# Construction and evaluation of trading systems: Warsaw index futures.

AbstractThis paper presents and compares 15 trading systems constructed for the Warsaw Stock Exchange futures contracts. These trading systems are constructed applying technical analysis and artificial neural networks (ANN). The efficiency of constructed trading systems is measured by the profit, which could be gained on the analyzed market when an investor uses various methods of buy and sell signals generating. Investigation is conducted for daily observations of stock index WIG20 futures from December 1, 1999 to November 28, 2003. The conclusion is that the combination of the technical analysis and artificial intelligence in order to gain profit from trading on the Polish futures market can bring much better investment results than trade in the traditional way. (JEL G10, C45)

Introduction

The stock exchange market in Poland was created from scratch after the political system transformation. The Warsaw Stock Exchange (WSE) started operation in 1991 with five companies listed. The Polish derivatives market came into existence recently, as the first futures were launched in 1998. The law frames for short sale trading of stock was just set in 2003. Before that it was impossible to make short sales on the Warsaw Stock Exchange. This, of course, did not refer to financial futures, which have been present on the WSE since 1998.

Investors apply different strategies either to maximize profit (or rate of return) or to minimize risk of loss (or probability of loss). These strategies are constructed using a great variety of quantitative methods. The question is to what extent can these methods be applied to financial markets to gain profit? To answer this question, it is necessary to test different trading systems using actual data. The future contracts are chosen to analyze the possibility of making profits not only when the prices increase but also when they decrease.

The exact forecast of prices on the stock exchange would allow earning without any risk and losses. However, most of the available prices forecasting methods, such as econometric models or artificial neural networks, give the outcomes that are of a mostly inaccurate. Therefore, relying on the indication of such forecasts is still very risky and can increase losses. Hence, the concept of reducing the inaccuracy of forecasts by filtering them, in a sense, through investment strategies, in particular by the technical analysis, are indicators that the trading systems are based on.

Thus, the aim of the paper is to answer the question of whether including the ANN forecasts of stock market prices to trading systems makes them more efficient and whether this kind of combination is more profitable than investing based only on the forecast indications.

Materials and Methods

In the research, technical analysis and neural nets are used to construct trading systems. Numerous authors recommend both methods. Technical analysis is widely described in literature by Murphy [1999] and Schwager [1997]. Neural network applications for financial markets have been discussed by Azoff [1994], Bosarge [1993, pp. 371-402], Chen [1994, pp. 1199-202], Dutta and Shekhar [1993, pp. 257-73], Gately [1995], Goonatilake and Treleaven [1995], Hawley et al. [1993, pp. 27-46), Hoptroff [1993, pp. 59-66], Hsieg [1993, pp. 12-5], Lowe [1994, pp. 3623-28], Refenes [1995], and Witkowska [2002].

Technical analysis comes from the assumption that stock price is set by the intersection of supply and demand, and an investor can make money by frequently buying and selling stocks. A technical analyst does not look at income statements, balance sheets, company policies, or anything fundamental about the company. The technician looks at the actual history of trading and price in a security or index. This is usually done in the form of a chart. The security can be a stock, future, index, or a sector. It is flexible enough to work on anything that is traded in the financial markets.

The technical analyst believes that the market price reflects all known information about the individual security. It includes all public and insider information. The market price reflects all the different investor opinions regarding that security. Securities move in trends, and these trends continue until something happens to change the trend.

Technical analysis indicators are used to determine the trend of a market, the strength of the market, and the direction of the market. Some technical analysis indicators can be quantified in the form of an equation or algorithm. Others can show up as patterns (e.g., head and shoulders, trend lines, support, and resistance levels). At some point, the technical analyst will receive a signal. This signal is the result of one technical analysis indicator or a combination of two or more indicators. The signal indicates to the technical analyst a course of action whether to buy, sell, or hold.

Artificial neural networks are information transforming systems which structure and function are motivated by the cognitive progress and organizational structure of neuro-biological systems. The basic components of the networks are highly interconnected processing elements called neurons, which work independently in parallel. Synaptic connections (weights) are used to carry messages from one neuron to another. Thus, neural nets are non-linear models which parameters (weights) are estimated during so-called training procedures. There are two main methods of ANN training: supervised and unsupervised. In the research, the authors apply the back propagation algorithm (supervised learning) to generate prices that are employed in the trading system.

