From 22fbb16682c75094c1ae4a36e43eeeed4c9da804 Mon Sep 17 00:00:00 2001 From: klein panic Date: Thu, 23 Jan 2025 16:20:09 -0500 Subject: [PATCH] added PricePrediction paper --- docs/ManPages/PricePrediction.aux | 2 + docs/ManPages/PricePrediction.log | 227 ++++++++++++++++++++++++++++++ docs/ManPages/PricePrediction.pdf | Bin 0 -> 128660 bytes docs/ManPages/PricePrediction.tex | 145 +++++++++++++++++++ 4 files changed, 374 insertions(+) create mode 100644 docs/ManPages/PricePrediction.aux create mode 100644 docs/ManPages/PricePrediction.log create mode 100644 docs/ManPages/PricePrediction.pdf create mode 100644 docs/ManPages/PricePrediction.tex diff --git a/docs/ManPages/PricePrediction.aux b/docs/ManPages/PricePrediction.aux new file mode 100644 index 0000000..a79beaf --- /dev/null +++ b/docs/ManPages/PricePrediction.aux @@ -0,0 +1,2 @@ +\relax +\gdef \@abspage@last{3} diff --git a/docs/ManPages/PricePrediction.log b/docs/ManPages/PricePrediction.log new file mode 100644 index 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+\usepackage{amssymb} +\usepackage{geometry} +\geometry{a4paper, margin=1in} + +\title{LSTM Model and Stock Price Prediction} +\author{} +\date{} + +\begin{document} + +\maketitle + +\section*{Stock Price Equation} + +The price of a stock \( P(t) \) at discrete time \( t \in \{t_1, t_2, t_3, \ldots\} \) is given by: + +\[ +P(t) = P(t-1) + F_{\text{macro}}(t) + F_{\text{micro}}(t) + F_{\text{technical}}(t) + F_{\text{noise}}(t) +\] + +\begin{itemize} + \item \( P(t-1) \): Price of the stock at the previous time step. + \item \( F_{\text{macro}}(t) \): Macro-level influences. + \item \( F_{\text{micro}}(t) \): Micro-level influences. + \item \( F_{\text{technical}}(t) \): Technical analysis factors. + \item \( F_{\text{noise}}(t) \): Stochastic noise term. +\end{itemize} + +\subsection*{Macro Influences} + +\[ +F_{\text{macro}}(t) = \alpha_1 G(t) + \alpha_2 I(t) + \alpha_3 R(t) +\] + +\begin{itemize} + \item \( \alpha_i \): Weights determining the strength of each factor. + \item \( G(t) \): GDP growth/market sentiment, modeled as: + \[ + G(t) = y \sin\left(\frac{2\pi t}{T_B}\right) + N_2 Z_2(t) + \] + \item \( I(t) \): Inflation rate, modeled as: + \[ + I(t) = \Theta e^{-\lambda_0 t} + N_2 Z_2(t) + \] + \item \( R(t) \): Risk-free interest rate: + \[ + R(t) = r_0 + N_3 Z_3(t) + \] +\end{itemize} + +\subsection*{Micro Influences} + +\[ +F_{\text{micro}}(t) = \beta_1 E(t) + \beta_2 S(t) + \beta_3 C(t) +\] + +\begin{itemize} + \item \( E(t) \): Earnings per share, \( E(t) = E_0 e^{\mu t} \left[1 + \sin\left(\frac{\pi t}{T_E}\right)\right] \) + \item \( S(t) \): Scale growth rates: + \[ + S(t) = \frac{\text{Max scale level}}{1 + e^{-K_0(t-t_0)}} + N_5 Z_5(t) + \] + \item \( C(t) \): Competition index: + \[ + C(t) = \frac{1}{t + \text{Season growth cycle}} + N_6 Z_6(t) + \] +\end{itemize} + +\subsection*{Technical Factors} + +\[ +F_{\text{technical}}(t) = \delta_1 M(t) + \delta_2 V(t) +\] + +\begin{itemize} + \item \( M(t) \): Momentum, \( M(t) = P(t+1) - P(t+5) \) + \item \( V(t) \): Volatility: + \[ + V(t) = \sqrt{\frac{1}{W} \sum_{i=1}^N [P(t-i) - \overline{P}(t)]^2} + \] + where \( \overline{P}(t) = \frac{1}{N} \sum_{i=1}^N P(t-i) \). +\end{itemize} + +\subsection*{Noise Term} + +\[ +F_{\text{noise}}(t) = \sigma Z(t) +\] + +\begin{itemize} + \item \( \sigma Z(t) \): Noise term, where \( Z(t) \sim N(0, 1) \). +\end{itemize} + +\section*{LSTM Architecture} + +\begin{enumerate} + \item Feature vector \( X(t) \): + \[ + X(t) = \begin{bmatrix} + P(t-2) \\ + P(t-1) \\ + P(t) \\ + G(t) \\ + E(t) \\ + S(t) \\ + C(t) \\ + M(t) \\ + V(t) + \end{bmatrix} + \] + \item LSTM components: + \[ + f(t) = \sigma(W_f X(t) + U_f h(t-1) + b_f) + \] + \[ + i(t) = \sigma(W_i X(t) + U_i h(t-1) + b_i) + \] + \[ + \tilde{C}(t) = \tanh(W_c X(t) + U_c h(t-1) + b_c) + \] + \[ + C(t) = f(t) \cdot C(t-1) + i(t) \cdot \tilde{C}(t) + \] + \[ + o(t) = \sigma(W_o X(t) + U_o h(t-1) + b_o) + \] + \[ + h(t) = o(t) \cdot \tanh(C(t)) + \] + +\end{enumerate} + +\section*{Loss Function} + +\[ +\text{MSE} = \frac{1}{T} \sum_{t=1}^T [P(t) - \hat{P}(t)]^2 +\] +\[ +\text{MAE} = \frac{1}{T} \sum_{t=1}^T |P(t) - \hat{P}(t)| +\] + +\end{document} +