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https://github.com/vbprojects/npmmtradingstrategy

This project implements a financial trading strategy in Julia which nowcast local highs and lows to create trading signals, comparing stable rule set classifiers and gradient boosted tree models for trading performance.
https://github.com/vbprojects/npmmtradingstrategy

feature-engineering financial-machine-learning financial-modeling julia machine-learning python time-series-analysis

Last synced: about 2 months ago
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This project implements a financial trading strategy in Julia which nowcast local highs and lows to create trading signals, comparing stable rule set classifiers and gradient boosted tree models for trading performance.

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README 

          
# N-Period Min Max Prediction Through Stable Rule Set Classifiers for Financial Trading Signals

## Authors: Varun Bhatnagar, Miranda Goodman 

This project needs Julia 1.9 to run. It also needs a valid Python distribution as it will install Python dependencies.



Package dependencies



Plots, LinearAlgebra, Statistics, DataFrames, CSV, NLsolve, Memoize, MLJBase, Pkg, MLJModels, ScikitLearn, Flux, Zygote, StatsBase, PyCall, Dates, MLJParticleSwarmOptimization, StatisticalMeasures, MLJTuning, Distributions, MethodChains, SIRUS, EvoTrees



Python Dependencies



ta, pandas, pandas_datareader, yfinance



Results are stored in the notebooks folder under airlines.ipynb, beverages.ipynb, and tech.ipynb. Data download commences on the first run, ensure that you have a stable internet connection. Startup and first recompilation times for Julia are long and Python dependencies will be downloaded by the script itself on the first launch to its own Anaconda environment. The Julia installations, Python installations, and data downloads can take more than 10 gigabytes of space, be aware of space constraints when downloading data. Unfortunately, julia's package manager at this time does not allow for sending a requirements.txt, Packages can be downloaded with these commands.



```

using Pkg

Pkg.add(split("Plots LinearAlgebra Statistics DataFrames CSV NLsolve Memoize MLJBase MLJModels ScikitLearn Flux Zygote StatsBase PyCall Dates MLJParticleSwarmOptimization StatisticalMeasures MLJTuning Distributions SIRUS EvoTrees", " "))

Pkg.add(url="https://github.com/uniment/MethodChains.jl")

```



# Introduction



Stock market forecasting and trading strategies have been extensively

studied by statisticians when concerning traditional statistical models.

Numerous companies and strategies exist to profit off

even traditional forecasting methods, however, with the advent of newer

machine learning techniques like Gradient Boosted Trees, Long-Term

Short-term memory networks, and even Transformer models, long standing

assumptions of the inability of previous data to create profitable

trading strategies above the average annualized returns of a single

stock have been challenged. We hope to show that a novel

combination of machine learning techniques can outperform previous

methods and generate profitable returns despite the stochastic nature of

financial data, particularly financial securities relating to the

various sectors of the American Market.



This study seeks to answer the following research questions:



1\. Can a higher profit margin be achieved using NPMM labeling along

with financial feature engineering methods and a Stable and

Interpretable Rule Sets model?



2\. How do Stable Rule Set models compare to Gradient Boosted Tree

Methods within financial time series modeling?



3\. What are the decisions being made by Stable Rule Set models in

regard to financial engineering



The focus of this research is to optimize a trading strategy pursuant to

buying and selling assets at optimal times. Given model predictions, we

emit a buy or sell

signal which alternates over some interval. We must buy the asset to

sell it and must sell the asset before buying again. This gives a

simplistic view of markets where we cannot sell without holding the

asset at all (short the asset) or simply buy more of the asset over a

time interval. However, the evaluation of trading strategies that

consider multiple buys, sells, shorts, and other financial derivatives

makes validation difficult. Thus, we stick to our simple trading

strategy for evaluation. 



The difficulty in justifying the use of this financial strategy is in

considering the opportunity cost of holding the asset or buying and

then not selling the asset till the end of the

time interval. Consider a risk-free asset that grows at a constant rate.

