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Abstract. Smoothing time series allows removing noise. Moving averages are used in finance to smooth stock price series and forecast trend direction. We propose optimised custom moving average that is the most suitable for stock time series smoothing. Suitability criteria are defined by smoothness and accuracy. Previous research focused only on one of the two criteria in isolation. We define this as multi-criteria Pareto optimisation problem and compare the proposed method to the five most popular moving average methods on synthetic and real world stock data. The comparison was performed using unseen data. The new method outperforms other methods in 99.5% of cases on synthetic and in 91% on real world data. The method allows better time series smoothing with the same level of accuracy as traditional methods, or better accuracy with the same smoothness. Weights optimised on one stock are very similar to weights optimised for any other stock and can be used interchangeably. Traders can use the new method to detect trends earlier and increase the profitability of their strategies. The concept is also applicable to sensors, weather forecasting, and traffic prediction where both the smoothness and accuracy of the filtered signal are important.

To use human factors together with financial ones in portfolio management task we analyze lengthy series of successes and losses of numerous automated high frequency trading systems that buy and sell assets. We found that in spite of sparse, bimodal non-Gaussian time series, modern Markowitz solutions can be applied to weigh up contributions of diverse trading strategies. Training history should be rather short in situations where technological, social, financial, economic and political situations are changing swiftly. The Markowitz portfolio coefficients finding algorithm can be improved by careful application of the regularization and matrix structurization methods.

Abstract. For a long time moving averages has been used for a financial data smoothing. It is one of the first indicators in technical analysis trading. Many traders debated that one moving average is better than other. As a result a lot of moving averages have been created. In this empirical study we overview 19 most popular moving averages, create a taxonomy and compare them using two most important factors -smoothness and lag. Smoothness indicates how much an indicator change (angle) and lag indicates how much moving average is lagging behind the current price. The aim is to have values as smooth as possible to avoid erroneous trades and with minimal lag -to increase trend detection speed. This large-scale empirical study performed on 1850 real-world time series including stocks, ETF, Forex and futures daily data demonstrate that the best smoothness/lag ratio is achieved by the Exponential Hull Moving Average (with price correction) and Triple Exponential Moving Average (without correction).

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Abstract:In a constantly changing market environment, it is a challenge to construct a sustainable portfolio. One cannot use too long or too short training data to select the right portfolio of investments. When analyzing ten types of recent (up to April 2018) extremely high-dimensional time series from automated trading domains, it was discovered that there is no a priori 'optimal' length of training history that would fit all investment tasks. The optimal history length depends of the specificity of the data and varies with time. This statement was also confirmed by the analysis of dozens of multi-dimensional synthetic time series data generated by excitable medium models frequently considered in studies of chaos. An algorithm for determining the optimal length of training history to produce a sustainable portfolio is proposed. Monitoring the size of the learning data can be useful in data mining tasks used in the analysis of sustainability in other research disciplines.

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