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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>State of the Market</title>
<meta charset="utf-8" />
<meta name="author" content="Dean Markwick" />
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class: center, middle, inverse, title-slide
# State of the Market
## ⚔<br/>with xaringan
### Dean Markwick
### 2021/07/06
---
---
class: center
# Stock Market States
You will hear the stock market being in a **bull** or **bear** state.
--
.pull-left[
Bull Market
It is moving up on average
]
--
.pull-right[
Bear Market
It is moving downwards
]
--
<img src="https://upload.wikimedia.org/wikipedia/commons/4/45/Bulle_und_B%C3%A4r_Frankfurt.jpg" width="300" />
## How do we model this?
---
# Markov State Models
### Each observation depends on what state the world is in.
--
.pull-left[
Bull market
A state with average > 0
]
--
.pull-right[
Bear market
A state with average < 0
]
--
### Pick how many states before fitting the model
---
# Markov State Models
--
## What if we wanted more states?
--
- Sideways state: Average = 0
- Strong bull/bear state.
--
## What if the states are different?
--
- Each bull market might have a different average.
---
# Infinite State Markov Models
--
### Let the data decide how many states.
--
### Each states has its own parameters.
--
- Dirichlet process like model.
```r
require(dirichletprocess)
mdobj <- GaussianMixtureCreate()
dphmm <- DirichletHMMCreate(trainFrame$y, mdobj,
alpha = 1, beta = 1)
dphmm <- Fit(dphmm, 1000)
```
---
# Data
* We have the daily returns of the SPY ETF that represents the top 500 companies.
* Downloaded from [www.alphavantage.co](www.alphavantage.co) for free
--
* We normalise the daily return by the rolling 30 day volatility
* Fit the infinite state hidden Markov model using my `dirichletprocess` package.
---
# Fitting Infinite State Hidden Markov Models
Every new day two things happen:
--
1. That days return belongs to the previous state
--
2. It creates a new state
--
We iterate through each data point in sequence seeing if it belongs to the previous state or creates its own state.
--
Once all the states are assigned we update the underlying parameters of each state using all the data that belongs to the state.
--
Repeat this until converged!
--
---
# Results
I plot the price graph of the SPY ETF over time.
<img src="img/priceAndState.png" width="700" style="display: block; margin: auto;" />
---
# State Parameters
Bayesian model, so we get uncertainty for free.
<img src="img/averages.png" width="700" style="display: block; margin: auto;" />
---
# What Have We Learnt?
* No longer have to set the number of states before hand.
* Average length of market states.
* How the parameters have changed with each state.
---
# Further Reading
* Original blog post
* <http://dm13450.github.io/2020/06/03/State-of-the-Market.html>
* https://github.com/dm13450/dirichletprocess
* [www.alphavantage.co](www.alphavantage.co) for free market data
</textarea>
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