Data

The trading systems are constructed for the index futures. The underlying instrument of this contract is the stock index WIG20, which calculates for 20 companies of the highest capitalization and volume on the Warsaw Stock Exchange. At this moment, the Warsaw Stock Exchange has index futures, currency futures, and individual stock futures, but WIG20 futures allow a trader to be present in the market during increasing trends, as well as decreasing trends. Investigation is conducted for daily observations from December 1, 1999 to November 28, 2003. Tests include the following series of WIG20 futures: FW20H0, FW20M0, FW20U0, FW20Z0, FW20H1, FW20M1, FW20U1, FW20Z1, FW20H2, FW20M2, FW20U2, FW20Z2, FW20H3, FW20M3, FW20U3, FW20Z3. All the series are joined into the continuous, spread-adjusted futures as it is described by Schwager [1997, pp. 245-6, 664-9].

In addition, observations of DAX, DJIA, NIKKEI and exchange rates of EURO/PLN (PLN-Polish zloty), and USD/PLN are employed.

Construction of Trading System

In order to analyze the impact of the forecast application on efficiency of the technical trading rules, the same investing systems will be tested out in three different ways. The first one includes the perfect forecast, i.e. the next session close prices (it is assumed that future prices are known by the investor). The second way covers the analysis of the next session prices predicted by artificial neural networks. The third one refers to the analysis of prices in the past, not their forecasts. All three solutions will deal with the same methods of trading decision making that are based on the technical analysis indicators, such as moving averages, Bollinger bands, oscillators, or breakouts. The following is a description of each.

1) Channel breakout -- buy signal: long position for the next day open if the predicted next day close price is higher than the maximal price from the last five days; sell signal: short position for the next day open if the predicted next day close price is smaller than the minimal price from the last five days; out of the market signal: if the predicted next day close price does not fulfill any of these conditions.

2) Bollinger bands -- buy signal: long position for the next day open, if the predicted next day close price is higher than the upper Bollinger band line; sell signal: short position for the next day open if the predicted next day close price is smaller than the lower Bollinger band line; out of the market signal: if the predicted next day close price does not fulfill any of these conditions.

UL = MA(n) + k * [square root of ([[n.summation over (i=1)] ([C.sub.i] - MA(n))[.sup.2]]/n)],

LL = MA(n) - k * [square root of ([[n.summation over (i=1)] ([C.sub.i] - MA(n))[.sup.2]]/n)] (1)

where UL is the upper Bollinger band line, LL is the lower Bollinger band line, MA(n) is the moving average from the last n sessions, C is the close price, and k is the parameter that describes the distance between the upper line and lower line from the moving average.

3) Momentum oscillator -- buy signal: long position for the next day open if the predicted next day close price is higher than the close price before five days (momentum oscillator is above zero); sell signal: short position for the next day open if the predicted next day close price is smaller than the close price before five days (momentum oscillator is below zero); out of the market signal: signal does not occur.

M = C - [C.sub.n] (2)

where C is the next day close price and [C.sub.n] is the close price before n days.

4) Moving averages -- buy signal: long position for the next day open, if MA3 crosses up MA15 (both moving averages include the predicted next day close price); sell signal: short position for the next day open if MA3 crosses down MA15; out of the market signal: signal does not occur.

MA(n) = [[n.summation over (i=1)] [C.sub.i]]/n (3)

Additionally, to compare the results, an investment without trading rules is also tested. The buy signal occurs when the predicted next day close price is higher than the present-day close price. The sell signal occurs when the predicted next day close price is lower than the present-day close price.

To summarize, one may say that there are five methods of buy-sell signals generating (moving average, Bollinger band, oscillator, breakout, and "no system method"), and three types of input information: perfect forecasts, i.e. actual future close prices, forecasts of close prices estimated applying neural nets, and past close prices. A combination of five methods and three types of input information will make 15 trading systems, which are the subject of the next part of the paper.

Calculation of Forecasts

From the investor's point of view, the longer forecast horizon the better. However, the research shows that prediction error usually increases with the lengthening of the forecast horizon. Therefore, in the investigation, one session ahead of forecasts is applied.

