In general, traders test their trading strategies by applying them to historical market data (backtesting), and then reapply those that have made the most profit on that past data. In this article, we propose AITA (Artificial Intelligence Trading Assistant ), our framework for generating trading systems by applying the new trading strategy called DNN-forwardtesting [1] by determining the best strategy based on the prediction issued by a deep neural network. In this work, we show the experiment with AITA involves the use of 10 stocks that are first ifltered according to their volatility using the Kmean++ model. Having determined the assets with average volatility, we use this historical data to train a deep feed-forward neural network to predict price trends over the next 30 days of the open stock market. Finally, the trading system, created by AITA, calculates the most efective technical indicator by applying it to the DNN forecasts to generate the trading strategy.
Stock market forecasting is considered a field of research with promising returns for investors. However, there rately and suficiently precisely due to their complexity, chaotic and non-linear nature. In fact, traditional statistical models, which have been widely applied to market trend forecasting so far, can easily handle only linear or stationary sequences.
In our experiment, we used as benchmark the ARIMA
which is strength being in its robustness and eficiency
in terms of short-term forecasting [
In this paper we propose AITA, our framework that uses historical stock price data to train a set of DNNs to predict future (next month) stock prices. These predictions are exploited in a new way to determine the most () < (ℎ) and () , () ∈ [ () , (ℎ) , () , () , (ℎ)].
() ) , where
Volatility measures1.
Volatility quantifies the dispersion of returns. Unfortunately, this dispersion can not be measured and volatility is not directly observable, but it is possible to estimate it [8]. AITA framework is designed to use the Historical - The Parkinson (PK) estimator incorporates the stock’s daily high and low prices as follow: = 1 √ 4 2
tor √ ∑=1 ( (ℎ) () )2. It is derived from the assumption that the true volatility of the asset is proportional to the (ℎ) and low
() () () )2.
= prices of observations. logarithm ( ) of the ratio of the high
The
Garman-Klass (GK) is calculated as
follows: (ℎ) 1 ∑=1 2
1 (
() )2 − 1 ∑=1 (2(2) − 1)( This method is robust for opening jumps in price and trend movements. However, the estimator assumes that price movements are log-normally distributed, which may not always be the case in practice.
- The Rogers-Satchell (RS) estimator uses the range of prices within a given time interval as a proxy for the volatility of the asset as follows: = √ 1 ∑=1 (( (ℎ) () )( (ℎ) () ) + ( () () )(
() that the range of prices within the interval is a good proxy for the volatility of the asset, which may not always be the case. Additionally, the estimator may be sensitive to outliers and extreme price movements. () ). RS assumes The
Yang-Zhang (YZ) estimator may have limitations in certain situations, and it is often recommended to use multiple estimators and compare their results to gain a more complete understanding of the underlying volatility.
Two distinct trading strategy classes are used in AITA framework:
- Trend Following. One way to trade a trend is to look at an asset with a resistance line. Once the price breaks through resistance, a trader places an order in the direction of the breakout2. Trend-following, or momentum, strategies have the attractive property of generating trading returns with a positively skewed statistical distribution. Consequently, they tend to hold on to their profits and are unlikely to have severe ‘drawdowns’ ([10]).
- Mean Reversion. The idea of mean reversion strategies is that the maximum and minimum price of a security is temporary, and that it will tend to the average over time (see [11]). Elliott et al.[12] explains how mean-reverting processes might be used in pairs trading and developed several methods for parameter estimation. estima- version strategies, although theoretically opposing ideas,
It is worth noting that trend following and mean reare not in conflict with each other and they are therefore both applicable at the same time to the same security. [9] in- Sortino ratio (SoR) is a variant of the risk-adjusted profit
Profit and risk metrics are crucial considerations in trading AITA framework evaluates the following, for the potential profitability of the investments and to manage the risk exposure.
(i) The Maximum drawdown (MDD) measures the largest decline from the peak in the whole trading period, to show the worst case, as follows: = ∈(0,) [ ∈(0, )
a risk-adjusted profit measure, which refers to the return
− ]. (ii) The Sharpe ratio (SR) is per unit of deviation as follows: = [] [] . (iii) The measure, which applies DD as risk measure: = (iv) The Calmar ratio (CR) is another variant of the riskadjusted profit measure, which applies MDD as risk mea[] . ()
To check the goodness of trades, we mainly focused in the time interval ( = 1, ..., ) , where = on the Total Returns () for each stock ( = 1, ..., ) (+Δ)− () , and furthermore analysing the standard () = ized returns = ( − )/ , with ( = 1, ..., ) , where overtime for the studied period. 2https://en.wikipedia.org/wiki/Breakout_(technical_analysis) corporates 2 √ ℎ =
0.34 1.34+ +1 . studies have shown that the YZ estimator can perform well in a variety of settings, including in the presence of jumps and in the presence of non-normality in the 1https://dynamiproject.files.wordpress.com/2016/01/measuring_ historic_volatility.pdf data. However, like any estimator, it is not perfect and is the standard deviation of , e denote the average
are almost completely uncorrelated. However, this is a measure of the global synchrony in the overall period.
