📊 Data Preprocessing & Moving Average Analysis

🔹 Data Transformation & Feature Engineering

• 📆 Extracting Year & Month → Created Year, Month, and Month_name columns for easier time-based analysis.

• 📈 Daily Returns Calculation → Added a Returns column using percentage change in closing price to analyze stock volatility.

• 📊 Moving Averages Computed:

  • MA30 (Short-term)

  • MA90, MA100 (Medium-term)

  • MA200 (Long-term) → Helps identify trends & potential trading signals.

• ⚡ Volatility Analysis → Rolling 30-day standard deviation (Volatility) calculated to track price fluctuations.

📉 Moving Average Chart – Key Takeaways

• 🚀 Overall Uptrend → All moving averages trend upward from late 2023 to early 2025, confirming a bullish market.

• 🔄 MA Order Confirms Uptrend → Shorter moving averages (MA30) staying above longer ones (MA200) reinforces the bullish trend.

• 📊 MA Smoothness & Reactivity:

  • MA30 (Dashed Blue) → Fastest to react, capturing short-term fluctuations.

  • MA90 & MA100 (Orange & Green) → Smoother, reflecting intermediate trends.

  • MA200 (Red) → Slowest, showing the long-term price direction.

• 🏆 Bullish Market Sentiment → Consistent higher price movement across all MAs.

• 📉 Potential Support Levels → MAs can act as dynamic support zones during pullbacks.

• ⚠ Crossover Signals:

  • Bullish: When shorter MA crosses above a longer MA (e.g., MA30 > MA90).

  • Bearish: When shorter MA crosses below a longer MA (use with confirmation).

• 🔥 Long-Term Strength → A rising MA200 reinforces the presence of a sustained long-term uptrend.

📏 Rice Rule – Optimal Bin Calculation

• What is the Rice Rule?

  • A rule of thumb for determining the optimal number of bins in a histogram for better frequency distribution analysis.

Why Use the Rice Rule?

• Helps avoid over-smoothing (too few bins) or over-segmentation (too many bins).

• Provides a clearer view of data distribution without excessive noise.

📊 Stock Volume Distribution Analysis

🔹 Efficient Bin Size Calculation (Rice Rule)

• 📏 Formula Used → Bins = ⌈2 * n^(1/3)⌉

• 🔢 Total Data Points (n) → 532

• 📊 Optimal Bins Calculated → 17 (Ensures a well-distributed histogram).

📉 Histogram Interpretation – Stock Volume Distribution

• 📈 Right-Skewed Distribution → Majority of trading volumes are low, with a long tail on the right.

• 🔄 Typical Volume Range → Most frequent trading volume falls between 5M – 10M shares.

• ⚡ Lower Volume Dominance → Low trading volume days occur significantly more often than high-volume days.

• 🚀 Infrequent High Volume Days → Some spikes in trading volume, but rare occurrences.

• 📊 Concentrated Trading Activity → Most trading volume remains in the lower range, suggesting stable trading with occasional surges.

📊 Correlation Heatmap Analysis

🔹 Understanding the Correlation Matrix

The heatmap visually represents relationships between different stock indicators.

• Dark Red (Strong Positive Correlation) → Values move together.

• Dark Blue (Strong Negative Correlation) → Values move opposite.

• Lighter Colors (Weak/No Correlation) → No significant relationship.

📈 Key Insights from the Heatmap

✅ Strong Positive Correlations (Darker Red Shades)

• 🔹 Close, High, Low, Open → Near-perfect correlation (~1) as they are all based on daily stock price movements.

• 🔹 Moving Averages (MA30, MA90, MA100, MA200) → Strongly correlated with each other & price variables, since they smooth out price trends.

📊 Moderate Positive Correlations

• 🔸 Volatility & Moving Averages → Higher volatility aligns with stronger price trends, leading to larger MA fluctuations.

• 🔸 RSI & MACD → These momentum indicators tend to move together, confirming trend strength.

🔄 Weak or Near-Zero Correlations

• 🔹 Returns & Most Other Variables → Daily returns are highly random, leading to low correlation with other metrics.

• 🔹 Volume & Price Variables → Slight negative correlation, meaning high trading volume doesn’t always coincide with price increases.

📉 Negative Correlations (Darker Blue Shades)

• 🔹 Volume & Moving Averages → Suggests that during strong uptrends, trading volume sometimes decreases.

• 🔹 MACD & Volume → Weak negative correlation, indicating MACD trends don’t strongly align with volume spikes.

📊 Bollinger Bands Analysis

📌 What Are Bollinger Bands?

Bollinger Bands are volatility indicators that help identify overbought & oversold conditions:

• Middle Line (Green) → Simple Moving Average (SMA) (60-day) smooths price trends.

• Upper Band (Red) → SMA + (2.5 × Standard Deviation) → Suggests overbought conditions.

• Lower Band (Orange) → SMA - (2.5 × Standard Deviation) → Suggests oversold conditions.