In the absence of volatility, it would not be optimal

to sell the asset after buying before the end of the interval as we keep

expecting the asset to increase in value, thus selling the asset and

then buying at a later date only disqualifies us from collecting the

appreciation of the asset over the interval where we did not hold

it. While the financial securities we are concerned about are not

risk free, the sentiment generally holds. Optimal

trades, periods of times before paired and ordered buys and sells, must

occur when the asset is undervalued to when the asset is overvalued to

profit from the volatility. However, that volatility is difficult to

predict and makes our opportunity cost not only money we may lose on the

trade but also that profit relative to the appreciation of the

underlying asset. The rise of machine learning techniques like

XGBoost and Deep Learning have led to many being able to create

theoretically profitable methods. The method we plan on implementing is

a Stable Rule Set Classifier (SBC) and a XGBoost model.



Additionally, the response variable for supervised machine learning

models is not well defined and several competing labeling techniques

exist within this space. One prominent example within the literature is

up-down labeling, where we label whether an asset at any given time step

will go up or down one time interval in the future. Difficulties with

this strategy are with volatility of the stock. While a less difficult

problem on paper than forecasting, much of the problems with both

remain. For example, the naïve assumption that the asset will rise if

the asset rose in the previous interval or vice versa can become a

suboptimal convergence point for algorithms of this nature. The response

itself is also noisy and relates heavily to the volatility of the underlying

asset (Han, Y., Kim, J., & Enke, D. (2023)). While up-down labeling

makes this a classification problem, the realm of regression where a

signal is emitted given some threshold of model output is littered with

failed methods. While continuous label methods hope to overcome the

biases relating to categorical methods, the difficulty comes in

adjusting for look-ahead bias, where the label itself relies heavily on

future data to set a target using a past interval and becomes too

difficult to predict while also retaining the model's volatility (We et.

all 2020). N-Period Min Max Labeling hopes to address failures in

categorical methods by creating a simple and learnable label. Another

difficulty with supervised learning for financial time series is feature

engineering. Financial assets generally come with five features- the

opening price over the interval, closing price, high price, low price,

and volume of assets traded. There has been a large effort by technical

traders to create a variety of indicators based of these features

including looking at how values modulate over time to create an

extensive set of variables that could be related to our response. We use

a combination of feature selection techniques and Partial Least Squares

regression to attempt to capture as much relevant information from these

indicators as possible.



A diagram of a software system Description automatically generated



Figure 1. Visual of modeling process (Wu et. all,

2020)



Figure 1 represents the general process necessary for

implementing our various techniques. We plan on using N-Period

Min Max Labeling for our Labeling Method, a Stable Rule Set Classifier

and a XGBoost model, and Partial Least Squares Regression for our

feature processing.



#  LITERATURE REVIEW



## NPMM Labeling



This study uses a labeling strategy and data sources from the paper

written by Han, Y., Kim, J., & Enke, D. (2023). The labeling schema is

an N-period min max labeling technique which identifies the local

maximums and minimums of a stock trade only labeling at definite time

points in the stock trade. Then for a trading strategy, one would want

to sell a stock at the maximum (When the stocks are worth the most) and

buy at the minimum (When the stock is not worth much). There has not

been much prior work done on NPMM labeling in the financial world. Much

research prior to the work done by Han, Y., Kim, J., & Enke, D. (2023)

who attempted to label all points in the stock market using up-down

labeling - a strategy that led to small price change sensitivity and

inaccurately labeled training sets. Up-down labeling views all changes in

the stock market as being equally important, which is not always the

case. *Wu, Wang, Su, Tang,* and *Wu* (2020) found that up-down labeling does

not accurately predict continuous trends in the stock market. This

created flaws between the data labels and the actual market results.

With NPMM only labeling at definite points, it allows the training set

to not be as affected by small price changes. The data for both this

study and the work done by Han, Y., Kim, J., & Enke, D. (2023) comes

from Yahoo Finance.



A graph showing a line graph Description automatically generated



Figure 2. Visual of Up Down Labelling (Han et al.,

2023)



Up-down labeling is only looking at the overall trend

of the market. Are the trends going up or are they going down? In figure

2 the green triangle symbols show when the stock trends are increasing,

and the red triangle symbols show when the stock trends are decreasing.

This approach to stock market analysis is almost oversimplified because

it is susceptible to small price change variability, something that is

avoided with NPMM labeling.