(ii) The Dynamic Time Warping (DTW) algorithm calculates the optimal match between the two series by minimising the Euclidean distance between pairs of samples at the same time. The minimum path cost is = 209.95 , and such a large distance between the two stocks supports our hypothesis of a complete absence of influence between them.
In this section, we maintain the same forecasting objective of Section 4.1, i.e., = 30 days following the training date. We empirically found that the neural network performs better is the Multi Layer Perceptron when its input layer is fed with the = 5 previous values, i.e., the prices of the previous market week. In other words, to forecast the price of a day , the input neurons will be presented to the prices of days − 1, … , − 5 , respectively. The network then outputs its price prediction via a single 3.2. Stocks Selected neuron in the output layer.
ANF and EOG are certainly assets with a sometimes con- The resulting optimal geometry has two hidden layers
troversial trend and consequently well profitable if rightly composed by 10 ∗ and 5 ∗ neurons, respectively, as
analyzed. In order to prove that, the dataset is general in [
After showing that DNNs are the best forecast technique for our stock prices dataset, we can introduce the novel trading system of AITA framework.
The AITA (algorithmic) trading strategy is encoded in a set of entry and exit trading rules which are in turn based on the value of a single indicator chosen from a set of twelve common technical indicators, i.e., Simple Moving Average (SMA), Exponential Moving Average (EMA), Moving Average Convergence Divergence (MACD), Bollinger Bands (BBs), Stochastics (ST), William %R (W%R), Momentum (MO), Relative Strength Index (RSI), Average True Range (ATR), Price Oscillator (PO) (see [16]), Triple Exponential Moving Average (TEMA, [17]) and Average Directional Index (ADX). We also tested some further meaningful combinations of the above indicators, like in [18], and [19], such as ST+MO+MACD, PO+W%R and PO+RSI.
AITA performed a DNN-forwardtesting of the strategies based on each of the above indicators on the the 30(( () < (( () > () ) ∨ ( (ℎ) < () ) ∨ ( (ℎ) > (ℎ))) ∧ (( () < (ℎ))) ∧ (( () > () ) ∨ ( () < () ) ∨ ( () > () )) () )) (+ > − ) ∧ ( > 25) (− > + ) ∧ ( > 25)
days price forecasts following the training date ending on October 16th, 2021, generated by the DNNs developed in Section 4.2. In this paper, we propose AITA framework, a stock mar
Our results show that the best indicator for ANF is ket trading system that exploits deep neural networks
the Triple Exponential Moving Average, whereas the Av- as part of its main components, improving on previous
erage Directional Index is more suitable for EOG. The work [
Table 4 As discussed, neural networks outperform the most Performance of AITA forwardtesting-selected indicators. common statistical methods in stock price forecasting predicting future allows for a very accurate selection #Trades TR ($) ShR SoR CaR of the indicator to be applied, which takes into account ANF 3 6.126 2.194 3.340 12.403 trends that would be very dificult to capture through EOG 3 1.374 1.253 2.556 5.814 backtesting.
To validate this claim, we applied our methodology on two very diferent assets with medium volatility, and the results show that our DNN-forwardtesting-based trading system achieves a profit equal to or higher than that of a traditional backtesting-based.
Given the promising potential of this approach, we will further test its reliability with more refined feature selection (e.g., [21, 4]) and balancing (buy, sell and hold trades) strategies (e.g., [22, 23]).
Finally, since such neural networks can be seen as black-box decision-making systems, we could also study the monitoring of machine ethics and the rules [24, 25, 26] related to their activity.
Then, we evaluated the profit deriving from the application of such a strategy on the real data of the 30-day trading period following October 16th, 2021, having as starting point a budget of $100 invested in compound mode. The results are shown in Table 4.
As a baseline to compare such metrics, we re-evaluated the same set of technical indicators through the traditional backtesting technique on the historical data for the 30 days before October 16th, 2021, to see if it would result in diferent choices and maybe diferent profits.
The results show that a trader using backtesting would choose ADX for the EOG share, as with our forwardtesting technique, so the profit would be the same in this case. However, the TEMA indicator would not be chosen for the ANF share. Indeed, the most promising indicator, given the past 30 days of market, would be RSI (with overbought 70 and oversell 30). However, if applied to the future, it would result in a loss of 1.16%, as shown in Table 5.