📈 Key Insights from the Chart

✅ Uptrend Confirmation → The Close Price (Blue Line) is generally trending upwards, indicating bullish momentum.
✅ Volatility Expansion & Contraction →

• Late 2024: Bands widen, signaling increased volatility & larger price swings.

• Calm Periods: Bands narrow, suggesting low volatility & consolidation.
  ✅ Potential Trading Signals →

• Price Near Upper Band → May indicate an overbought market (possible pullback).

• Price Near Lower Band → May indicate an oversold market (possible reversal).

📊 Stochastic Oscillator Analysis

📌 What is the Stochastic Oscillator?

A momentum indicator that measures the closing price relative to the high-low range over a set period:

• %K (Blue Line) → Measures the current momentum of the stock price.

• %D (Red Line) → A 3-day moving average of %K, smoothing out short-term noise.

• Overbought/Oversold Levels →

  • Above 80 (Green Line) → Potential overbought conditions.

  • Below 20 (Red Line) → Potential oversold conditions.

📈 Key Insights from the Chart

✅ Momentum Fluctuations → The oscillator moves frequently between overbought & oversold zones, signaling volatile price action.
✅ Crossovers as Trading Signals →

• %K (Blue) crossing above %D (Red) below 20 → Potential buy signal 📈.

• %K (Blue) crossing below %D (Red) above 80 → Potential sell signal 📉.
  ✅ Price Reversals →

• When %K & %D remain high (above 80) → Possible trend continuation or pullback.

• When %K & %D stay low (below 20) → Possible trend reversal upwards.

About ARIMA Model :

The ARIMA (AutoRegressive Integrated Moving Average) model is a powerful tool for time series forecasting. It combines three key components:

AutoRegressive (AR): This component uses the relationship between an observation and a certain number of lagged observations (previous values).

Integrated (I): This component involves differencing the raw observations to make the time series stationary, eliminating trends and seasonality.

Moving Average (MA): This component uses the dependency between an observation and a residual error from a moving average model applied to lagged observations.

ARIMA is widely used for forecasting future values in a time series based on its own past values, making it particularly effective for predicting stock prices. 

Data Omission and Preparation :

To forecast stock prices for the year 2024 using an ARIMA model, the data from 2024 is omitted. This approach ensures that the model is trained only on historical data up to 2023, allowing for an unbiased prediction of future prices.

df1 = df.dropna()

df1 = df1[df1['Year'] < 2024]

df_AR = df1 

df_AR.dropna(inplace=True)

Stationarity Test (ADF Test) :

1. • Before applying the ARIMA model, it's crucial to check if the time series data is stationary. A time series is considered stationary if its statistical properties like mean, variance, and autocorrelation remain constant over time. The Augmented Dickey-Fuller (ADF) test is used for this purpose:

   • The ADF test is applied to the 'Adj Close' prices. A p-value greater than 0.05 indicates non-stationarity, meaning the series requires differencing. The more negative the ADF statistic, the stronger the evidence against the null hypothesis (non-stationarity) and in favor of the alternative hypothesis (stationarity) but here value return positive

result = ts.adfuller(df_AR['Adj Close'].dropna())

print('ADF Statistic:', result[0])

print('p-value:', result[1])

Output:

ADF Statistic: 0.8237393757666592

p-value: 0.9920098611114088

1. • Since the series was non-stationary, differencing was applied to transform the data. The ADF test was then rrun on the differenced data ('Close_diff'), confirming stationarity with a significantly lower p-value.

df_AR['Close_diff'] = df_AR['Adj Close'].diff().dropna()

result = ts.adfuller(df_AR['Close_diff'].dropna())

print('ADF Statistic:', result[0])

print('p-value:', result[1])

Output:

ADF Statistic: -12.968433937493867

p-value: 3.117741156742175e-24

1. • With the ADF Statistic of -12.968 and a p-value well below 0.05, the data is confirmed to be stationary, making it ready for ARIMA modeling.

The ARIMA model requires the specification of three parameters:

• p (AutoRegressive Order): The number of lag observations included in the model.

• d (Differencing Order): The number of times the data has been differenced to make it stationary.

• q (Moving Average Order): The size of the moving average window.

To determine the appropriate values for p and q, AutoCorrelation Function (ACF) and Partial AutoCorrelation Function (PACF) plots are used:

• ACF Plot: Helps identify the value of q by showing the correlation between an observation and lagged values.

• PACF Plot: Helps identify the value of p by showing the correlation of the residuals with lagged observations after removing effects already explained by earlier lags.

from statsmodels.graphics.tsaplots import plot_acf, plot_pacf

fig, ax = plt.subplots(1, 2, figsize=(16, 4))

plot_acf(df_AR['Close_diff'].dropna(), lags=40, ax=ax[0])

plot_pacf(df_AR['Close_diff'].dropna(), lags=40, ax=ax[1])

plt.show()

Analysis :

• The ACF plot shows the correlation between a time series with its lagged values.

• In this plot, there's a significant spike at lag 1, indicating a strong correlation between the current value and the previous value.

• The subsequent lags show no significant correlation.

• The PACF plot shows the correlation between a time series with its lagged values, controlling for the effects of the intervening values.

