Update app.py

app.py

@@ -11,7 +11,7 @@ from ta.volatility import BollingerBands
 
 # Helper functions
 def fetch_stock_data(ticker: str, start_date: str, end_date: str) -> pd.DataFrame:
-    """Fetch stock data from Yahoo Finance."""
+    """Fetch stock or crypto data from Yahoo Finance."""
     return yf.download(ticker, start=start_date, end=end_date)
 
 def plot_z_score(close_prices: pd.Series, periods: list, z_thresh: float, n_days: int) -> go.Figure:
@@ -40,15 +40,12 @@ def plot_z_score(close_prices: pd.Series, periods: list, z_thresh: float, n_days
 
         fig.add_trace(go.Scatter(x=close_prices[buy_signals].index, y=close_prices[buy_signals],
                                  mode='markers', marker=dict(color='green', symbol='triangle-up', size=10),
-                                 # name=f'Buy Signal {period} days (Correct: {buy_correct_pct:.1f}% in {n_days} days)'), row=1, col=1)
                                  name=f'Buy Signal {period} days'), row=1, col=1)
         fig.add_trace(go.Scatter(x=close_prices[sell_signals].index, y=close_prices[sell_signals],
                                  mode='markers', marker=dict(color='red', symbol='triangle-down', size=10),
-                                 # name=f'Sell Signal {period} days (Correct: {sell_correct_pct:.1f}% in {n_days} days)'), row=1, col=1)
                                  name=f'Sell Signal {period} days'), row=1, col=1)
         fig.add_trace(go.Scatter(x=close_prices.index, y=z_scores, mode='lines', name=f'Rolling Z-Score {period}'), row=2, col=1)
 
-        
         # Add threshold lines
         fig.add_hline(y=z_thresh, line=dict(color='red', dash='dash'), row=2, col=1)
         fig.add_hline(y=-z_thresh, line=dict(color='green', dash='dash'), row=2, col=1)
@@ -288,13 +285,14 @@ st.set_page_config(page_title="Technical Analysis", layout="wide")
 st.title('Technical Analysis Indicators')
 
 # Sidebar for method selection
-selected = st.sidebar.radio("Select Indicator", ["Rolling Z-Score", "Rate of Change (ROC)", "Stochastic Oscillator", "Relative Strength Index (RSI)", "MACD", "Bollinger Bands", "K Reversal", "Awesome Oscillator", "Williams %R", "Aroon Oscillator"])
+with st.sidebar.expander("Method Selection", expanded=True):
+    selected = st.radio("Select Indicator", ["Rolling Z-Score", "Rate of Change (ROC)", "Stochastic Oscillator", "Relative Strength Index (RSI)", "MACD", "Bollinger Bands", "K Reversal", "Awesome Oscillator", "Williams %R", "Aroon Oscillator"])
 
 # Sidebar for input parameters
-st.sidebar.header("Input Parameters")
-ticker = st.sidebar.text_input('Enter Stock Ticker', 'ASML.AS')
-start_date = st.sidebar.date_input('Start Date', pd.to_datetime('2019-01-01'))
-end_date = st.sidebar.date_input('End Date', pd.to_datetime('2024-12-31'))
+with st.sidebar.expander("Input Parameters", expanded=True):
+    ticker = st.text_input('Enter Stock or Crypto Symbol (e.g., AAPL or BTC-USD)', 'AAPL')
+    start_date = st.date_input('Start Date', pd.to_datetime('2019-01-01'))
+    end_date = st.date_input('End Date', pd.to_datetime(pd.Timestamp.now().date() + pd.Timedelta(days=1)))
 
 # Fetch data
 if 'data' not in st.session_state or st.sidebar.button('Fetch Data'):
@@ -303,40 +301,51 @@ if 'data' not in st.session_state or st.sidebar.button('Fetch Data'):
 data = st.session_state.data
 close_prices = data['Close']
 