## Technical Indicators and PLS



Through the use of technical indicators paired with both our models this

research aims to achieve higher accuracy results. A technical indicator

is on a per stock basis, and it is a measurement or calculation that

provides one with some kind of information about the stock. Combining

these indicators forms trading strategies. One of the most used

technical indicators is MACD which looks at the direction a stock is

headed. It summarizes if a stock is moving upward (meaning the stock is

worth more money) or downward (meaning we're losing money). MACD also

looks at how strongly the stock is moving in that direction and for how

long. Using this information in combination with other indicators gives

a stronger understanding of the overall market. This research was

exemplified by the work of Wen, C., Zhu, H., & Dai, Z. (2023) who

combined over 100 different technical indicators and used a PLS strategy

for reduction. *Kelly* and *Pruitt* (2013, 2015) developed the PLS

method, but it was the work of *Huang et al.* (2015), *Stivers* (2018),

and *Hoang et al.* (2020) that showed the reliability and superior

performance of PLS compared to other reduction techniques. This research

will use PLS to do reduction on the technical indicators. PLS finds a

limited set of variables that maximizes covariance between independent

and dependent variables. Even for classification tasks, PLS can

outperform Linear Discriminate Analysis or LDA when there lacks

similarity between the covariance of independent variables to the

dependent variables. LDA is also used for dimensionality reduction but

makes assumptions that the independent and dependent variables have the

same covariance which is not the case with stock market prediction. PLS

does not make this assumption. PCA is also usually thought of for

dimensionality reduction but can easily struggle when handling noisy

data. The stock market has very noisy data and Wen, C., Zhu, H., & Dai,

Z. (2023) research found that PLS is better at handling these types of

data sets.



## Stable Interpretable Rule Sets



Gradient Boosted Tree models have become common place for modeling

tabular datasets. Difficulties in their use arise when considering the

interpretability of their predictions, especially for applications where

potential mishaps equate to incorrigible losses. While better

understanding of model insights may not increase any empirical accuracy,

human trust in models and evaluation of the decision-making processes of

black-box models have become a prominent field of study. State of the

art methods like Shapely Additive Explanations (SHAP) assign feature

importance per instance which can be averaged over a set of predictions

to get a better understanding of how features are used in the model

(Lundberg, 2017).



Instead of assessing interpretability through feature importance, Stable

Interpretable Rule Set (SIRUS) models give a set of rules whose

conditions contribute additively to the prediction.

These models fit random forests composed of shallow

decision trees and extract a set of rules which when a condition is

met increase the model's certainty in the prediction of a classification

target. SIRUS models inherit performances of random forests while

exhibiting robustness to data perturbations, and within the context of

noisy financial time series data, these properties make the model an

interesting candidate for implementation of trading strategies. (Bénard

et al., 2019)



# Novel Implementation



This research was completed in stages to accurately predict stock market

trends. The first stage was the gathering and labeling of the data.

Stock market data is noisy and difficult to analyze when considering

small price change variability. This research addresses these concerns

achieving a solution that is unique from most historical labeling

methods. This study then considers many of the market and technical

indicators as features. There were 92 technical indicators applied to

one stock at a time and 5 market indicators. PLS will be used as a

reduction technique on the technical indicators and will be added to the

list of indicators, but there is still a significant amount of

hyperparameters being used in the model. To reduce the hyperparameters

we will use an adaptive particle swarm cross validation which reduces

the grid for optimizing our parameters. The data and features will be

fed into a gradient boosted tree model and a stable rule regressor.

These models will be validated using a time series cross validation.



## Data Sets



The data set used in this paper comes from Yahoo Finance and contains

data from the United States stock market for years 2000 until 2022.

Stock trends from 2000 until 2021 will be used as training data and

stock market data from 2022 will be unseen data used for testing. We

will specifically be looking at various assets grouped by type. For

example, we will be looking at technology stocks which include Apple,

Microsoft, Google, and Tesla. We will also be looking at beverage stocks

like the Coco-Cola company. A full list of stocks used for training can

be found in our results section.



Financial assets generally come with five features- the opening price,

closing price, high price, low price, and volume of assets traded over

each interval. This holds true for this study. We use a combination of

feature selection techniques and PLS regression to capture as much

relevant information from both these features and our technical

indicators as possible.



