Generating Trading Signals by ML algorithms or time series ones?

07/14/2020
by   Omid Safarzadeh, et al.
0

This research investigates efficiency on-line learning Algorithms to generate trading signals.I employed technical indicators based on high frequency stock prices and generated trading signals through ensemble of Random Forests. Similarly, Kalman Filter was used for signaling trading positions. Comparing Time Series methods with Machine Learning methods, results spurious of Kalman Filter to Random Forests in case of on-line learning predictions of stock prices

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1 Introduction

2 Introduction

Prediction of stock market prices has a wide literature and is a difficult task. Nowadays, Wall-Street companies employ trading algorithms to process High Frequency stock prices. These algorithms should be able to prepare trading signals (long /short /Do nothing) based on financial technical analysis. Some of these analysis, technical indicators, are derived from stock price fluctuations to signal on the direction of market. In absence of shocks to Market Fundamentals, Wall-Street companies generally use technical analysis to track and trace HF stock movements. This research will examine how ML algorithms can be used to generate trading signals. To do so, several steps needs to be done before apply ML algorithms to data.

2.1 Data

In this research, I will use Minuets by Minuets data of several stocks from NYSE. Blomberg Financial station will be the source of stock data. Here is a sample data for Abbott Laboratories company. The data is from 1 Dec. 2017 to 15 Feb. 2018 minutes by minutes intervals. There is 20277 observations of Abbott Laboratories stock price. I will also consider other assets from SP100 stock index.

Date Open Close Low High Value Volume Number_Ticks
1 12/1/2017 16:31 170.01 170.40 170.01 170.71 8119385.00 47651 291
2 12/1/2017 16:32 170.38 170.67 170.37 170.69 5024126.00 29450 207
3 12/1/2017 16:33 170.68 170.39 170.36 170.95 5591862.00 32758 220
4 12/1/2017 16:34 170.42 170.42 170.28 170.50 4946603.50 29027 221
5 12/1/2017 16:35 170.44 170.50 170.30 170.57 5864560.50 34406 184
6 12/1/2017 16:36 170.50 170.47 170.24 170.50 4071876.25 23904 150

Figure 1: Abbott Laboratories NYSE: ABT

2.2 Technical Indicators

The above mentioned data needs to be processed to generate some information about direction of markets. Generally, this will need technical analysis with some parameter calibration to extract proper information of historical behavior of financial asset. It is very common in literature to use financial indicators to provide more information on direction of stock prices, (see [murphy1999technical] , [teixeira2010method]). These technical indicators are calculated based on daily trading data (open, high, low and close prices) to provide patterns and trends of stock behavior in the incoming trading days. Main stream finance literature ignores them, due to their lack of mathematical foundations following asset pricing models. [godfrey1964random] believed that stock prices are following random walk process, leading that future prices are independent than todays prices; implying no memory price time series. Efficient Market Hypothesis [fama1965behavior] supports random walk theory of prices by stating that, stock prices already include all information about stock value and only new information will change the price. But these theories are violated by some financial economist scholars by providing evidence of market anomalies ([bondt1985does] and [jensen1978some]). Hence, analyzing future prices based on historical data can be seen as another empirical evidence of anomalies in markets.

[lui1998use]

survey analysis revealed that almost 85 % of foreign exchange traders use both technical and fundamental analysis. They also found that technical analysis is the favorite tool of market traders. The use of technical indicators, ease the complexity of market prediction and transfers it to a pattern recognition problem. we can use technical indicators to provide some features of future market directions. This data transformation, will also eliminates the needs of human interpretation of indicators and helps to implement automated trading algorithm. This transformation is explained in details by

[creamer2010automated].

2.3 Technical Indicators Data

Following [kara2011predicting] paper, I will use the following technical indicators as features of daily stock prices and their parameters (see [creamer2010automated] for more details on parameters adjustments):

  • CCI (Commodity Channel Index)

  • Simple Moving Average (SMA) where

  • Exponential Moving Average (EMA) where

  • Moving Average Convergence Divergence (MACD)

  • Momentum: change in prices () for periods. When it is above (below) zero, indicates is upward (downward) trend.

