# Extracting Features/Patterns in a price data using Wavelet Transform(PART-1)

Not a Blog Just Writing Notes for myself :)

## Why Not use FFT or Fourier Transform to extract patterns or components in stock price data instead of using Wavelet transform directly?

Fourier Transform will work very well when the frequency spectrum is stationary. That is, the frequencies present in the signal are not time-dependent; if a signal contains a frequency of x Hz this frequency should be present equally anywhere in the signal.
The more non-stationary/dynamic a signal is, the worse the results will be.

Our Stock Data is dynamic in nature. A much better approach for analyzing dynamic signals is to use the Wavelet Transform instead of the Fourier Transform.

## What’s the Difference between Fourier Transform and Wavelet Transform?

So wavelet transform also transform the signal into its frequency domain…

# The Curse of Dimensionality in Finance

In Big Data we often come across when we have more features than the sample data for our model, so we reduce the features using PCA or SVD or any other algorithm to reduce the features

Similarly in the field of Finance when one is making a Volatility model or let’s say making a portfolio using Efficient modern portfolio, we often come across with this curse Let’s take an Example

To obtain an Efficient Modern Portfolio of N assets one must estimate

1. N expected returns
2. N volatility
3. N(N-1)/2 (Here the problem arises)

Let’s say you want to select stocks for…

# Linear Programming/Optimization in Finance using Python

Not a Blog, Just Writing Notes for Myself :-)

In most of the Financial models, we have a linear or Quadratic Optimizer which needs to be maximized or minimized accordingly with a certain set of constraints.

In the CAPM model, we assumed linearity in the models and solved for expected stock prices using regression in Python.

For E.g. In this Blog at the end, where quadratic optimizer has an objective to minimize the volatility with certain constraints

As the number of stocks in our portfolio increases, certain limitations are introduced as well.

Linear optimization helps us overcome the problem of…

# Time-series Auto-correlation Vs Partial Auto Correlation

Not A blog Just Writing Notes For Myself :)

Problem Statement: We have monthly data of a Stock and we are gonna predict the average monthly price of a stock by comparing previous months prices So before that, we need to see how much predictor variable is related to our dependent variable/output

Here’s the notation for our situation We have

Sti = Price of the Stock This Month

Sti_1 =Price of the Stock previous Month

Sti_2 = Price of the Stock 2 month ago

The most important concept in time series is that it helps us to predict the future…

# Portfolio Construction using Efficient Frontier Optimization

Not a Blog just Notes for myself :)

Let’s Take Two Asset in risk-return Space which is also known as a mean-variance framework where on our X-axis we have variance or std-dev (risk) while on the Y-axis we have our returns pf the Asset

`We Got 2 Assests A and BA has a std deviation of 10%(Volatility) and return 4%B has 14% volatility, and a 6% returnLet's combine A and B to Build our portfolio and calculate our risk and return?Let's Split the money equally in the both the assetSo our return of our portfolio will…`

# Factor Models using Machine learning Approach

Not a blog writing notes for myself :)

## Why Factor investing is important and why it matters?

Securities(stocks, bonds…etc) earn their risk premium(It represents payment to investors for tolerating the extra risk in a given investment over that of a risk-free asset) through exposure to a small number of rewarded risk factors

Factors are fundamentally broad, persistent characteristics that can both impact and drive asset returns. They are generally persistent over time and have consistently demonstrated an ability to explain stock returns

Factors are the foundation of investing just as nutrients are the foundation of our food. — Outlook article

What Types of Factors models are there?

1. Macro-Economic Factors… ## Abhishek Chikara

Finance 🤜🤛 Machine Learning Linkedin:https://www.linkedin.com/in/abhishek-chikara-96b68597/