-# Display results based on the selected method
-if selected == "Rolling Z-Score":
+# Expander for "How to" section
+with st.expander("How to Use This App", expanded=False):
     st.markdown("""
-    ### Rolling Z-Score
-    
-    The rolling z-score method identifies overbought and oversold conditions by standardizing stock prices over different periods.
-    
-    **How it Works:**
-    
-    1. **Calculate Rolling Mean and Standard Deviation:**
-       - For each time period (e.g., 20 days), compute the rolling mean and rolling standard deviation of the stock prices.
-    
-    2. **Compute Z-Score:**
-       - For each day, calculate the z-score using:
-    """)
-    st.latex(r'''
-    \text{Z-Score} = \frac{\text{Close Price} - \text{Rolling Mean}}{\text{Rolling Standard Deviation}}
-    ''')
-    st.markdown("""
-    3. **Identify Signals:**
-       - **Overbought Condition:** Z-score above a set threshold (e.g., 2.0) suggests the stock may be overbought.
-       - **Oversold Condition:** Z-score below a set threshold (e.g., -2.0) suggests the stock may be oversold.
-    
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the number of days for the z-score calculation.
-    3. Set the z-score threshold.
-    4. Click 'Fetch Data' to load the stock data.
-    5. The chart will display the rolling z-scores and highlight buy/sell signals based on the thresholds.
-    
-    **Results:**
-    The chart shows the close prices with highlighted buy/sell signals and their correctness percentage over a specified period.
+    1. Use the sidebar to select an indicator and input parameters.
+    2. Enter the stock or cryptocurrency symbol (e.g., 'AAPL' for Apple or 'BTC-USD' for Bitcoin).
+    3. Choose the date range for the data.
+    4. Click 'Fetch Data' to load and visualize the data.
+    5. Use the parameter settings for each method to fine-tune the analysis.
     """)
 
+# Display results based on the selected method
+if selected == "Rolling Z-Score":
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Rolling Z-Score
+        
+        The rolling z-score method identifies overbought and oversold conditions by standardizing stock prices over different periods.
+        
+        **How it Works:**
+        
+        1. **Calculate Rolling Mean and Standard Deviation:**
+           - For each time period (e.g., 20 days), compute the rolling mean and rolling standard deviation of the stock prices.
+        
+        2. **Compute Z-Score:**
+           - For each day, calculate the z-score using:
+        """)
+        st.latex(r'''
+        \text{Z-Score} = \frac{\text{Close Price} - \text{Rolling Mean}}{\text{Rolling Standard Deviation}}
+        ''')
+        st.markdown("""
+        3. **Identify Signals:**
+           - **Overbought Condition:** Z-score above a set threshold (e.g., 2.0) suggests the stock may be overbought.
+           - **Oversold Condition:** Z-score below a set threshold (e.g., -2.0) suggests the stock may be oversold.
+        
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the number of days for the z-score calculation.
+        3. Set the z-score threshold.
+        4. Click 'Fetch Data' to load the stock data.
+        5. The chart will display the rolling z-scores and highlight buy/sell signals based on the thresholds.
+        
+        **Results:**
+        The chart shows the close prices with highlighted buy/sell signals and their correctness percentage over a specified period.
+        """)
+
     periods = st.sidebar.multiselect('Periods to Compare', options=[10, 20, 30, 40, 50], default=[20])
     z_thresh = st.sidebar.slider('Z-Score Threshold', min_value=0.5, max_value=3.0, value=2.0, step=0.1)
     n_days = st.sidebar.number_input('Number of Days', min_value=1, value=10)
@@ -344,68 +353,59 @@ if selected == "Rolling Z-Score":
     st.plotly_chart(fig)
 