There are many methods of obtaining a security or derivative price forecasts. The most popular are: econometric models, deterministic chaos models, models based on stochastic process theory such as ARIMA and (G)ARCH models, as well as artificial neural networks and related methods. Examples of applying these methods to stock price prediction are discussed by Beinsen and Kuhrer [1999], Kohara et al. [1996, pp. 142-8], Papla and Jajuga [1998, pp. 5-16], Refenes et al. [1994, pp. 375-88], White [1993, pp. 315-48], and Witkowska [2002].

In the research, the forecasts of prices are estimated using the most popular artificial neural network type, Multilayer Perceptron (MLP), which is trained applying back-propagation algorithm. To apply neural nets, the output and input variables must be selected. Variables are denoted due to the following system: C is the close price, O is the open price, H is the maximal price, L is the minimal price, D is the absolute increase, V is the volume, and numbers in brackets denote delays. For instance, C(0) denotes close price from the last session in the observation period, C(-1) is the close price lagged by one, etc.

The output variable is defined as the difference between the next session close price C(1) and the latest session close price C(0).

D(1) = C(1) - C(0) (4)

The set of input variables consists of three subsets: variables related to the WIG20 futures, the technical analysis indicators, and the external factors (Table 1).

The forecast horizon is divided into 12 separate sub-periods that are each about three or four months long. Every sub-period is a testing set for its own neural network. Due to this operation, training sets for consecutive networks could be enlarged.

The output variable generated by ANN is the difference between the last session close price and the next session close price [Equation (4)]. However, the next day close price is the value that will be applied in further empirical tests. The research shows that forecasts with output variables that are defined as the increases characterize smaller prediction errors compared to the forecast with output variables that are directly defined as the level of phenomena (i.e., price itself). The output data are transformed into the price forecast [^.C](1), which is the next session close price.

[^.C](1) = C(0) + [^.D](1). (5)

Forecast generated by ANN can be evaluated in terms of average errors calculated for:

[E.sub.i] = [^.C.sub.i](1) - [C.sub.i](0). (6)

The forecast errors of the future close prices are: MAPE = 1.39% and RASE = 1.85%. The direction of changes is predicted correctly in 59.2% of cases.

Empirical Results

To evaluate the efficiency of chosen trading rules, the authors compare the results obtained from three types of input data that are introduced to the trading systems. The assumption is made that a hypothetical trader invests with only one future contract. Empirical results are presented in the tables that contain the transaction efficiency parameters.

In Table 2, there are results obtained for all buy-sell signals generating methods applying perfect forecasts as input data. This allows one to recognize the potential of chosen trading strategies.

According to the results presented in Table 2, in the case of the hypothetical situation in which a trader knows exactly what will happen during the next session (i.e., he or she has the perfect forecast of the close price value), the most profitable method of investing would be the one without a trading system. More than 130,000 zl per one future contract could be earned from December 1999 to November 2003. This is the maximum profit that could be obtained from one future contract during this time on the market.

It is worth mentioning that buy-sell signals, generated by all investigated technical analysis indicators shown in Table 2, let the investor gain the profit. When applying these methods, 60-87% profitable transactions are obtained. When applying Bollinger bands, the smallest maximum net loss in one transaction and the highest proportion of average net profit to average net loss are obtained. The highest maximum net profit in one trade and average net profit are gained using moving average.

In Table 3, the authors present results obtained for trading systems with one session ahead of the price forecasts as input data. In contrast to the previous situation, the present solution is possible. If the forecasts are close enough to the real values, then the data misplacement effect should remain. In this case, the strategy "without system" is no longer the most efficient one. The highest net profit could be gained with the momentum method and it is 22,170 zl. All the trading systems remain profitable.

To verify how the forecast application in trading system influences the investment outcomes, the buy sell signal generating rules are tested out in the traditional way, i.e., on the historical data. Obtained results are presented in Table 4. The biggest profit could be gained again from the momentum strategy and it is 10,230 zl. However, this amount of money is only 46% of the profit obtained in the same strategy but with ANN forecast implementation, so the income is much smaller when there is no available forecast. If an investor relied only on past prices and on the strategy without system, the loss would have reached the level of 30,000 zl.

