Trend Following Strategies in Python: How to Use Indicators to Follow the Trend.

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Understanding the Relative Strength Index

The RSI stands out as the most recognized momentum indicator, especially effective in ranging markets. Its values span from 0 to 100, simplifying interpretation. The widespread use of the RSI among traders can create a self-fulfilling prophecy, as market movements often respond to its signals.

The calculation of RSI is straightforward. We begin by determining the price differences for each period by subtracting each closing price from the preceding one. Next, we compute the smoothed average of positive differences and divide that by the smoothed average of negative differences. This yields the Relative Strength, which is then plugged into the RSI formula to produce a value between 0 and 100.

To compute the RSI, an OHLC array (not a data frame) is required. This entails working with a four-column array. The function for calculating the RSI is as follows:

# Function to add a specified number of columns to an array def adder(Data, times):

for i in range(1, times + 1):

new_col = np.zeros((len(Data), 1), dtype=float)

Data = np.append(Data, new_col, axis=1)

return Data

# Function to delete a specified number of columns starting from an index def deleter(Data, index, times):

for i in range(1, times + 1):

Data = np.delete(Data, index, axis=1)

return Data

# Function to remove a specified number of rows from the beginning def jump(Data, jump):

Data = Data[jump:, ]

return Data

# Example of adding 3 empty columns to an array my_ohlc_array = adder(my_ohlc_array, 3)

# Example of deleting the 2 columns after the column indexed at 3 my_ohlc_array = deleter(my_ohlc_array, 3, 2)

# Example of deleting the first 20 rows my_ohlc_array = jump(my_ohlc_array, 20)

The OHLC acronym stands for Open, High, Low, and Close, representing standard historical data. The moving average function can be defined as:

def ma(Data, lookback, close, where):

Data = adder(Data, 1)

for i in range(len(Data)):

try:

Data[i, where] = (Data[i - lookback + 1:i + 1, close].mean())

except IndexError:

pass

Data = jump(Data, lookback)

return Data

def ema(Data, alpha, lookback, what, where):

alpha = alpha / (lookback + 1.0)

beta = 1 - alpha

Data = ma(Data, lookback, what, where)

Data[lookback + 1, where] = (Data[lookback + 1, what] * alpha) + (Data[lookback, where] * beta)

for i in range(lookback + 2, len(Data)):

try:

Data[i, where] = (Data[i, what] * alpha) + (Data[i - 1, where] * beta)

except IndexError:

pass

return Data

def rsi(Data, lookback, close, where, width=1, genre='Smoothed'):

Data = adder(Data, 7)

for i in range(len(Data)):

Data[i, where] = Data[i, close] - Data[i - width, close]

for i in range(len(Data)):

if Data[i, where] > 0:

Data[i, where + 1] = Data[i, where]

elif Data[i, where] < 0:

Data[i, where + 2] = abs(Data[i, where])

if genre == 'Smoothed':

lookback = (lookback * 2) - 1

Data = ema(Data, 2, lookback, where + 1, where + 3)

Data = ema(Data, 2, lookback, where + 2, where + 4)

if genre == 'Simple':

Data = ma(Data, lookback, where + 1, where + 3)

Data = ma(Data, lookback, where + 2, where + 4)

Data[:, where + 5] = Data[:, where + 3] / Data[:, where + 4]

Data[:, where + 6] = (100 - (100 / (1 + Data[:, where + 5])))

Data = deleter(Data, where, 6)

Data = jump(Data, lookback)

return Data

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Introduction to Correlation

Correlation represents the extent of a linear relationship between two or more variables. It is confined between -1 and 1, with 1 indicating a perfect positive correlation, -1 representing a perfect negative correlation, and 0 denoting no linear correlation. While this measure isn't flawless and may be affected by outliers and non-linear relationships, it provides quick insights into statistical properties. Two well-known types of correlation are:

• Spearman correlation assesses the relationship between two continuous or ordinal variables, where variables may vary together but not necessarily at a constant rate, relying on value ranks.
• Pearson correlation evaluates the linear relationship between two continuous variables, characterized by proportional changes in each variable.