 elif selected == "Rate of Change (ROC)":
-    st.markdown("""
-    ### Rate of Change (ROC)
-
-    The Rate of Change (ROC) method measures the percentage change in stock prices over a specified period. It helps identify momentum and potential reversal points in the stock price.
-
-    **How it Works:**
-
-    1. **Calculate ROC:**
-       - For each day, calculate the ROC using the formula:
-    """)
-    st.latex(r'''
-    \text{ROC} = \frac{\text{Current Price} - \text{Price} \, n \, \text{days ago}}{\text{Price} \, n \, \text{days ago}} \times 100
-    ''')
-    st.markdown("""
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the ROC crosses above zero, indicating potential upward momentum.
-       - **Sell Signal:** Occurs when the ROC crosses below zero, indicating potential downward momentum.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the number of days for the ROC calculation.
-    3. Click 'Fetch Data' to load the stock data.
-    4. The chart will display the ROC and highlight buy/sell signals based on the ROC crossing zero.
-
-    **Results:**
-    The chart shows the stock prices with highlighted buy/sell signals based on ROC.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Rate of Change (ROC)
+        The Rate of Change (ROC) method measures the percentage change in stock prices over a specified period. It helps identify momentum and potential reversal points in the stock price.
+        **How it Works:**
+        1. **Calculate ROC:**
+           - For each day, calculate the ROC using the formula:
+        """)
+        st.latex(r'''
+        \text{ROC} = \frac{\text{Current Price} - \text{Price} \, n \, \text{days ago}}{\text{Price} \, n \, \text{days ago}} \times 100
+        ''')
+        st.markdown("""
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the ROC crosses above zero, indicating potential upward momentum.
+           - **Sell Signal:** Occurs when the ROC crosses below zero, indicating potential downward momentum.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the number of days for the ROC calculation.
+        3. Click 'Fetch Data' to load the stock data.
+        4. The chart will display the ROC and highlight buy/sell signals based on the ROC crossing zero.
+        **Results:**
+        The chart shows the stock prices with highlighted buy/sell signals based on ROC.
+        """)
 
     n_days = st.sidebar.number_input('Number of Days', min_value=1, value=14)
     fig = plot_roc(close_prices, n_days)
     st.plotly_chart(fig)
 
 elif selected == "Stochastic Oscillator":
-    st.markdown("""
-    ### Stochastic Oscillator
-
-    The Stochastic Oscillator compares a stock's closing price to its price range over a specified period. It helps identify overbought and oversold conditions.
-
-    **How it Works:**
-
-    1. **Calculate %K and %D:**
-       - The %K line is calculated as follows:
-    """)
-    st.latex(r'''
-    \%K = \frac{\text{Current Close} - \text{Lowest Low}}{\text{Highest High} - \text{Lowest Low}} \times 100
-    ''')
-    st.markdown("""
-       - The %D line is the 3-period moving average of %K.
-
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when %K crosses above a set threshold (e.g., 20), indicating potential upward momentum.
-       - **Sell Signal:** Occurs when %K crosses below a set threshold (e.g., 80), indicating potential downward momentum.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the buy and sell thresholds.
-    3. Click 'Fetch Data' to load the stock data.
-    4. The chart will display the Stochastic Oscillator and highlight buy/sell signals based on thresholds.
-
-    **Results:**
-    The chart shows the closing prices with highlighted buy/sell signals and the %K and %D lines.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Stochastic Oscillator
+        The Stochastic Oscillator compares a stock's closing price to its price range over a specified period. It helps identify overbought and oversold conditions.
+        **How it Works:**
+        1. **Calculate %K and %D:**
+           - The %K line is calculated as follows:
+        """)
+        st.latex(r'''
+        \%K = \frac{\text{Current Close} - \text{Lowest Low}}{\text{Highest High} - \text{Lowest Low}} \times 100
+        ''')
+        st.markdown("""
+           - The %D line is the 3-period moving average of %K.
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when %K crosses above a set threshold (e.g., 20), indicating potential upward momentum.
+           - **Sell Signal:** Occurs when %K crosses below a set threshold (e.g., 80), indicating potential downward momentum.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the buy and sell thresholds.
+        3. Click 'Fetch Data' to load the stock data.
+        4. The chart will display the Stochastic Oscillator and highlight buy/sell signals based on thresholds.
+        **Results:**
+        The chart shows the closing prices with highlighted buy/sell signals and the %K and %D lines.
+        """)
 