## Labeling Schema



This study uses an NPMM labeling schema combined with both market and

technical indicators to predict stock market trends. Remember from

previous studies, NPMM labeling does not always have the highest win

ratio of a labeling strategy especially when compared to up-down

labeling. However, NPMM labeling had a higher profit factor than other

labeling strategies. When we think about stock market prediction, we

care less about accuracy and more about profit. So, breaking this down

further, when NPMM labels a trade, it is not always correct even

compared with other labeling schemas. Though when NPMM labeling is

right, it is right by significantly more than other labeling schemas and

when NPMM labeling is wrong it is less wrong compared to the other

schemas. This means when using NPMM labeling as a schema, we have a

higher probability of making money even though it is less accurate than

other models. NPMM labeling is described in figure 3 below. A NPMM

labeling technique identifies the local maximums and minimums of a stock

trade only labeling at definite time points in the stock trade. In

figure 3 the maximums are labeled in green, and the minimums are labeled

in red. For a trading strategy, one would want to sell a stock at the

maximum (When the stocks are worth the most) and buy at the minimum

values (When the stock is not worth much).



A graph showing a line graph Description automatically generated



Figure 3: Diagram showing an NPMM labeling

schema.



## Using Technical and Market Indicators



We will pair each stock from our data set sample (Tesla, apple, and

beverage stocks) with five market indicators: S&P 500, NASDAQ, VIX

score, Dow Jones Industrial Average, and the Russel 2000 index. The S&P

500 stands for the Standard and Poor 500. It is a stock market index

that looks at the largest 500 companies in the United States and how

much of an influence each of them has over the market based on a market

capitalization index. It is one of the single largest indicators of how

the stock market is doing as a whole. The NASDAQ is similar to the S&P

500, but only looks at tech companies and how they are influencing the

stock market. The NASDAQ incorporates the market capitalization of over

3000 tech companies. The VIX score looks at the volatility of the market

and analyzes the likelihood of stock market trends drastically changing.

It is often referred to more commonly as the fear index because when the

entire market moves drastically it usually means that a lot of stocks

are going to drop quickly. Stocks rarely will drastically move up all at

once, but they all can drop at the same time. This was seen most

recently during the economic trouble in 2008 and during the COVID 19

pandemic. The Dow Jones Industrial Average looks at larger publicly

owned companies with the idea that the companies with greater stocks

have greater control over the performance of the stock market. The

Russel 2000 index is almost the opposite of the S&P 500. Instead of

looking at bigger-sized companies with a greater market capitalization,

Russel 2000 looks at larger companies but with a lot of small market

capitalization.



This study applied 92 technical indicators for each

stock and market indicator making a matrix to analyze 552 x N

values. 552 is obtained by multiplying our 92 indicators by the

specific stock and by the 5 market indicators.



# Methodology



## Data Preparation



We obtained market data from the earliest year data was available for a

specific asset after 2000 to 2022. We then used the *ta* library in

python to add technical indicators to each of the training datasets. We

concatenated the columns of our axillary market indicators to each of

the tickers present in our composites. We then used PLS to create an

additional feature for our training dataset on top of the other

technical indicators present.



## Model Selection



Due to the large search space of possible Gradient Boosted Tree

Parameters, we opted to use an Adaptive Particle Swarm Approach with

resampling done through Cross Validation. We used a Time Series Cross

Validation Split on the N-Period Min Max data from 2000 to 2021 for

hyperparameter tuning. Model selection during hyperparameter tuning was

conducted by comparing the Briar Loss of probabilistic predictions made

by EvoTree and Stable Rule Set Classifiers to whether or not an extremum

was a min or max. We used 3 particles for each step and trained a total

of 50 models. For our Stable Rule Set Classifier, we opted to use

default settings as listed by the Julia SIRUS.JL

package. We did not record significant change in performance due

to parameter tuning for Stable Rule Set Classifiers.



> (J. Zhang et al., 2011)



## Evaluation Criteria



For evaluation purposes, we held 2022 from training. For evaluating the

test set, a different methodology was used. Instead

of attempting to predict whether or not a point was a local extremum and

then classify it as a minimum or maximum, all instances in the test were

classified, then a signal to sell was generated if the probability of

the prediction was greater than some threshold θ, and a signal to buy if

less than 1 – θ. Threshold values lie between 0.5 and 1, the

choice impacting the amount of trade and confidence of whether the trade

would represent buying or selling at the appropriate extrema.



