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Dec 1st Yijun:

upload presentation slides slide link: https://docs.google.com/presentation/d/1Kt_2Gl56Jo87mZmZWoMJRLoHvzGIbVSMc4lp8nnDthQ/edit?usp=sharing

Nov 25th Saksham:

Breaking Down this Project -

Apply GARCH model to be able to understand if there is volatility clustering and how to predict future volatility.

Volatility - degree of variation in an asset's price over time. High Volatility = large price swings, $Volatility = \sqrt{variance}$

Volatility Clustering - Tendencies of High Volatility followed by Low Volatility

Variance of Returns = $\frac{1}{n} \sum_{i=1}^n{(R_i-\bar{R})}^2$

Use Logaritmic Returns = $R_t=\ln({\frac{P_t}{P_{t-1}}})$

Garch(1,1) Model -

(1,1) just means we are comparing one lag of both variance and errors

$\sigma_t^2=\omega+\alpha*\epsilon_{t-1}^2+\beta*\sigma_{t-1}^2$

$\sigma_t =$ Volatility at time t

$\omega =$ Long Term Average Variance

$\alpha =$ Weight for recent Error

$\beta =$ Weight for recent variance

$\epsilon =$ Error Residual From previous time step

$\alpha + \beta$ represent persistence of volatility meaning closer they are to 1 the higher the volatility is present. so if less than 1 then volatility returns to $\omega$

Applying Garch

Step 1. Data Collection and Storage

  1. Collect Minute by Minute Data of the last 30 days from the election (Oct 5 - Nov 5) of Price using Binance API or get historical data
  2. Compute the returns too
    1. Store values in form of a struct in a data file vector 
          struct dataPoint{
      int month, day, hour, minute;
      double bitcoinPrice;
      double returns;
    };
  3. Plot the Returns on a line graph to visualize high and low volatilites

Step 2. Test the Data

  1. Autocorrelation Analysis
    1. $ACF(k)=\frac{\sum_{t=k+1}^T(y_t-\bar y)(y_{t-k}-\bar y)}{\sum_{t=1}^T{(y_t - \bar y)}^2}$
      1. $y_t$ value of the series at time t
      2. $\bar y$ mean of the series
      3. k lag
    2. Do this for lag of $0,1,2,3...60$. If the $|ACF(k)| \ge \pm 1.96 \sqrt(T)$ it suggests a signficiant correlation at lag k
    3. If possible lets graph this with also the right side of inequality as one line to see the correlation. Axis: (lag k, ACF(k))

Step 3. GARCH Model

  1. Fit a GARCH(1,1) model to estimate and predict volatility
  2. Mathematical $\sigma_t^2=\omega+\alpha*\epsilon_{t-1}^2+\beta*\omega_{t-1}^2$
    1. Assign $\omega=0.01$, $\alpha=0.1$, $\beta = 0.85$
    2. $\sigma_0^2 = Var(r_t)$
    3. $e_t \textasciitilde N(0, \sigma _t^2) = y_t-\mu$
    4. Store all the variances based on model

Step 4. Forecasting

  1. One step ahead Forecasting - $\sigma_{t+1}^2 = \omega+\alpha*\epsilon_t^2+\beta*\sigma_t^2$
  2. Start with $\sigma_0^2=Var(r_t)$

Nov 25th Seung-min Yu

Working on the Binance API connection (Paused)

Relevant Paper: https://arxiv.org/html/2405.12988v1 granularity of data: 1 minute frequency of data: daily crypto target: Bitcoin duration/length: 30 days real-time data version will use this API: https://github.com/niXman/binapi Collect Minute by Minute Data of the last 14 or 30 days from the election of Returns Plot the return

Use Kaggle data

https://www.kaggle.com/datasets/mczielinski/bitcoin-historical-data