     buy_thresh = st.sidebar.slider('Stochastic Buy Threshold', min_value=0, max_value=100, value=5)
     sell_thresh = st.sidebar.slider('Stochastic Sell Threshold', min_value=0, max_value=100, value=95)
@@ -413,34 +413,30 @@ elif selected == "Stochastic Oscillator":
     st.plotly_chart(fig)
 
 elif selected == "Relative Strength Index (RSI)":
-    st.markdown("""
-    ### Relative Strength Index (RSI)
-
-    The RSI measures the magnitude of recent price changes to evaluate overbought or oversold conditions.
-
-    **How it Works:**
-
-    1. **Calculate RSI:**
-       - Compute the average gains and average losses over a specified period (typically 14 days).
-       - Calculate the RSI using the formula:
-    """)
-    st.latex(r'''
-    \text{RSI} = 100 - \frac{100}{1 + \frac{\text{Average Gain}}{\text{Average Loss}}}
-    ''')
-    st.markdown("""
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the RSI crosses below a set threshold (e.g., 30), indicating the stock may be oversold.
-       - **Sell Signal:** Occurs when the RSI crosses above a set threshold (e.g., 70), indicating the stock may be overbought.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the buy and sell thresholds.
-    3. Click 'Fetch Data' to load the stock data.
-    4. The chart will display the RSI and highlight buy/sell signals based on thresholds.
-
-    **Results:**
-    The chart shows the stock prices with highlighted buy/sell signals and the RSI line.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Relative Strength Index (RSI)
+        The RSI measures the magnitude of recent price changes to evaluate overbought or oversold conditions.
+        **How it Works:**
+        1. **Calculate RSI:**
+           - Compute the average gains and average losses over a specified period (typically 14 days).
+           - Calculate the RSI using the formula:
+        """)
+        st.latex(r'''
+        \text{RSI} = 100 - \frac{100}{1 + \frac{\text{Average Gain}}{\text{Average Loss}}}
+        ''')
+        st.markdown("""
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the RSI crosses below a set threshold (e.g., 30), indicating the stock may be oversold.
+           - **Sell Signal:** Occurs when the RSI crosses above a set threshold (e.g., 70), indicating the stock may be overbought.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the buy and sell thresholds.
+        3. Click 'Fetch Data' to load the stock data.
+        4. The chart will display the RSI and highlight buy/sell signals based on thresholds.
+        **Results:**
+        The chart shows the stock prices with highlighted buy/sell signals and the RSI line.
+        """)
 
     buy_thresh = st.sidebar.slider('RSI Buy Threshold', min_value=0, max_value=100, value=30)
     sell_thresh = st.sidebar.slider('RSI Sell Threshold', min_value=0, max_value=100, value=70)
@@ -448,106 +444,92 @@ elif selected == "Relative Strength Index (RSI)":
     st.plotly_chart(fig)
 
 elif selected == "MACD":
-    st.markdown("""
-    ### Moving Average Convergence Divergence (MACD)
-
-    The MACD is a trend-following momentum indicator that shows the relationship between two moving averages of a stock's price.
-
-    **How it Works:**
-
-    1. **Calculate MACD:**
-       - Compute the MACD line using the formula:
-    """)
-    st.latex(r'''
-    \text{MACD} = \text{EMA}_{12} - \text{EMA}_{26}
-    ''')
-    st.markdown("""
-       - Compute the Signal line as the 9-day EMA of the MACD line.
-       - The MACD Histogram is the difference between the MACD line and the Signal line.
-
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the MACD line crosses above the Signal line, indicating potential upward momentum.
-       - **Sell Signal:** Occurs when the MACD line crosses below the Signal line, indicating potential downward momentum.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Click 'Fetch Data' to load the stock data.
-    3. The chart will display the MACD line, Signal line, and Histogram, and highlight buy/sell signals based on MACD crossovers.
-
-    **Results:**
-    The chart shows the stock prices with highlighted buy/sell signals, MACD line, Signal line, and Histogram.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Moving Average Convergence Divergence (MACD)
+        The MACD is a trend-following momentum indicator that shows the relationship between two moving averages of a stock's price.
+        **How it Works:**
+        1. **Calculate MACD:**
+           - Compute the MACD line using the formula:
+        """)
+        st.latex(r'''
+        \text{MACD} = \text{EMA}_{12} - \text{EMA}_{26}
+        ''')
+        st.markdown("""
+           - Compute the Signal line as the 9-day EMA of the MACD line.
+           - The MACD Histogram is the difference between the MACD line and the Signal line.
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the MACD line crosses above the Signal line, indicating potential upward momentum.
+           - **Sell Signal:** Occurs when the MACD line crosses below the Signal line, indicating potential downward momentum.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Click 'Fetch Data' to load the stock data.
+        3. The chart will display the MACD line, Signal line, and Histogram, and highlight buy/sell signals based on MACD crossovers.
+        **Results:**
+        The chart shows the stock prices with highlighted buy/sell signals, MACD line, Signal line, and Histogram.
+        """)
 