While signals generated may not be alternating, in evaluation given a

buy signal we only buy if we are not holding the asset and given sell

signal we only sell if holding the asset. We consider signals that are

acted on buy orders and sell orders. Applying this strategy to the time

series could lead to misleading results, particularly if at the end of

the time series we are still holding the asset. Instead, we consider the

performance of trades, or pairs of buy orders and sell orders.

Considering that the value of a trade per asset is

the sale price minus the buy price, we looked at the mean value of

trades, the standard deviation, mean value of winning trades or trades

that are positive, the mean value of losing trades or trades that are

negative, and the win rate or percentage of trades that are

positive.



We split our evaluation data over three composites, tech, beverage, and

airline. Tech assets are

generally high growth, however 2022 presents an interesting case study

on the performance of the algorithm given that 2022 represented a period

of high volatility with a sharp decline in the first 3 quarters and

uptick in the last. Beverage assets are generally stable and

airline assets are just another easily grouped asset class we could

train to show some amount of generalization.



#  Results



The following represent performance by EvoTree

(XGBoost implementation in Pure Julia) and Stable Rules Classifier

performance all at thresholds of 80%.



Note: predictions are modes of possible categories, for thresholding we

took the ratio of predicted categories instead of the value for each,

i.e. If a class must be chosen what is the probability of it being

positive. For Stable Rule Set Classifiers consider that the output is

normalized with respect to the possible maximum of the decisions.



EvoTrees/XGBoost => GBT, Stable Rule Set Classifier => SBC



## Beverages



Tickers: "KO", "PEP", "CELH", "MNST", "KDP", "FIZZ", "BUD", "SBUX", "TAP"



Win Rate GBT/SBC

70.91% / 70.00%



Mean GBT/SBC Value of Trade

$0.156 / $0.265



Std. GBT/SBC Value of Trade

$2.363 / $2.742



Mean GBT/SBC Win

$ 0.985 / $ 1.253



Mean GBT/SBC Loss

$-1.880 / $-2.067



Mean GBT/SBC NPMM return rate

15.826 % / 18.612%



Std. GBT/SBC NPMM Return Rate

27.489% / 21.576%



Mean Asset Return Rate

4.553 %



Std. Asset Return Rate

14.733 %



Time Series Cross Validation Accuracy



Fold 1

Fold 2

Fold 3

Fold 4

Fold 5



GBT

91.9%

92.7%

94.2%

91.5%

91.1%



SBC

82.1%

87.1%

76.1%

77.8%

83.7%



Best Hyper Parameters GBT



Max Depth

4



Column Sample

56.213 %



Row Sample

38.569%



Learning Rate

1.0



Number of Rounds

21



L2 Regularization

0.0



Alpha Regularization

0.456



Lambda regularization

3.127



Gamma Regularization

0.0



Minimum Weight

3.0



Number of Bins

97



Tree Type

Binary



SBC Logic



if Stochastic < 67.058784 then 0.003 else 0.02 +



if Williams %R < -32.94121 then 0.003 else 0.02 +



if Keltner Channel P Band < 0.7670374 then 0.002 else 0.015 +



if Keltner Channel H Indicator Band < 1.0 then 0.012 else 0.058 +



if Stochastic RSI < 0.64570004 then 0.003 else 0.019 +



if Williams %R < -50.015392 then 0.0 else 0.001 +



if Bollinger Band P Band < 0.65591186 then 0.004 else 0.023



## Technology



Tickers: "AAPL", "MSFT", "NVDA", "ORCL", "AMZN", "GOOG", "INTC", "META",

"TSLA"



