
B20PI                  0.03%        -8.51%        10.10%        0.0144
B25PI                  0.04%       -11.17%         9.83%        0.0139
B30PI                  0.03%        -6.31%        12.81%        0.0114
B35PI                  0.09%       -42.86%        12.31%        0.0215
B40PI                  0.07%       -12.94%        14.08%        0.0178
B45PI                 -0.04%       -29.99%        37.04%        0.0277
B50PI                  0.00%       -11.04%        25.34%        0.0145
B55PI                  0.09%       -56.56%        19.91%        0.0222

Statistics    [[sigma].sup.2]     Skewness      Kurtosis

OMX                   0.0001        0.1091       120.109
B10PI                 0.0003       -0.4763       116.504
B15PI                 0.0003        0.3868        90.592
B20PI                 0.0002       -0.1975        46.610
B25PI                 0.0002       -0.2786        85.154
B30PI                 0.0001        0.4813       118.122
B35PI                 0.0005       -42.383       808.476
B40PI                 0.0003        0.2294       141.020
B45PI                 0.0008        0.9122       263.344
B50PI                 0.0002        22.017       455.150
B55PI                 0.0005       -56.995     1.743.122

Table 6. Accuracy measures

Index              MSE

                   Min          Max            R

OMXBBPI         1.6621    1225.7970       0.9930
OMXB10PI        3.0194    1126.2233       0.9976
OMXB15PI        0.6544     255.9466       0.9959
OMXB20PI        1.6067    1018.8959       0.9944
OMXB25PI        6.0231    4102.9815       0.9924
OMXB30PI        1.1114     768.3996       0.9941
OMXB35PI       32.3703    12511.1941      0.9979
OMXB40PI       23.3740    14266.0530      0.9950
OMXB45PI        1.7379     533.0337       0.9973
OMXB50PI        0.1799      46.9391       0.9972
OMXB55PI       14.3340    4076.4000       0.9978

Index              MAD

                   Min          Max            R

OMXBBPI         8.7018     268.7274       0.9948
OMXB10PI       10.3737     234.3422       0.9909
OMXB15PI       13.5605     325.8130       0.9940
OMXB20PI       13.0732     373.7323       0.9957
OMXB25PI       14.0097     429.6435       0.9966
OMXB30PI        9.2630     245.0824       0.9934
OMXB35PI       12.4236     344.9284       0.9953
OMXB40PI       15.4866     455.2855       0.9966
OMXB45PI      131.1743    2914.7334       0.9927
OMXB50PI        8.8081     172.3010       0.9741
OMXB55PI        8.9603     196.4084       0.9905

Index              MFE

                   Min          Max            R

OMXBBPI        -1.9284      -0.0230      -0.9961
OMXB10PI       -2.9640      -0.0302      -0.9983
OMXB15PI        0.0013       0.3593       0.9568
OMXB20PI       -0.5268      -0.0088      -0.9589
OMXB25PI       -2.2898      -0.0263      -0.9980
OMXB30PI       -1.4507      -0.0165      -0.9952
OMXB35PI       -7.7225      -0.0783      -0.9996
OMXB40PI       -5.6418      -0.0606      -0.9996
OMXB45PI        0.0167       1.3688       0.9935
OMXB50PI        0.0061       1.0234       0.9895
OMXB55PI       -9.1658      -0.0873      -0.9999

Index             MAPE

                   Min          Max            R

OMXBBPI         0.0026       0.0785       0.9946
OMXB10PI        0.0037       0.0798       0.9881
OMXB15PI        0.0041       0.1111       0.9964
OMXB20PI        0.0036       0.1060       0.9972
OMXB25PI        0.0033       0.1047       0.9983
OMXB30PI        0.0027       0.0742       0.9964
OMXB35PI        0.0045       0.1137       0.9963
OMXB40PI        0.0039       0.1246       0.9982
OMXB45PI        0.0054       0.1374       0.9968
OMXB50PI        0.0032       0.0665       0.9794
OMXB55PI        0.0042       0.0923       0.9930

Table 7. Specific EMA n periods

OMX            Length     Value      Length     Value

[DELTA] n-1    48         16.8919    72         17.9785
n              49         17.8924    73         18.3045
[DELTA] n+1    50         17.0239    74         18.0503

B10            Length     Value      Length     Value
[DELTA] n-1    48         26.3956    72         29.7238
n              49         27.4999    73         30.1584
[DELTA] n+1    50         26.7611    74         29.9486

B15            Length     Value      Length     Value
[DELTA] n-1    48         -1.2942    72         -1.6810
n              49         -0.5737    73         -1.5041
[DELTA] n+1    50         -1.3271    74         -1.6611