     fig = plot_macd(close_prices)
     st.plotly_chart(fig)
 
 elif selected == "Bollinger Bands":
-    st.markdown("""
-    ### Bollinger Bands
-
-    Bollinger Bands consist of a middle band (Simple Moving Average) and two outer bands (standard deviations from the SMA). They help identify overbought and oversold conditions.
-
-    **How it Works:**
-
-    1. **Calculate Bollinger Bands:**
-       - Compute the middle band as the Simple Moving Average (SMA) of the stock prices over a specified period (typically 20 days).
-       - Calculate the upper and lower bands using the formulas:
-    """)
-    st.latex(r'''
-    \text{Upper Band} = \text{SMA} + k \cdot \text{Standard Deviation}
-    ''')
-    st.latex(r'''
-    \text{Lower Band} = \text{SMA} - k \cdot \text{Standard Deviation}
-    ''')
-    st.markdown("""
-       - Where \( k \) is a factor typically set to 2.
-
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the stock price crosses below the lower band, indicating the stock may be oversold.
-       - **Sell Signal:** Occurs when the stock price crosses above the upper band, indicating the stock may be overbought.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Click 'Fetch Data' to load the stock data.
-    3. The chart will display the Bollinger Bands and highlight buy/sell signals based on price crossing the bands.
-
-    **Results:**
-    The chart shows the stock prices with highlighted buy/sell signals and the Bollinger Bands.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Bollinger Bands
+        Bollinger Bands consist of a middle band (Simple Moving Average) and two outer bands (standard deviations from the SMA). They help identify overbought and oversold conditions.
+        **How it Works:**
+        1. **Calculate Bollinger Bands:**
+           - Compute the middle band as the Simple Moving Average (SMA) of the stock prices over a specified period (typically 20 days).
+           - Calculate the upper and lower bands using the formulas:
+        """)
+        st.latex(r'''
+        \text{Upper Band} = \text{SMA} + k \cdot \text{Standard Deviation}
+        ''')
+        st.latex(r'''
+        \text{Lower Band} = \text{SMA} - k \cdot \text{Standard Deviation}
+        ''')
+        st.markdown("""
+           - Where \( k \) is a factor typically set to 2.
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the stock price crosses below the lower band, indicating the stock may be oversold.
+           - **Sell Signal:** Occurs when the stock price crosses above the upper band, indicating the stock may be overbought.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Click 'Fetch Data' to load the stock data.
+        3. The chart will display the Bollinger Bands and highlight buy/sell signals based on price crossing the bands.
+        **Results:**
+        The chart shows the stock prices with highlighted buy/sell signals and the Bollinger Bands.
+        """)
 
     fig = plot_bollinger_bands(close_prices)
     st.plotly_chart(fig)
 
