Algorithmic Trading Python 2023 - 3.2 - Python Codes for Population & Samples #maths #technology

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Greetings everyone! Welcome to my channel, Quantum Unicorn. Please join me on a remarkable journey as we explore the world of stock trading and financial analysis using the powerful programming language, Python. I'm excited to share my knowledge and insights with you as we delve into the exciting and dynamic field of stock trading modeling and financial analysis. I look forward to embarking on this journey with you and creating a vibrant community of like-minded individuals. Let's make the most of this opportunity to learn and grow together. Welcome aboard!

We will delve into the exciting world of Python and its application in the analysis of financial data. Before we get started, let's explore how Python is utilized in the financial industry.

Quantitative analysts and engineers of investment banks use Python to build all kinds of models, predict returns, and evaluate risks. Engineers use Python to crawl financial news and to dig out users' reactions and sentiments. This new source of data from social media can greatly help quantitative analysts to improve the performance of the models.

Investment banks rely on the expertise of quantitative analysts and engineers who use Python. But the use of Python is not limited to investment banks, it has also become a popular tool among data scientists in consumer banks. They use Python to analyze credit risk models and customer behavior, reducing the risk of lending.

With the ability to predict customer behavior, they can also create recommendation models to improve the accuracy of recommendations for new customers across different markets, which is called "customer migrations".

So, what makes Python so well-suited for financial data analysis? There are two main reasons:
Easy To Learn: Python is a simple and straightforward language, as it doesn't have any complex language syntax or intricate guidelines. Moreover, Python’s syntax is so similar to English, many find it easier to learn than other programming languages. With some time and dedication, you can learn to write Python, even if you've never written a line of code before

Used In Machine Learning And Artificial Intelligence: Python is a popular language for machine learning and artificial intelligence due to its ability to perform complex calculations and handle diverse activities. The language is equipped with libraries for neural system experimentation, making it a valuable tool in this field.

In practice, it is always necessary to generate and transform original variables into other forms. For example, we need to get the stock returns from the stock prices. Therefore, in the next step, we will learn how to generate new variables from our original variables. We will learn an advanced workflow using DataFrame to implement a trend-following strategy for trading stocks. By the end of the first module, you will be able to visualize and apply stock data to bring your trading ideas to life.

Now, let’s take a quick look at the packages of Python that will be used for the tutorial:
Pandas is a python package, that provides fast, flexible, and expressive data structures. It aims to be the fundamental high-level building blocks, for doing practical real-world data analysis. For example, DataFrame and the series from Pandas, are excellent data structures to store table and time series data. With DataFrame, we can easily pre-process data such as handling missing values and computing pairwise correlation.
NumPy is a fundamental package for the numerical computing of arrays and matrix. It is also a convenient tool for generating random numbers, which could be helpful if we want to shuffle data or generate a dataset with normal distribution.
Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python. It can create publication-quality plots, make interactive figures, and customize visual style and layout.
Statsmodels is a powerful library for statisticians. It contains modules for regression and time series analysis. In this tutorial, we will use Statsmodels to obtain multiple linear regression models.

00:00 Introduction
00:45 Main
13:20 End

[NeedCodeLeetCode]

Demo Codes:

data = pd.DataFrame()
data['Population'] = [47, 48, 85, 20, 19, 13, 72, 16, 50, 60]

a_sample_without_replacement = data['Population'].sample(5, replace = False)
a_sample_with_replacement = data['Population'].sample(5, replace = True)

print('Population mean is', data['Population'].mean())
print('Population variance is', # denominator of the population variance is N
print('Population standard deviation is', # denominator of the population variance is N
print('Population size is', data['Population'].shape[0]) # shape[0] displays only the number of rows

sample_length = 500
sample_variance_collection0 = [data['Population'].sample(50, replace=True).var(ddof=0) for i in range(sample_length)]
sample_variance_collection1 = [data['Population'].sample(50, replace=True).var(ddof=1) for i in range(sample_length)]

print('Population variance is',
print('Average of sample variance with n is',
print('Average of sample variance with n-1 is',

[NeedCodeLeetCode]

First, let’s import the pandas library using the alias "pd".
import pandas as pd

Next, let’s create an empty DataFrame by calling the DataFrame() constructor without any arguments.
data = pd.DataFrame()

Here, the code adds a new column to the DataFrame called "Population", and assigns a list of values to this column. The list contains ten values. This could be the basis for further analysis and manipulation of the data using pandas or other Python libraries.
data['Population'] = [47, 48, 85, 20, 19, 13, 72, 16, 50, 60]