Win Rate GBT/SBC

61.23% / 56.65%



Mean GBT/SBC Value of Trade

$-1.209 / $ -3.529



Std. GBT/SBC Value of Trade

$ 9.875 / $19.816



Mean GBT/SBC Win

$ 3.390 / $4.374



Mean GBT/SBC Loss

$ -8.548 / $-13.858



Mean GBT/SBC NPMM return rate

‑30.482% / ‑30.066%



Std. GBT/SBC NPMM Return Rate

14.674% / 17.293%



Mean Asset Return Rate

-43.221 %



Std. Asset Return Rate

19.574 %



Time Series Cross Validation Accuracy



Fold 1

Fold 2

Fold 3

Fold 4

Fold 5



GBT

91.9%

92.7%

94.2%

91.5%

91.1%



SBC

82.1%

87.1%

76.1%

77.8%

83.7%



Best Hyper Parameters GBT



Max Depth

6



Column Sample

41.541%



Row Sample

28.421%



Learning Rate

0.2055



Number of Rounds

21



L2 Regularization

1.076



Alpha Regularization

0.515



Lambda regularization

0.0



Gamma Regularization

10.0



Minimum Weight

5.0



Number of Bins

74



Tree Type

Binary



SBC Logic



if Keltner Channel P Band < 0.80790466 then 0.002 else 0.012 +



if Williams %R < -29.655165 then 0.003 else 0.016 +



if Stochastic < 70.34483 then 0.003 else 0.017 +



if Keltner Channel L Indicator Band < 1.0 then 0.119 else 0.006 +



if Bollinger Band P Band < 0.6683319 then 0.005 else 0.02 +



if Keltner Channel H Indicator Band < 1.0 then 0.007 else 0.032



## Airlines



Tickers: "AAL", "CPA", "DAL", "UAL", "AAL", "ALK"



Win Rate GBT/SBC

67.56% / 59.77%



Mean GBT/SBC Value of Trade

$-0.044/ $ -0.131



Std. GBT/SBC Value of Trade

$ 2.007/ $2.613



Mean GBT/SBC Win

$ 0.774/ $1.079



Mean GBT/SBC Loss

$ -1.795/ $-1.955



Mean GBT/SBC NPMM return rate

-8.969% / -13.609%



Std. GBT/SBC NPMM Return Rate

13.116% / 11.491%



Mean Asset Return Rate

-20.084%



Std. Asset Return Rate

11.876%



Best Hyper Parameters GBT



Max Depth

4



Column Sample

60.229%



Row Sample

28.594%



Learning Rate

0.68171



Number of Rounds

25



L2 Regularization

6.167



Alpha Regularization

0



Lambda regularization

1.0083



Gamma Regularization

1.5328



Minimum Weight

1.0



Number of Bins

125



Tree Type

Binary



Time Series Cross Validation Accuracy



Fold 1

Fold 2

Fold 3

Fold 4

Fold 5



GBT

90.1%

91.7%

90.9%

91.9%

91.9%



SBC

80.8%

74.1%

79.2%

84.6%

81.1%



SBC Logic



if Keltner Channel L Indicator Band < 1.0 then 0.139 else 0.013 +



if Stochastic < 66.666664 then 0.002 else 0.014 +



if Stochastic RSI < 0.6425483 then 0.004 else 0.015 +



if Williams %R < -51.76471 then 0.001 else 0.004 +



if Daily Returns < 0.3911308 then 0.001 else 0.004 +



if Keltner Channel H Indicator Band < 1.0 then 0.008 else 0.034 +



if Keltner Channel P Band < 0.7508161 then 0.002 else 0.009



# Discussion



## Reliability of Results



During the evaluation year of 2022, the model outperformed the

underlying asset composites, and for most well-performing assets

outperformed the S&P 500 index. However, there are several reasons why

this performance may not be indicative of broader algorithmic

effectiveness. Notably, the evaluation year, 2022, saw large downturns

for many industries leading the S&P 500 to decrease by ‑19.64%. As the

technology sector saw the largest depreciation, our composite assets

returned an average of ‑43.22%. It also does not benefit us to not

consider market conditions in 2022 in the assessment of our models,

financial phenomena happen constantly and the ability of trading

strategies to be more profitable than the overall market in adverse

conditions is surprising and speaks to the effects of the labeling

method involved. However, further composites and market conditions must

be evaluated to ascertain whether these models can result in long-term

gains.



## Comparison of Gradient Boosted Trees and Stable Rule Sets



While EvoTrees/XGBoost performed better on N-Period Min Max

classification, they did not generate better profit for beverage and

technology composites. This highlights the discrepancy between our

prediction target and our evaluation metrics. Increases in validation

accuracy of local extrema classification do not necessarily lead to

increased profits. Stable Rule Set Classifiers did not seem to select

any auxiliary features, preferring momentum and volatility-based

indicators of the underlying asset itself. While this

may vary with increasing the maximum amount of rules, the performance of

both GBT and SBC models were not so different as to justify the

computational or interpretability cost of using GBT models or increasing

the complexity of SBC models.



SBC models tended to have a higher absolute value of mean trades,

suggesting that time intervals between orders were higher.