• In this plot, there's a significant spike at lag 1, indicating a direct relationship between the current value and the previous value.

• Similar to the ACF, subsequent lags show no significant correlation.

• Based on the ACF and PACF plots, we can assume : 

p = 1: One autoregressive term due to the significant spike at lag 1 in the PACF.

d = 1 : Differencing is done for the 1st time to make data stationary.

q = 0: No moving average term as there are no significant spikes in the ACF after lag 1.

Data Split  :

• Training Set : Comprising 80% of the data, it is used to train the ARIMA model.

• Testing Set : Comprising the remaining 20% of the data, it is used to evaluate the model's forecasting performance.

train_size = int(len(df_AR) * 0.8)

train, test = df_AR['Adj Close'][:train_size], df_AR['Adj Close'][train_size:]

• train_size : This variable determines the number of data points (80%) to include in the training set.

• train : This series contains the adjusted closing prices used for training the ARIMA model.

• test : This series contains the remaining data, which will be used to validate the model's predictions.

Using Auto-ARIMA for Best Model Configuration :

After initial testing with manually set ARIMA parameters, the model's predictions were significantly deviated from the actual stock prices for the first 30 days of 2024. To refine the model and achieve more accurate forecasting, we used the auto_arima function. This approach helps in identifying the best possible ARIMA model configuration by automatically searching through a range of parameters.

stepwise_model = pm.auto_arima(df_AR['Adj Close'], start_p=0, start_q=0,

                           max_p=5, max_q=5, m=12,

                           start_P=0, seasonal=True,

                           d=1, D=1, trace=True,

                           error_action='ignore',

                           suppress_warnings=True,

                           stepwise=True)

• 'start_p', 'start_q', 'max_p', 'max_q' : These parameters define the range of values for the AR and MA terms, which are part of the model's configuration.

• 'm=12' : Specifies a seasonal cycle of 12 periods, typically representing monthly data.

• 'd=1', 'D=1' : Indicates the order of differencing required to make the time series stationary.

• 'seasonal=True' : Enables the search for seasonal parameters, making the model a SARIMA (Seasonal ARIMA).

After running the auto_arima function, the best model identified was ARIMA(5,1,0)(2,1,0)[12], which had the lowest AIC score, indicating a better fit for the data. 

Fitting the Selected ARIMA Model:  :

non_seasonal_order = (5, 1, 0)  # (p, d, q)

seasonal_order = (2, 1, 0, 12)  # (P, D, Q, M)

model = ARIMA(df_AR['Adj Close'], order=non_seasonal_order, seasonal_order=seasonal_order)

model_fit = model.fit()

• non_seasonal_order : Specifies the ARIMA model's parameters for non-seasonal data.

• seasonal_order : Defines the seasonal component of the model.

Model Summary :

After fitting the ARIMA model to the dataset, the model_fit.summary() command provides a comprehensive summary of the model's performance and parameters. 

Predicting :

After fitting the model, predictions for the test set are generated using the code below :

start = len(train)

end = len(train) + len(test) - 1

predictions = model_fit.predict(start=start, end=end, typ='levels')

• 'start and end' : These indices define the range of data points for which predictions are made.

• 'typ='levels' : Ensures that predictions are made on the original scale of the data, rather than differenced values.

Plotting :

plt.figure(figsize=(14, 7))

plt.plot(df_AR.index[-len(test):], test, label='Actual')

plt.plot(df_AR.index[-len(test):], predictions, label='Predicted')

plt.title('ARIMA Model for Adjusted closing price : Actual vs Predicted Prices')

plt.xlabel('Date')

plt.ylabel('Price')

plt.legend()

plt.show()

ARIMA Model Forecast Visualization :

I forecasted the stock prices for the next 30 days using the ARIMA model and visualized the results to analyze the predicted trends.

# Forecast the next 30 days

forecast = model_fit.forecast(steps=30)

forecast_dates = pd.date_range(start=df_AR.index[-1], periods=30, freq='B')

plt.figure(figsize=(12, 6))

plt.plot(arima_predictions.index, arima_predictions['ARIMA'], label='ARIMA')

plt.title('ARIMA Predictions')

plt.xlabel('Date')

plt.ylabel('Close Price')

plt.legend()

plt.grid(True)

plt.show()

• The forecast function of the ARIMA model was used to predict the stock prices for the next 30 business days. This step is crucial for extending the model's insights into future price movements, allowing for better strategic decisions based on anticipated market trends.

• The plot illustrates the predicted stock prices over the forecasted period. The x-axis represents the dates, while the y-axis shows the predicted close prices. The trend indicates how the ARIMA model expects the stock price to evolve, providing a visual reference for the model's accuracy and the market's potential future direction.

Plotting :

plt.figure(figsize=(14, 7))

plt.plot(df_AR.index[-len(test):], test, label='Actual')

plt.plot(df_AR.index[-len(test):], predictions, label='Predicted')

plt.title('ARIMA Model for Adjusted closing price : Actual vs Predicted Prices')

plt.xlabel('Date')

plt.ylabel('Price')

plt.legend()

plt.show()