Conclusions

The research result shows that the trading systems tested out on the data in advance, with the perfect forecast, had much better investment results than the ones tested out in the traditional way (Table 5). Due to the misplacement data application, the systems that are not profitable actually turn out to be income producing. This is proven in the third stage of the research. Changing the perfect forecast into the forecast obtained from ANN results in maintaining the effect of the data misplacement, and the trading rules kept making profits. Compared to the results obtained from the strategies tested on historical data (the traditional way), the implementation of the ANN forecasts also caused the improvement of the other factors that are useful by evaluation of trading systems, i.e., percentage of profitable transactions and average profit--average loss ratio.

The perfect forecasts application shows that the biggest profit is produced by the strategy without any system. Any result obtained from other strategies is not comparable. This leads to the conclusion that technical analysis indicators are not useful in the case of complete information about the state of the market or perfect forecast. However, the situation changes when the ANN forecast is applied instead of actual data. Bollinger bands, momentum, and moving averages turn out to be better than the strategy without a system. Only the channel breakout strategy has a worse outcome.

Testing all the strategies in the traditional way, which is the verification of the results obtained from both, perfect, and ANN forecasts implementation, revealed that, again, three of the systems based on technical analysis indicators are income producing, except for channel breakout.

Testing the strategy without system using the third method (i.e., in the traditional way, with historical data) is, in fact, the implementation of the naive forecasts. Since it is assumed that if the last session close price was higher than the close price from the session before, an investor would buy and, in the opposite case, he or she would sell. So the naive forecast consists on the assumption that the next session close price will differ plus or minus from the last session close in the same value than as the last day. This naive forecast application brings the worst results among all of the strategies and methods of testing. Using the ANN forecast in the strategy without system significantly improves its outcomes.

The results presented in the paper show that technical analysis indicators are highly effective when they operate on the data in advance, i.e. the data that could not be known in this particular moment in time, for example, when setting today's sell or buy signal, tomorrow's price is applied. In situations like this, it is likely to happen only in a process of trading strategy testing with historical data. The result of the data misplacement in the trading system is a significant improvement of investment outcomes. Naturally, this improvement is only revealed on paper, and the theoretical profit does not show the real one. However, the conducted research proves that the unusual efficiency of technical analysis indicators in tests can be, to some degree, maintained in the real investment process by including forecasts in the trading systems.

References

Azoff, E. M. Neural Network Time Series Forecasting of Financial Markets, 1st ed., Chichester: Wiley, 1994.

Beinsen, L.; Kuhrer, M. "Comparison of Exchange Rate Forecasts by Neural Networks and By Econometric Methods," paper presented on International Atlantic Economic Conference in Vienna, Austria, March 1999.

Bosarge, W. "Adaptive Processes to Exploit the Nonlinear Structure of Financial Markets," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 371-402.

Chen, C. H. "Neural Networks for Financial Market Prediction." Proceedings IEEE International Conference of Neural Networks, Orlando, USA, 1994, pp. 1199-202.

Dutta, S.; Shekhar, S. "Bond Rating: A Non-Conservative Application of Neural Networks," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 257-73.

Gately, E. Neural Networks for Financial Forecasting, New York: Wiley, 1995.

Goonatilake, S.; Treleaven, P. Intelligent Systems for Finance and Business, New York: Wiley, 1995.

Hawley, D. D.; Johnson, J. D.; Raina, D. "Artificial Neural Systems: A New Tool for Financial Decision-Making," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 27-46.

Hoptroff, R. G. "The Principles and Practice of Time Series Forecasting and Business Modelling Using Neural Nets," Neural Computing & Application, 1, 1993, pp. 59-66.

Hsieg, C. H. "Some Potential Applications of Artificial Neural Systems in Financial Management," Journal of Systems Management, April 1993, pp. 12-5.

Kohara, K.; Fakuhara, Y.; Nakamura, Y. "Selective Learning for Neural Network Forecasting of Stock Markets," Neural Computing & Applications, 4, 1996, pp. 142-8.

Lowe, D. "Novel Exploitation of Neural Network Methods in Financial Markets," Proceedings IEEE International Conference Neural Networks, Orlando, 1994, pp. 3623-8.

Murphy, J. J. Technical Analysis of the Financial Markets, New York: Prentice-Hall, 1999.

Papla, D.; Jajuga, K. "Chaos Theory in Financial Time Series Analysis--Some Theoretical Aspects and Empirical Results," Dynamic Econometric Models, 3, 1998, pp. 5-16.