## Feature Selection



In our evaluation even with emphasis on feature

reduction techniques, it is not clear whether feature selection will

heavily influence the outputs of these experiments especially given the

validation scores of the models involved. There may be a wide

range of potential feature interactions present with the given technical

indicators that produce well-performing classifiers.

Heavy regularization penalties employed in our

hyperparameter search is a definite indicator of collinearity and noise

within our feature set, but the Stable Rule Set Classifier was able to

see past the nearly 400 features unrelated to the asset being evaluated

and pin 7 rules that have some theoretical substance. Keltner and

Bollinger bands are often thought of as predictions on price floors and

ceilings, while Stochastic, Stochastic RSI, and Williams %R can be used

to indicate over buying or selling, which represent changes in price

direction. PLS is not present in the SBC logic, which should be expected

as feature reduction generally leads to less interpretable results (Liu

& Motoda, 2002).



# Future Work



## NPMM Labeling as Instance Selection



As we and the authors of the N-Period Min Max Labeling paper have

applied the method, it functions less as a true target and more a method

of instance selection. Instance selection is a family of methods that

increase data quality by removing noise or difficult to classify data

points that may affect the rest of the time

series model. The target provided by NPMM labeling at first glance seems

tangentially related to a trading strategy. We cannot

be certain in a testing environment whether a point is or is not an

extremum, however, local extremas seem to provide valuable information

on price direction that applies to all points in the time series.

If this form of instance selection is robust, it may be applicable to

more informative targets, such as opportunity cost or even forecasting

methods (Liu & Motoda, 2002).



## Paper Trading Implementation



SBC models produce interpretable and easily programmable models that can

be implemented on a variety of architectures and platforms. One such

platform to consider would be Pine Script, a language by Trading View

meant for back testing trading strategies. Other

platforms exist that can be implemented with Julia and Python such as

Alpaca, that can be used to test the model's ability in a real

environment with fees for making transactions, potential non-liquidity,

and other fun problems that do not appear in simulated trading.



## Fuzzy Inference Models



The connection between Stable Rule Set Classifiers and Fuzzy Inference

models is most apparent when considering their outputs. Both produce

rules that have an additive effect on the output, however, fuzzy

inference makes rules from fuzzy sets while Stable Rule Set Classifiers

use deterministic sets. For example, if we were to want to predict

whether or not it rains tomorrow, we might consider 2 variables,

humidity, and temperature. A stable rule set classifier may arrive at a

rule like if the temperature is less than 50 degrees and humidity is greater

than 70% then it will rain. Fuzzy inference systems create fuzzy sets

for which a data point can have a chance of belonging. For example,

the model may output a rule like if it is cold and humid it will rain.

The probability a point may be in the category cold could be Gaussian

centered at 30 degrees while humid is also Gaussian centered at 90%. We can

then calculate the probability that the rule is true based on the

probability that the point falls into the sets cold and humid.

They both provide interpretable rule sets, but fuzzy

inference systems can communicate the confidence of a prediction based

on the probability that new data points fit with previously established

categories, which could lead to trading strategies that prevent losses

when market conditions change and make the model potentially

unprofitable (Hassanniakalager et. al 2020).



# Concluding thoughts



Going over the research questions we posed in our introduction, we now

have insight into these answers.



1.  Can a higher profit margin be achieved using NPMM labeling along

    with financial feature engineering methods and a Stable and

    Interpretable Rule Sets model?



While both methods outlined in this paper seem to outperform composites

and the overall market, it is difficult to truly validate the use of

these algorithms have given market anomalies in 2022. Paper trading or live

trading over an extended period of time may increase our confidence in

these methods.



1.  How do Stable Rule Set models compare to Gradient Boosted Tree

    Methods within financial time series modeling?



Stable Rule Set Models seem to outperform Gradient Boosted Tree Models

in conditions where stocks are generally non-volatile with growth rates.



1.  What are the decisions being made by Stable Rule Set models in

    regard to financial engineering



Stable Rule Set Models seem to prefer the individual stock's momentum and

volatility-based technical indicators, forgoing PLS and auxiliary market

indicators. More complex models may turn to these indicators, however,

the trade-off between interpretability and complexity still exists. It

may not be worth using more complex models given the simplicity and near

equivalence of profitability between Gradient Boosted Trees and Stable

Rule Set Models.



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