  • Relative Strength Index (RSI) where

  • Bollinger Bands (BB) where

  • Chaikin Oscillator

  • Stochastic Oscillators

Figure 2: Bolinger Bands financial technical indicators applied to ABT prices

For each of above indicators, there are some parameters such as number of day lags of stock and so on. Here I will use parameters adjustments proposed in [creamer2010automated], [kara2011predicting] and [booth2015performance]. Using these features, I could provide almost 90 features for each trading days.

3 Trading Signals

Once, the raw data is processed and proper features are extracted to signal the direction of stock prices, the question is what position we should take today, to collect proper profit tomorrow. This means that we have three actions for today state which has some values in tomorrow state. These trading signals will be Long (Buy), Short (Sell) , and "Do Nothing". I am adding the third one as it will take into account some market frictions. Generally, it is common in literature to not consider market frictions such as tax, transaction costs and etc. But introducing the above three actions will be useful when the tomorrow’s return is not enough if investors have to also cover market frictions. Hence if prediction of market direction signals a bull market, we long the stock and if it is bear market we short the position. Here, I will also consider closing long (or short) positions the day after we opened the position. So our trading strategy will be as:

(1)
(2)
(3)
(4)

This means, we will execute the trade if the predicted profit for next minute is higher than market friction. Then depending on market direction we will open long/short position and we will close the position the next minute.

4 Stationarity Test

Time series data are prone to have "random sampling" problem as the order of data is important. In addition, due to external shocks of markets, the underlying random process might not have stationary distribution. So one needs to be careful of using ML algorithms as shuffling data will cost losing auto correlation of data. This means non-stationarity of distribution of data generating process will contradict the assumption of identically distribution of data. This justifies stationarity test of distribution of data before approaching any prediction procedure. It is well-known that stock prices are random walk and also exhibit auto correlation in time series analysis. Detecting such behavior is possible by using unit root tests in Times Series analysis. This is tested via augmented Dickey Fuller test (ADF) which is well known in Econometrics literature (see [dickey1979distribution]

). Appendix A, provides the R-codes and sample ADF test report for one security. This test is applied for all above mentioned stock prices and similar results have been found. Moreover, density plot of log returns are also demonstrated. The Kolmogorov–Smirnov test applied to detect the probability distribution of log-return times series, and result was close to skewed-Laplace time series. The green plot is empirical density of series and red lines shows skewed Laplace distribution fitted to data.

Figure 3: Skewed Laplace Density plot fitted to log returns of Abbott Laboratories NYSE: ABT

5 Methodology

Two approaches has been explored by scholars to predict stock market prices: Time Series analysis and Machine Learning. The former approach considers Financial data as a linearly correlated time dependent information and tries to explain tomorrow prices based on historical data. Machine learning techniques try to capture nonlinear relationship of high dimensional stock prices. Neural Networks, Random Forests and Support Vector Regressions has been widely applied to forecast market prices in literature.

[gately1995neural] explains in details how to construct, use and apply neural networks to predict stock prices. [cavalcante2016computational] surveys on recent developments of Machine learning techniques which are used to forecast financial markets.

6 Performance Measure

The main question of this research is which algorithm we should use to predict and generate trading signals? Which one has superior results? Well, this won’t be difficult if we look from investor’s viewpoint. Investors don’t care about methodology but their profit within a given period. Let’s call explained methods in previous section as an Expert. So we are facing two expert types: Time Series and Machine Learning ones. As we are using High Frequency data, we need to define a proper Test time interval. Although it is rule of thumb to split data into 80-20 groups of data as test and train data. Because of sensitivity of stock prices to financial news (which are exogenous to markets) we might need to reconsider this rule. Recall that for some trading days we will have 400 observations for one asset, which will be very volatile. For example for Abbott Laboratories (ABT), we have 20000 observations from 1 Dec. 2017 to 15 Feb. 2018. (Figure 1). The proper time interval to check performance of several trading experts might be last two hours time period for all Experts. So for this time period, I will prepare profitability of each Expert based on proposed trading signal of each expert and then calculate the return of each signal within this time period. This will be out of bag sample for all Experts. For Cross-validation of each expert, we need to consider the same size time period. More details of how to cross-validate the results of each Expert will be discussed later.