 elif selected == "K Reversal":
-    st.markdown("""
-    ### K Reversal
-
-    The K Reversal indicator helps identify potential reversal points based on the stock's high and low prices over a specified period.
-
-    **How it Works:**
-
-    1. **Calculate K Reversal:**
-       - Compute the highest high and lowest low over a specified period (e.g., 14 days).
-       - Calculate the K value using the formula:
-    """)
-    st.latex(r'''
-    K = \frac{\text{Close Price} - \text{Lowest Low}}{\text{Highest High} - \text{Lowest Low}} \times 100
-    ''')
-    st.markdown("""
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the K value crosses below a set threshold (e.g., 20), indicating the stock may be oversold.
-       - **Sell Signal:** Occurs when the K value crosses above a set threshold (e.g., 80), indicating the stock may be overbought.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the period for the K Reversal calculation.
-    3. Set the buy and sell thresholds.
-    4. Click 'Fetch Data' to load the stock data.
-    5. The chart will display the K Reversal indicator and highlight buy/sell signals.
-
-    **Results:**
-    The chart shows the stock prices with the K Reversal indicator and highlighted buy/sell signals.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### K Reversal
+        The K Reversal indicator helps identify potential reversal points based on the stock's high and low prices over a specified period.
+        **How it Works:**
+        1. **Calculate K Reversal:**
+           - Compute the highest high and lowest low over a specified period (e.g., 14 days).
+           - Calculate the K value using the formula:
+        """)
+        st.latex(r'''
+        K = \frac{\text{Close Price} - \text{Lowest Low}}{\text{Highest High} - \text{Lowest Low}} \times 100
+        ''')
+        st.markdown("""
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the K value crosses below a set threshold (e.g., 20), indicating the stock may be oversold.
+           - **Sell Signal:** Occurs when the K value crosses above a set threshold (e.g., 80), indicating the stock may be overbought.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the period for the K Reversal calculation.
+        3. Set the buy and sell thresholds.
+        4. Click 'Fetch Data' to load the stock data.
+        5. The chart will display the K Reversal indicator and highlight buy/sell signals.
+        **Results:**
+        The chart shows the stock prices with the K Reversal indicator and highlighted buy/sell signals.
+        """)
 
     k_period = st.sidebar.number_input('K Reversal Period', min_value=1, value=14)
     k_buy_thresh = st.sidebar.slider('K Reversal Buy Threshold', min_value=0.0, max_value=100.0, value=10.0)
@@ -556,44 +538,39 @@ elif selected == "K Reversal":
     st.plotly_chart(fig)
 
 elif selected == "Awesome Oscillator":
-    st.markdown("""
-    ### Awesome Oscillator
-
-    The Awesome Oscillator measures market momentum by comparing the 34-period and 5-period simple moving averages of the midpoints of each candlestick.
-
-    **How it Works:**
-
-    1. **Calculate the Midpoint:**
-       - For each candlestick, compute the midpoint using:
-    """)
-    st.latex(r'''
-    \text{Midpoint} = \frac{\text{High} + \text{Low}}{2}
-    ''')
-    st.markdown("""
-    2. **Compute the Moving Averages:**
-       - Calculate the 34-period and 5-period simple moving averages (SMA) of the midpoints.
-
-    3. **Calculate the Awesome Oscillator:**
-       - Use the formula:
-    """)
-    st.latex(r'''
-    \text{AO} = \text{SMA}_{5}(\text{Midpoint}) - \text{SMA}_{34}(\text{Midpoint})
-    ''')
-    st.markdown("""
-    4. **Identify Signals:**
-       - **Buy Signal:** Occurs when the AO crosses above the signal line (e.g., 0), indicating potential upward momentum.
-       - **Sell Signal:** Occurs when the AO crosses below the signal line, indicating potential downward momentum.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the signal line period.
-    3. Set the buy and sell thresholds.
-    4. Click 'Fetch Data' to load the stock data.
-    5. The chart will display the Awesome Oscillator and highlight buy/sell signals based on thresholds.
-
-    **Results:**
-    The chart shows the stock prices with the Awesome Oscillator and highlighted buy/sell signals.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Awesome Oscillator
+        The Awesome Oscillator measures market momentum by comparing the 34-period and 5-period simple moving averages of the midpoints of each candlestick.
+        **How it Works:**
+        1. **Calculate the Midpoint:**
+           - For each candlestick, compute the midpoint using:
+        """)
+        st.latex(r'''
+        \text{Midpoint} = \frac{\text{High} + \text{Low}}{2}
+        ''')
+        st.markdown("""
+        2. **Compute the Moving Averages:**
+           - Calculate the 34-period and 5-period simple moving averages (SMA) of the midpoints.
+        3. **Calculate the Awesome Oscillator:**
+           - Use the formula:
+        """)
+        st.latex(r'''
+        \text{AO} = \text{SMA}_{5}(\text{Midpoint}) - \text{SMA}_{34}(\text{Midpoint})
+        ''')
+        st.markdown("""
+        4. **Identify Signals:**
+           - **Buy Signal:** Occurs when the AO crosses above the signal line (e.g., 0), indicating potential upward momentum.
+           - **Sell Signal:** Occurs when the AO crosses below the signal line, indicating potential downward momentum.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the signal line period.
+        3. Set the buy and sell thresholds.
+        4. Click 'Fetch Data' to load the stock data.
+        5. The chart will display the Awesome Oscillator and highlight buy/sell signals based on thresholds.
+        **Results:**
+        The chart shows the stock prices with the Awesome Oscillator and highlighted buy/sell signals.
+        """)
 