Although not perfect, this measure allows for swift insights into statistical characteristics.

In Python, we can implement a correlation function for two variables as follows, ensuring it utilizes an array rather than a data frame:

from scipy.stats import pearsonr

def rolling_correlation(Data, first_data, second_data, lookback, where):

Data = adder(Data, 1)

for i in range(len(Data)):

try:

Data[i, where] = pearsonr(Data[i - lookback + 1:i + 1, first_data], Data[i - lookback + 1:i + 1, second_data])[0]

except ValueError:

pass

Data = jump(Data, lookback)

return Data

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The Correlation-Adjusted Relative Strength Index

The fundamental concept of this indicator is that when the correlation between the indicator and market price is high, it’s prudent to heed its signals. The strategy encompasses these steps:

1. Calculate a 2-period RSI on the market price.
2. Determine a 3-period rolling correlation between the market price and its 2-period RSI to assess their movement together.
3. Compute a 3-period RSI on the rolling correlation established in the previous step.

> Note: The selection of lookback periods is subjective and can vary. For manual trading, a 13-period RSI may be employed.

# Indicator Parameters lookback_corr = 3 lookback_rsi = 2

# Calculating the 2-period RSI on the market price my_data = rsi(my_data, lookback_rsi, 3, 4)

# Determining the rolling 3-period correlation between market price and 2-period RSI my_data = rolling_correlation(my_data, 3, 4, lookback_corr, 5)

# Computing the 3-period RSI of the 3-period correlation my_data = rsi(my_data, lookback_corr, 5, 6)

The trading criteria can be summarized as follows:

• A buy (Long) signal triggers when the 2-period RSI is at or below 5, while the 3-period RSI of the correlation is at or above 50.
• A sell (Short) signal occurs when the 2-period RSI is at or above 95, with the 3-period RSI of the correlation at or above 50.

The high correlation condition serves to filter signals, suggesting that the current RSI is more predictive when the correlation with market price is elevated. Conversely, a low correlation implies a likely lack of reaction in line with the expected outcome. The signal function can be structured as follows:

def signal(Data, rsi_col, corr_rsi, buy, sell):

Data = adder(Data, 10)

for i in range(len(Data)):

if Data[i, rsi_col] <= 5 and Data[i, corr_rsi] > 50 and Data[i - 1, buy] == 0 and Data[i - 2, buy] == 0 and Data[i - 3, buy] == 0 and Data[i - 4, buy] == 0:

Data[i, buy] = 1

elif Data[i, rsi_col] >= 95 and Data[i, corr_rsi] > 50 and Data[i - 1, sell] == 0 and Data[i - 2, sell] == 0 and Data[i - 3, sell] == 0 and Data[i - 4, sell] == 0:

Data[i, sell] = -1

return Data

Two methods for validating this concept include:

1. Comparing the above strategy with a conventional 2-period RSI strategy without correlation. This provides a direct comparison, albeit without the correlation filter, highlighting the added value of this technique.
2. Comparing the strategy while inverting the condition of the correlation, meaning we will only consider signals if the RSI of the correlation is below 50.

The first test conducted on hourly EURUSD values employs a 1-hour holding period, assuming the short-term RSI serves as a timing indicator. Each signal entails buying or short-selling and holding until the subsequent bar. The results indicate that the correlation filter performs better. However, this doesn’t establish a solid strategy since the equity curve below is based solely on simple rules without risk management or accounting for transaction costs.

The second test juxtaposes the correlation-adjusted RSI against a modified correlation condition, further validating our initial intuition.

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All About Trading!

Sharing Trading Strategies, Knowledge, and Technical Tools in Detail. abouttrading.substack.com

Always conduct your back-tests. It's essential to question the reliability of others' strategies. My indicators and trading style may suit me but may not align with your approach.

I firmly believe in self-discovery through practice rather than mere imitation. Grasp the concept, function, intuition, and conditions of a strategy, then develop an even better version for thorough back-testing and refinement before implementation or rejection. My decision to withhold specific back-testing results encourages readers to engage deeply with the strategy and develop it further.

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