6.1 Times Series approach

6.1.1 Arima

ARIMA process simply, takes to account some lag of historical prices and weights them to predict today’s prices. Although it might look simple, the question of number of lags to take into account is not an easy task. But it is common among scholars to select the proper lag by considering information criterion such as Akaike information criterion (AIC), and Hannan Quinn Information Criterion (HQIC). In this we assume stock log-returns (say ) are related to past prices. Then we can model:

(6)

(p,q) are called lag parameters. Given that log-return prices follow stationary process (refer to appendix A for more detail.), we can estimate above procedure through MLE estimator. The proper lag parameters of ARIMA model is selected by AIC condition:

(7)

For example, the ARIMA process applied to Abbott Laboratories log-returns , from: "2017-12-01" to: "2018-02-16 17:01:00", and the following result is obtained. This implies that we can model the mentioned stock price as follow

(8)

Now according to above formula we can generate our forecast for future log-returns of underlying asset. For ARIMA process, I will keep 120 last observations for out of bag test and 120 as cross-validation of trading strategy.

The forecast results for Abbott Laboratories for 120 Minutes are depicted in following figure. Red line corresponds to real price, and blue line depicts ARIMA(4,0,0) process forecast. If trading signals (as discussed in its section) are generated based on our forecast and allowing for short-selling in the market and getting advantage of selling strategy profits, ARIMA(4,0,0) will generate -%16.62 loss for this asset within the 115 minutes trading time.

Figure 4: Abbott Laboratories price, Online-learning ARIMA forecast
today forecast position tmw porfit_loss
4 60.15000 60.15101 Long 60.18000 0.03000
5 60.18000 60.17922 60.19000 -0.00000
6 60.19000 60.19020 60.19000 0.00000
7 60.19000 60.18903 60.19990 -0.00000
8 60.19990 60.19939 60.18500 0.00000
9 60.18500 60.18556 60.15000 -0.00000
10 60.15000 60.15084 60.17000 0.00000
11 60.17000 60.17031 60.18500 0.00000
12 60.18500 60.18608 Long 60.18640 0.00140
13 60.18640 60.18580 60.17000 0.00000
14 60.17000 60.17004 60.17000 0.00000
15 60.17000 60.17017 60.17500 0.00000
16 60.17500 60.17568 60.17000 -0.00000
17 60.17000 60.17035 60.17000 0.00000
18 60.17000 60.17002 60.21000 0.00000
19 60.21000 60.20926 60.24000 -0.00000
20 60.24000 60.23924 60.24500 -0.00000
21 60.24500 60.24342 Short 60.25000 -0.00500
22 60.25000 60.24882 Short 60.27000 -0.02000
23 60.27000 60.26938 60.25500 0.00000
24 60.25500 60.25535 60.26000 0.00000
25 60.26000 60.25933 60.29000 -0.00000
26 60.29000 60.28989 60.30000 -0.00000
27 60.30000 60.29965 60.37500 -0.00000
28 60.37500 60.37191 Short 60.40000 -0.02500
29 60.40000 60.39882 Short 60.38000 0.02000
30 60.38000 60.37778 Short 60.43000 -0.05000
31 60.43000 60.42778 Short 60.42000 0.01000
32 60.42000 60.42104 Long 60.40000 -0.02000
33 60.40000 60.39890 Short 60.39000 0.01000
34 60.39000 60.39084 60.39500 0.00000
35 60.39500 60.39587 60.42500 0.00000
36 60.42500 60.42476 60.40500 0.00000
37 60.40500 60.40548 60.41500 0.00000
38 60.41500 60.41382 Short 60.42500 -0.01000
39 60.42500 60.42560 60.43000 0.00000
40 60.43000 60.42968 60.42000 0.00000
41 60.42000 60.42006 60.40000 -0.00000
42 60.40000 60.40058 60.43000 0.00000
43 60.43000 60.42980 60.35000 0.00000
44 60.35000 60.35312 Long 60.37000 0.02000
45 60.37000 60.36878 Short 60.37000 -0.00000