Okay, next! Here,
the code creates two new variables called a_sample_without_replacement and a_sample_with_replacement.
a_sample_without_replacement = data['Population'].sample(5, replace = False)
a_sample_with_replacement = data['Population'].sample(5, replace = True)

The sample() method is a function in the pandas library that is used to randomly select a ‘subset of data from a DataFrame.
In this code, a_sample_without_replacement is assigned the result of calling sample() on the 'Population' column of the data DataFrame. The sample() method is passed two arguments: 5, which specifies the size of the sample to be taken, and replace = False, which specifies that the sample should be taken without replacement (which means each value can only be selected once).
In the second line of code, a_sample_with_replacement is assigned the result of calling sample() on the same column, but with replace = True. This means that the sample will be taken with replacement, so the same value can be selected multiple times.

The first line of code uses the print() function to display a string message that includes the mean value of the 'Population' column in the data DataFrame.
print('Population mean is', data['Population'].mean())

The .mean() method is a pandas DataFrame method that computes the average value of a column. It is applied to the 'Population' column in data.
The second line of code uses print() again to display the variance of the 'Population' column in data. The var() method is used to compute the variance, and is passed an argument ddof=0, which specifies that the denominator of the variance should be the population size (N), rather than the sample size (N-1). Actually, ddof=0 is an optional argument to the .var() method in Pandas librarye that specifies the "delta degrees of freedom" to use in the calculation of variance.
The degrees of freedom refer to the number of independent values that are used to calculate the statistic. In this case, ddof=0 specifies that the divisor in the variance calculation should be the number of observations in the population, rather than the number of observations minus one (which is the default value of ddof parameter).
In other words, ddof=0 indicates that the variance calculation should be based on the entire population, rather than a sample of the population.


print('Population variance is',
The third line of code is similar to the second line, but instead uses the std() method to compute the standard deviation of the 'Population' column, again with the population size (N) as the denominator.

print('Population standard deviation is',

The fourth line of code uses the shape attribute of the data['Population'] object to determine the number of rows in the DataFrame. The [0] index is used to extract the first element of the resulting tuple, which gives the number of rows.

print('Population size is', data['Population'].shape[0])

Overall, these four lines of code demonstrate some basic descriptive statistics that can be computed from a pandas DataFrame.


First, a new variable sample_length is created and assigned the value 500.
sample_length = 500

Next, two new variables are created called sample_variance_collection0 and sample_variance_collection1. These variables are assigned the result of two list comprehensions, which use the sample() method to take 50 samples from the 'Population' column of the data DataFrame, with replacement.
sample_variance_collection0 = [data['Population'].sample(50, replace=True).var(ddof=0) for i in range(sample_length)]
sample_variance_collection1 = [data['Population'].sample(50, replace=True).var(ddof=1) for i in range(sample_length)]

The variance of a random sample can be used to estimate the variance of the population from which the sample was drawn. To illustrate this concept, the code uses a for loop to randomly sample 50 observations from the 'Population' column of the data DataFrame 500 times.
The .var() method is then used to compute the variance of the sampled data. Two versions of the variance are computed: one with ddof=0, which calculates the variance with the denominator equal to the population size (N), and one with ddof=1, which calculates the variance with the denominator equal to the sample size (N-1).
These variance estimates are then collected into two separate lists, sample_variance_collection0 and sample_variance_collection1.
Overall, this code demonstrates the use of random sampling to estimate population variance, and the difference between using the sample size or the population size as the denominator of the variance calculation.

print('Population variance is',
print('Average of sample variance with n is',
print('Average of sample variance with n-1 is',

Okay, here comes our last set of code:
This code prints out the population variance of the 'Population' column of the data DataFrame, and the average of two sets of sample variances computed using different denominator values.
The first line uses the .var() method with ddof=0 to calculate the population variance, which is the average squared deviation of each observation from the population mean. This provides a baseline value for comparing the sample variances.
The second line computes the mean of the sample_variance_collection0 list. This provides an estimate of the variance of the population using a sample with replacement, where each observation has an equal chance of being selected.
The third line computes the mean of the sample_variance_collection1 list. This provides an estimate of the variance of the population using a sample with replacement, where each observation has an equal chance of being selected, but the denominator is adjusted to account for the fact that the sample variance tends to underestimate the population variance when the sample size is small.