Refenes, A. P. Neural Networks in the Capital Markets, Chichester: Wiley, 1995.

Refenes, A. N.; Zapranis, A.; Francis, G. "Stock Performance Modeling Using Neural Networks: A Comparative Study with Regression Models," Neural Networks, 7, 2, 1994, pp. 375-88.

Schwager, J. D. Technical Analysis. Schwager on Futures, Chichester: Wiley, 1997.

White, H. "Economic Prediction Using Neural Networks: The Case of IBN Daily Stock Returns," in Neural Networks in Finance and Investing, R. R. Trippi and E. Turban (eds.), Chicago: Probus Publishing Company, 1993, pp. 315-48.

Witkowska, D. Artificial Neural Networks and Statistical Methods. Selected Problems in Finance, Warsaw: C. H. Beck, 2002 (in Polish).

DOROTA WITKOWSKA* AND EDYTA MARCINKIEWICZ*

*Technical University of Lodz--Poland.

TABLE 1 Set of Input Variables Description Formula/Symbol A. Variables related to the WIG20 futures Close prices of WIG20 futures C(0), C(-1), C(-2), C(-4) Natural logarithms of simple ln[[C(0)]/[C(-1)]], ln[[C(-1)]/[C(-2)]], index numbers of prices ln[[C(-2)]/[C(-3)]], ln[[C(-3)]/[C(-4)]] Relative change (%) of close [[C(0) - C(-1)]/[C(-1)]], prices [[C(-1) - C(-2)]/[C(-2)]], [[C(0) - C(-4)]/[C(-4)]] Differences between maximal [D.sub.HL](0) = H(0) - L(0), and minimal prices, and [D.sub.CO](0) = C(0) - O(0), between close and open [D.sub.HL](-1) = H(-1) - L(-1), prices [D.sub.CO](-1) = C(-1) - O(-1), [D.sub.HL](-2) = H(-2) - L(-2), [D.sub.CO](-2) = C(-2) - O(-2) Relative change (%) of volume [[V(0) - V(-1)]/[V(-1)]] Difference between values of [C.sub.WIG20](0) - C(0) index WIG20 and index WIG20 futures Number of days to WIG20 future -- expiration date B. Variables related to the technical analysis indicators 3-day Simple Moving Average MA3 5-day Exponential Moving EMA5 Average 9-day Rate of Change ROC9 oscillator William's oscillator Wm%R 5-day Average True Range ATR5 C. Variables related to the external factors Close value of index WIG20 [C.sub.WIG20](0) Relative change (%) of WIG20 [[C.sub.WIG20](0) - [C.sub.WIG20](-1)] close values /[[C.sub.WIG20](-1)] Relative change (%) of WIG20 [[V.sub.WIG20](0) - [V.sub.WIG20](-1)] volume /[[V.sub.WIG20](-1)] Relative change (%) of EURO/ [[C.sub.EURO](0) - [C.sub.EURO](-1)] PLN close prices on Polish /[[C.sub.EURO](-1)] currency market Relative change (%) of USD/PLN [[C.sub.USD](0) - [C.sub.USD](-1)] close prices on Polish /[[C.sub.USD](-1)] currency market Relative change (%) of DAX [[C.sub.DAX](0) - [C.sub.DAX](-1)] close values /[[C.sub.DAX](-1)] Relative change (%) of DJIA [[C.sub.DJIA](0) - [C.sub.DJIA](-1)] close values /[[C.sub.DJIA](-1)] Relative change (%) of NIKKEI [[C.sub.NIKKEI](0) - [C.sub.NIKKEI](-1)] close values /[[C.sub.NIKKEI](-1)] TABLE 2 Reports on the Trading Systems with the Perfect Forecast Channel Bollinger Breakout Bands Momentum Commission [zl] 15 15 15 Number of 238 112 191 trades Number of 118 58 96 buy signals Number of 120 54 95 sell signals Max. net profit 3980 4730 4000 (in one trade) [zl] Max. net loss -1130 -540 -880 (in one trade) [zl] Average 463.69 689.17 656.74 net profit (per trade) [zl] Average net loss -205.31 -148.75 -168.23 (per trade) [zl] Ave. net profit/ 2.2585 4.6331 3.9039 Ave. net loss Number of 206 96 129 profitable transactions Number of loss 32 16 62 transactions % Profitable 86.55% 85.71% 67.54% transactions Gross profit [zl] 96,090 67,140 80,020 Net profit [zl] 88,950 63,780 74,290 Commision 7140 3360 5730 paid [zl] Moving Without Average a System Commission [zl] 15 15 Number of 70 516 trades