6.1.2 Kalman Filter

In this section linear State Space Model is considered to estimate future trading signals. To do so, I used Kalman filtering ,see [kalman1960new] , method to estimate tomorrow’s state of trade and then employed Expected Maximization Algorithm to estimate initial parameters for KF of each state. This will help to improve performance of KF in estimating trading signals. The State-Space model has two conditions: Hidden or latent process , state process, assumed to be a Markov process. The future , and the past past , are independent conditional on the present, . The observations, are independent given the states . This means that the dependence among the observations is generated by states. Consider linear Gaussian state space model or (DLM), order one, p-dimensional vector autoregression as the state equation

(9)

Note that is a iid, zero-mean normal vectors with covariance matrix Q; the process starts with a normal vector , such that . We do not observe the state vector

directly, but only a linear transformed version of it with noise added, hence observation model, follows :

(10)

is a measurement or observation matrix. The observed data vector,

, is q-dimensional, which can be larger than or smaller than p, the state dimension.The additive observation noise is vector of Normally distributed data. For simplicity,

are assumed to be uncorrelated.

Our goal is to produce estimators for the underlying unobserved signal , given the data , to time s. When , the problem is called forecasting or prediction. When , the problem is called filtering. Given a sequence of observations the goal in stochastic filtering is to compute the posterior distribution of the internal states

. If X, Y process is jointly Gaussian, then the distribution of any subset of X conditioned on any subset of Y will also be Gaussian. It follows that the filtering distributions are fully specified by their means and variances. When

, the problem is called smoothing. Hence the goal is to compute where . This is a non-causal process. So we use future observations to estimate the present state. Call:

.
When then is used for convenience. is initially known. Formula’s to estimate Kalman Filter ([kalman1960new] for the prove and more details):

(11)
(12)
(13)
(14)
(15)
(16)
(17)

6.1.3 Expectation Maximization algorithm

[shumway1982approach]

proposed an EM algorithm conjunction with the Kalman Filter algorithm and derive a recursive procedure for estimating the parameters by MLE. The basic idea, is that if we know the states and observations, so we have complete data. So the joint distribution will be :

(18)

so the Log-likelihood will be :

(19)
(20)
(21)

Now, we need to construct the iteration steps. First we need expectation step:

where

(22)
(23)
(24)

For min minimization step, one can derive the following updated estimations:

(25)
(26)
(27)
(28)
(29)

Now, one can estimate above parameters by employing EM algorithm together with KF in each iteration. The corresponding code follows can be found in appendix. Now, by iterating above procedure, we get the estimations for our initial parameters.

Using above formula’s, I estimated state-space model and plotted for ABT firm in following graph. (for detail of codes please refer to Appendix). The green plot demonstrates the minute by minute stock prices and the red ones is prediction by the model. Kalman Filter can be considered as an online learning method. Employing this method on 265 minutes (test data), profits 0.89 per share. Trading strategy was taking long position in case of our prediction for tomorrow price is higher than today’s price and taking short position if we predict price will fall tomorrow. The next day, the current position will be closed, no matter what happens. (Here tomorrow means next minute as I have used minutes by minutes data).