B20            Length     Value      Length     Value
[DELTA] n-1    48         3.9030     72         3.8013
n              49         4.5725     73         4.0022
[DELTA] n+1    50         3.9164     74         3.7921

B25            Length     Value      Length     Value
[DELTA] n-1    48         12.9816    72         13.2992
n              49         12.4433    73         13.4938
[DELTA] n+1    50         12.4940    74         13.3594

B30            Length     Value      Length     Value
[DELTA] n-1    48         -0.8090    72         -1.0331
n              49         -0.7337    73         -1.0938
[DELTA] n+1    50         -0.8259    74         -1.0489

B35            Length     Value      Length     Value
[DELTA] n-1    48         48.5003    72         53.5490
n              49         49.4215    73         53.8904
[DELTA] n+1    50         49.0251    74         53.8399

B40            Length     Value      Length     Value
[DELTA] n-1    48         27.4799    72         30.4082
n              49         28.1769    73         30.6541
[DELTA] n+1    50         27.8325    74         30.5571

B45            Length     Value      Length     Value
[DELTA] n-1    48         27.4799    72         30.4082
n              49         28.1769    73         30.6541
[DELTA] n+1    50         27.8325    74         30.5571

B50            Length     Value      Length     Value
[DELTA] n-1    48         -7.7923    72         -11.6259
n              49         -6.5802    73         -11.3281
[DELTA] n+1    50         -8.1394    74         -11.8352

B55            Length     Value      Length     Value
[DELTA] n-1    48         91.1323
n              49         92.8870
[DELTA] n+1    50         92.6323

OMX            Length     Value      Length     Value

[DELTA] n-1    92         18.5585    68         17.8225
n              93         16.7860    69         17.5205
[DELTA] n+1    94         17.0941    70         17.9050

B10            Length     Value      Length     Value
[DELTA] n-1    92         31.7560    68         29.2435
n              93         29.9830    69         28.9133
[DELTA] n+1    94         30.3801    70         29.4855

B15            Length     Value      Length     Value
[DELTA] n-1    92         -1.6872    68         -1.6458
n              93         -2.9569    69         -1.8497
[DELTA] n+1    94         -2.7588    70         -1.6735

B20            Length     Value      Length     Value
[DELTA] n-1    92         3.6671     54         3.9257
n              93         2.4339     55         3.9262
[DELTA] n+1    94         2.6372     56         3.9250

B25            Length     Value
[DELTA] n-1    92         13.6572
n              93         12.6594
[DELTA] n+1    94         12.8315

B30            Length     Value
[DELTA] n-1    92         -1.1431
n              93         -1.2483
[DELTA] n+1    94         -1.2375

B35            Length     Value
[DELTA] n-1    92         56.4880
n              93         55.6796
[DELTA] n+1    94         55.9748

B40            Length     Value
[DELTA] n-1    92         31.5226
n              93         30.5253
[DELTA] n+1    94         30.7368

B45            Length     Value      Length     Value
[DELTA] n-1    92         31.5226    39         -0.7431
n              93         30.5253    40         -0.6832
[DELTA] n+1    94         30.7368    41         -0.7549

B50            Length     Value
[DELTA] n-1    92         -13.1034
n              93         -15.3713
[DELTA] n+1    94         -15.0900

B55            Length     Value
[DELTA] n-1    92         116.1590
n              93         116.5919
[DELTA] n+1    94         115.1471

OMX

[DELTA] n-1
n
[DELTA] n+1
B10
[DELTA] n-1
n
[DELTA] n+1

B15            Length     Value
[DELTA] n-1    81         -1.6277
n              82         -1.6258
[DELTA] n+1    83         -1.6280
B20
[DELTA] n-1
n
[DELTA] n+1
B25
[DELTA] n-1
n
[DELTA] n+1
B30
[DELTA] n-1
n
[DELTA] n+1
B35
[DELTA] n-1
n
[DELTA] n+1
B40
[DELTA] n-1
n
[DELTA] n+1
B45
[DELTA] n-1
n
[DELTA] n+1
B50
[DELTA] n-1
n
[DELTA] n+1
B55
[DELTA] n-1
n
[DELTA] n+1

Fig. 2. Index [beta] coefficient values (risk evaluation)

B10Pl            0.5836
B15Pl            0.4255
B20Pl            0.7855
B25Pl            0.8008
B30Pl            0.3750
B35Pl            0.5116
B40Pl            1.1783
B45Pl            0.3286
B50Pl            0.8745
B55Pl            0.5635

Note: Table made from bar graph.