     signal_period = st.sidebar.number_input('Signal Line Period', min_value=1, value=9)
     ao_buy_thresh = st.sidebar.slider('AO Buy Threshold', min_value=-100.0, max_value=100.0, value=0.0)
@@ -602,35 +579,31 @@ elif selected == "Awesome Oscillator":
     st.plotly_chart(fig)
 
 elif selected == "Williams %R":
-    st.markdown("""
-    ### Williams %R
-
-    The Williams %R measures overbought and oversold levels.
-
-    **How it Works:**
-
-    1. **Calculate Williams %R:**
-       - Compute the highest high and lowest low over a specified look-back period (e.g., 14 days).
-       - Calculate the Williams %R using the formula:
-    """)
-    st.latex(r'''
-    \text{Williams \%R} = \frac{\text{Highest High} - \text{Close}}{\text{Highest High} - \text{Lowest Low}} \times -100
-    ''')
-    st.markdown("""
-    2. **Identify Signals:**
-       - **Buy Signal:** Occurs when the Williams %R crosses below a set threshold (e.g., -80), indicating the stock may be oversold.
-       - **Sell Signal:** Occurs when the Williams %R crosses above a set threshold (e.g., -20), indicating the stock may be overbought.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the look-back period.
-    3. Set the buy and sell thresholds.
-    4. Click 'Fetch Data' to load the stock data.
-    5. The chart will display the Williams %R and highlight buy/sell signals based on thresholds.
-
-    **Results:**
-    The chart shows the stock prices with the Williams %R and highlighted buy/sell signals.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Williams %R
+        The Williams %R measures overbought and oversold levels.
+        **How it Works:**
+        1. **Calculate Williams %R:**
+           - Compute the highest high and lowest low over a specified look-back period (e.g., 14 days).
+           - Calculate the Williams %R using the formula:
+        """)
+        st.latex(r'''
+        \text{Williams \%R} = \frac{\text{Highest High} - \text{Close}}{\text{Highest High} - \text{Lowest Low}} \times -100
+        ''')
+        st.markdown("""
+        2. **Identify Signals:**
+           - **Buy Signal:** Occurs when the Williams %R crosses below a set threshold (e.g., -80), indicating the stock may be oversold.
+           - **Sell Signal:** Occurs when the Williams %R crosses above a set threshold (e.g., -20), indicating the stock may be overbought.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the look-back period.
+        3. Set the buy and sell thresholds.
+        4. Click 'Fetch Data' to load the stock data.
+        5. The chart will display the Williams %R and highlight buy/sell signals based on thresholds.
+        **Results:**
+        The chart shows the stock prices with the Williams %R and highlighted buy/sell signals.
+        """)
 
     williams_r_period = st.sidebar.number_input('Look-back Period', min_value=1, value=14)
     williams_r_buy_thresh = st.sidebar.slider('Williams %R Buy Threshold', min_value=-100.0, max_value=0.0, value=-90.0)
@@ -639,46 +612,42 @@ elif selected == "Williams %R":
     st.plotly_chart(fig)
 