Figure 5: Abbott Laboratories Stock prices prediction with Kalman filter

Figure 6: Abbott Laboratories Stock prices prediction with Kalman filter- for 264 minutes
today forecast position tmw porfit_loss
1 59.11000 59.11086 59.11000 0.00000
2 59.11000 59.11033 59.11000 0.00000
3 59.11000 59.11012 59.14000 0.00000
4 59.14000 59.11005 Short 59.15000 -0.01000
5 59.15000 59.12856 Short 59.12000 0.03000
6 59.12000 59.14181 Long 59.11000 -0.01000
7 59.11000 59.12833 Long 59.09000 -0.02000
8 59.09000 59.11700 Long 59.11260 0.02260
9 59.11260 59.10031 Short 59.06000 0.05260
10 59.06000 59.10791 Long 59.02000 -0.04000
11 59.02000 59.07830 Long 59.04500 0.02500
12 59.04500 59.04227 Short 59.04000 0.00500
13 59.04000 59.04396 Long 59.05000 0.01000
14 59.05000 59.04151 Short 59.06500 -0.01500
15 59.06500 59.04676 Short 59.07800 -0.01300
16 59.07800 59.05803 Short 59.09000 -0.01200
17 59.09000 59.07037 Short 59.13000 -0.04000
18 59.13000 59.08250 Short 59.11500 0.01500
19 59.11500 59.11186 Short 59.16000 -0.04500
20 59.16000 59.11380 Short 59.15000 0.01000
21 59.15000 59.14235 Short 59.15500 -0.00500
22 59.15500 59.14708 Short 59.16500 -0.01000
23 59.16500 59.15197 Short 59.18000 -0.01500
24 59.18000 59.16002 Short 59.20000 -0.02000
25 59.20000 59.17237 Short 59.20440 -0.00440
26 59.20440 59.18945 Short 59.22500 -0.02060
27 59.22500 59.19869 Short 59.24500 -0.02000
28 59.24500 59.21495 Short 59.25000 -0.00500
29 59.25000 59.23352 Short 59.25000 -0.00000
30 59.25000 59.24371 Short 59.26000 -0.01000
31 59.26000 59.24760 Short 59.27000 -0.01000
32 59.27000 59.25526 Short 59.25000 0.02000
33 59.25000 59.26437 Long 59.23680 -0.01320
34 59.23680 59.25549 Long 59.24000 0.00320
35 59.24000 59.24394 Long 59.22000 -0.02000
36 59.22000 59.24150 Long 59.23500 0.01500
37 59.23500 59.22821 Short 59.24200 -0.00700
38 59.24200 59.23241 Short 59.24000 0.00200
39 59.24000 59.23834 Short 59.25000 -0.01000
40 59.25000 59.23936 Short 59.25500 -0.00500
41 59.25500 59.24594 Short 59.23000 0.02500
42 59.23000 59.25154 Long 59.25500 0.02500
43 59.25500 59.23823 Short 59.25500 -0.00000
44 59.25500 59.24859 Short 59.27000 -0.01500
45 59.27000 59.25255 Short 59.28000 -0.01000
46 59.28000 59.26334 Short 59.30000 -0.02000
47 59.30000 59.27363 Short 59.26500 0.03500
48 59.26500 59.28993 Long 59.27000 0.00500

6.2 Machine Learning Algorithms

6.2.1 Neural Network

[patel2015predicting] and [booth2015performance] compared different ML algorithms which are applied to predict stock price movements. They compared ensemble of random forests, with Neural Network, Support Vector Regression, and OLS, and found the superior results of the former over other methods. In this paper, I will compare performance of these methods: Ensemble of Random Forest, in contrast to Times series data. Although [langkvist2014review] survey, is hopeless on employing NN methods on stock market prediction, due to its non-stationarity movements, but there might be a better chance of trying NN with predicting trading signals (which, as discussed,is bounded time series) as an extension of this research.

6.2.2 Random Forest

[creamer2010automated] and [patel2015predicting] report that among several Machine learning algorithms, ensemble Random Forests perform better to predict direction of stock prices. Random forests (RF) algorithm introduced by [breiman2001random] as an average of some random regression trees to avoid over-fitting of each tree. Although some scholars implemented RF successfully to predict financial markets ([kara2011predicting]), but problem arises when data is time dependent, or sequential data. The novelty of this research on predicting trading signal might have some positive impact to solve this problem.