Number of 35 258 buy signals Number of 35 258 sell signals Max. net profit 4990 3570 (in one trade) [zl] Max. net loss -1130 -1130 (in one trade) [zl] Average 1079.52 397.21 net profit (per trade) [zl] Average net loss -314.29 -143.97 (per trade) [zl] Ave. net profit/ 3.4348 2.7590 Ave. net loss Number of 42 391 profitable transactions Number of loss 28 126 transactions % Profitable 60.00% 75.78% transactions Gross profit [zl] 38,640 152,660 Net profit [zl] 36,540 137,180 Commision 2100 15,480 paid [zl] TABLE 3 Reports on the Trading Systems Tested Applying Forecasts Channel Bollinger Breakout Bands Momentum Commission [zl] 15 15 15 Number of trades 222 122 208 Number of buy signals 103 64 104 Number of sell signals 119 58 104 Max. net profit 1220 4371 3970 (in one trade) [zl] Max. net loss -680 -1535 -1200 (in one trade) [zl] Average net 302.47 766.30 651.61 profit (per trade) [zl] Average net -212.87 -268.71 -285.29 loss (per trade) [zl] Ave. net profit/ 1.4209 2.8518 2.2840 Ave. net loss Number of profitable 93 42 87 transactions Number of loss 129 80 121 transactions % profitable 41.89% 34.43% 41.83% transactions Gross profit [zl] 7570 14,348 28,410 Net profit [zl] 760 10,688 22,170 Commision paid [zl] 6810 3660 6240 Moving Without Average a System Commission [zl] 15 15 Number of trades 90 416 Number of buy signals 45 208 Number of sell signals 45 208 Max. net profit 4880 1820 (in one trade) [zl] Max. net loss -3140 -2290 (in one trade) [zl] Average net 957.14 356.42 profit (per trade) [zl] Average net -412.73 -273.27 loss (per trade) [zl] Ave. net profit/ 2.3191 1.3043 Ave. net loss Number of profitable 35 190 transactions Number of loss 55 226 transactions % profitable 38.89% 45.67% transactions Gross profit [zl] 13,500 17,790 Net profit [zl] 10,800 5960 Commision paid [zl] 2700 11,830 TABLE 4 Reports on the Trading Systems Tested Without Any Forecasts Channel Bollinger Breakout Bands Momentum Commission [zl] 15 15 15 Number of trades 238 112 191 Number of buy signals 118 58 96 Number of sell signals 120 54 95 Max. net Max. net profit 1270 4110 3510 (in one trade) [zl] Max. net loss -1130 -1380 -1750 (in one trade) [zl] Number of loss 142 77 121 transactions % of profitable 40.34% 31.25% 36.65% transactions Gross profit [zl] 1740 4830 15,960 Net profit [zl] -5400 1470 10,230 Commission paid [zl] 7140 3360 5730 Moving Without Average a System Commission [zl] 15 15 Number of trades 70 516 Number of buy signals 35 258 Number of sell signals 35 258 Max. net Max. net profit 4440 1810 (in one trade) [zl] Max. net loss -3390 -1920 (in one trade) [zl] Number of loss 46 339 transactions % of profitable 34.29% 34.30% transactions Gross profit [zl] 7620 -14,800 Net profit [zl] 5520 -30,280 Commission paid [zl] 2100 15,480 TABLE 5 Comparison of Total Net Profits [zl] for All the Strategies Channel Bollinger Moving Without Breakout Bands Momentum Average a System Perfect forecasts-- 88,950 63,780 74,290 36,540 137,180 actual future data ANN forecasts 760 10,688 22,170 10,800 5960 Historical data-- -5400 1470 10,230 5520 -30,280 without forecasts

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Comment: | Construction and evaluation of trading systems: Warsaw index futures. |
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Author: | Witkowska, Dorota; Marcinkiewicz, Edyta |

Publication: | International Advances in Economic Research |

Geographic Code: | 4EXPO |

Date: | Feb 1, 2005 |

Words: | 4686 |

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