 elif selected == "Aroon Oscillator":
-    st.markdown("""
-    ### Aroon Oscillator
-
-    The Aroon Oscillator measures the strength of a trend in the stock's price.
-
-    **How it Works:**
-
-    1. **Calculate Aroon Up and Aroon Down:**
-       - Compute the Aroon Up, which measures the time since the highest high during the look-back period:
-    """)
-    st.latex(r'''
-    \text{Aroon Up} = \frac{N - \text{Days Since Highest High}}{N} \times 100
-    ''')
-    st.markdown("""
-       - Compute the Aroon Down, which measures the time since the lowest low during the look-back period:
-    """)
-    st.latex(r'''
-    \text{Aroon Down} = \frac{N - \text{Days Since Lowest Low}}{N} \times 100
-    ''')
-    st.markdown("""
-    2. **Calculate the Aroon Oscillator:**
-       - Use the formula:
-    """)
-    st.latex(r'''
-    \text{Aroon Oscillator} = \text{Aroon Up} - \text{Aroon Down}
-    ''')
-    st.markdown("""
-    3. **Identify Signals:**
-       - **Buy Signal:** Occurs when the Aroon Oscillator crosses above zero, indicating a potential upward trend.
-       - **Sell Signal:** Occurs when the Aroon Oscillator crosses below zero, indicating a potential downward trend.
-
-    **How to Use:**
-    1. Enter the stock ticker, start date, and end date.
-    2. Set the look-back period.
-    3. Click 'Fetch Data' to load the stock data.
-    4. The chart will display the Aroon Oscillator and highlight buy/sell signals based on thresholds.
-
-    **Results:**
-    The chart shows the stock prices with the Aroon Oscillator and highlighted buy/sell signals.
-    """)
+    with st.expander("Formula and Method Description", expanded=False):
+        st.markdown("""
+        ### Aroon Oscillator
+        The Aroon Oscillator measures the strength of a trend in the stock's price.
+        **How it Works:**
+        1. **Calculate Aroon Up and Aroon Down:**
+           - Compute the Aroon Up, which measures the time since the highest high during the look-back period:
+        """)
+        st.latex(r'''
+        \text{Aroon Up} = \frac{N - \text{Days Since Highest High}}{N} \times 100
+        ''')
+        st.markdown("""
+           - Compute the Aroon Down, which measures the time since the lowest low during the look-back period:
+        """)
+        st.latex(r'''
+        \text{Aroon Down} = \frac{N - \text{Days Since Lowest Low}}{N} \times 100
+        ''')
+        st.markdown("""
+        2. **Calculate the Aroon Oscillator:**
+           - Use the formula:
+        """)
+        st.latex(r'''
+        \text{Aroon Oscillator} = \text{Aroon Up} - \text{Aroon Down}
+        ''')
+        st.markdown("""
+        3. **Identify Signals:**
+           - **Buy Signal:** Occurs when the Aroon Oscillator crosses above zero, indicating a potential upward trend.
+           - **Sell Signal:** Occurs when the Aroon Oscillator crosses below zero, indicating a potential downward trend.
+        **How to Use:**
+        1. Enter the stock ticker, start date, and end date.
+        2. Set the look-back period.
+        3. Click 'Fetch Data' to load the stock data.
+        4. The chart will display the Aroon Oscillator and highlight buy/sell signals based on thresholds.
+        **Results:**
+        The chart shows the stock prices with the Aroon Oscillator and highlighted buy/sell signals.
+        """)
 
     aroon_period = st.sidebar.number_input('Look-back Period', min_value=1, value=25)
     aroon_osc = aroon_oscillator(data, aroon_period)
@@ -693,4 +662,4 @@ hide_streamlit_style = """
 footer {visibility: hidden;}
 </style>
 """
-st.markdown(hide_streamlit_style, unsafe_allow_html=True) 
+st.markdown(hide_streamlit_style, unsafe_allow_html=True)