Figure 7: Ensemble of Random Forests

Also, I will work on new weighting algorithm to combine several RF. This is normally called Ensemble of RF in literature. [saffari2009line] proposed online Random Forest algorithm which is based on the online bagging, randomized forests and online regression tree. Moreover, they implemented a weighting algorithm to punish some regression trees based on their out-of-bag-error to grow new regression trees. This idea looks similar to Adaboost learning algorithm of [freund1995desicion], which repeatedly uses a simple learning algorithm, called weak learner to different weightings of training data. While Adaboost performs relatively good for predicting direction of financial markets, one might be interested to see its performance on magnitude of future prices. Some scholars combined the Adaboost algorithm with RF algorithm in this manner. First they trained several RF on time intervals of time series data, then considered each RF an weak expert to predict tomorrow prices. Then they punished weak RF experts based on the outcomes of each expert to predict prices (see [creamer2010automated]. In this study, I used this idea, but with some modifications on weighting algorithm of each weak RF. Each RF will be applied to some interval of data. Then, I will weight each RF based on inverse of their absolute prediction error. Then will update the weights of each RF, to predict tomorrow’s (next minutes here) trading signals based on ensemble of weighted Random Forests. After that, I will try to benefit from new Minutes by Minutes data and update each prediction by correcting previous predictions measures. So for each next Min. we will best use of today’s information. In the following plot, I illustrated the the results of RF on test data set of Minutes by Minutes prices for ABT company. Next, I have considered our predictions as trading signals and check the profitability of proposed algorithm. For now, the algorithm has 7.5 % success in direction estimation.

Figure 8: Abbott Laboratories Stock prices prediction with Random Forest
row today.price forecast.tmw signal tmw profit.loss
1 1 60.0900 60.1054 Long 60.1200 0.0300
2 2 60.1200 60.1196 60.1350 0.0000
3 3 60.1350 60.1371 60.1554 0.0000
4 4 60.1554 60.1604 60.1700 0.0000
5 5 60.1700 60.1581 Short 60.1550 0.0150
6 6 60.1550 60.1379 Short 60.1600 -0.0050
7 7 60.1600 60.1461 Short 60.1500 0.0100
8 8 60.1500 60.1376 Short 60.1800 -0.0300
9 9 60.1800 60.1638 Short 60.1900 -0.0100
10 10 60.1900 60.1605 Short 60.1900 0.0000
11 11 60.1900 60.1690 Short 60.1999 -0.0099
12 12 60.1999 60.1693 Short 60.1850 0.0149
13 13 60.1850 60.1603 Short 60.1500 0.0350
14 14 60.1500 60.1422 60.1700 0.0000
15 15 60.1700 60.1576 Short 60.1850 -0.0150
16 16 60.1850 60.1686 Short 60.1864 -0.0014
17 17 60.1864 60.1678 Short 60.1700 0.0164
18 18 60.1700 60.1553 60.1700 0.0000
19 19 60.1700 60.1496 Short 60.1750 -0.0050
20 20 60.1750 60.1576 Short 60.1700 0.0050
21 21 60.1700 60.1633 60.1700 0.0000
22 22 60.1700 60.1666 60.2100 0.0000
23 23 60.2100 60.1836 Short 60.2400 -0.0300
24 24 60.2400 60.2069 Short 60.2450 -0.0050
25 25 60.2450 60.2074 Short 60.2500 -0.0050
26 26 60.2500 60.2189 Short 60.2700 -0.0200
27 27 60.2700 60.2838 Long 60.2550 -0.0150
28 28 60.2550 60.2648 60.2600 0.0000
29 29 60.2600 60.2836 Long 60.2900 0.0300
30 30 60.2900 60.3051 Long 60.3000 0.0100
31 31 60.3000 60.3109 Long 60.3750 0.0750

6.2.3 Other Prediction Models

[hochreiter1997long]

proposed Long Short-term Memory (LSTM) Networks, which are a type of recurrent neural networks and applied successfully to predict stock markets data. It will be worth to see the performance of LSTM method to predict the trading signals of stock prices, in future research.

7 Conclusion

The goal of this report is to compare the time series methods versus some machine learning based algorithms for stock price movements and generating trading signals. The use of on-line learning algorithms is forced by nature of stock markets price behavior, as they are prone to exogenous shocks. To avoid effect of these shocks (some news shocks and some macro-foundations shocks) using on-line learning algorithms will be helpful. The study shows, random forest algorithm performs considerably better than Arima (which is simply regressing today’s prices on history of prices). But employing Kalman filter together with Expectation Maximization algorithm, results way better than Ensemble of Random Forest Algorithm. One might need to check if Kalman Filter performs better than other Machine Learning algorithms such as Long-Short Term Memory in future research.

References