Time-Series Analysis

Quantitative Time-Series Analysis: 20 Years of GOOGLE

A deterministic financial analytics pipeline that transforms raw OHLCV data into actionable investment intelligence using statistical signal processing and risk modeling.

Core Technologies

Python 3.10Pandas (Time-Series)NumPy (Vectorization)Matplotlib/SeabornSciPy (Statistical Stats)

The Quantitative Approach

Price is Noise. Returns are Signal.

A common mistake in financial analysis is analyzing raw price levels (which are non-stationary and trend-dominated). To build a robust model, we must transform price into Returns—a stationary stochastic process centered around a mean.

The Engineering Goal: We built a reusable ETL (Extract, Transform, Load) pipeline that:

Ingests raw CSV data with strict temporal ordering.
Engineers rolling features (Volatility, Moving Averages).
Visualizes structural market regimes (Bull vs. Bear).
Quantifies the risk/reward trade-off mathematically.

python

def calculate_max_drawdown(price_series):
    """
    Quantifies 'Pain': The worst-case capital destruction 
    from a historical peak to a subsequent trough.
    """
    # 1. Calculate the running maximum (High Water Mark)
    rolling_peak = price_series.cummax()
    
    # 2. Calculate percentage drop from that peak
    drawdown = (price_series - rolling_peak) / rolling_peak
    
    # 3. Find the absolute worst drop
    max_drawdown = drawdown.min()
    
    return drawdown, max_drawdown

5,000+

Data Points

20 Years

Time Horizon

Sharpe/Beta/Vol

Metrics

Vectorized

Processing

Data Ingestion & Integrity Audit

The foundation of any time-series analysis is chronological integrity. If dates are parsed as strings, or if rows are not monotonic, rolling window calculations will fail.

We implemented a strict ingestion layer:

Schema Enforcement: Explicit casting of Date objects during CSV read to prevent string-parsing errors.
Monotonicity Check: Verifying df.index.is_monotonic_increasing to ensure time always moves forward.
Null Hygiene: Auditing for trading holidays or corrupted data points using Heatmaps before any calculation occurs.

pipeline/ingestion.py

# Enforce temporal structure at load time
df = pd.read_csv("google_stock.csv", parse_dates=["Date"])

# Set Date as the index for time-series slicing
df.set_index("Date", inplace=True)
df.sort_index(inplace=True)

# Validation Gate
assert df.index.is_monotonic_increasing, "Data is not chronological!"

Feature Engineering: Signal Extraction

Raw prices are difficult to model statistically. We transform them into three distinct signal types:

Momentum (Trend): We compute 50-day and 200-day Simple Moving Averages (SMA). The crossover of these two signals (Golden Cross vs. Death Cross) acts as a deterministic regime filter, separating "Noise" from "Structural Trend."
Stationarity (Returns): We convert absolute price to percentage change (pct_change()). This normalizes the data, allowing us to compare volatility in 2004 vs. 2024 on the same scale.
Compounding (Wealth): We calculate Cumulative Returns to visualize the exponential nature of long-term holding.

pipeline/features.py

# 1. Momentum Signals (Low-Pass Filters)
df["MA50"] = df["Close"].rolling(window=50).mean()
df["MA200"] = df["Close"].rolling(window=200).mean()

# 2. Daily Returns (Stationary Signal)
df["Daily_Return"] = df["Close"].pct_change()

# 3. Wealth Index (Compounding Logic)
df["Cumulative_Return"] = (1 + df["Daily_Return"]).cumprod()

Volatility Modeling (Risk Clustering)

Risk in financial markets is not constant; it clusters. Periods of calm are followed by sudden bursts of chaos (e.g., 2008 Financial Crisis, 2020 COVID Crash).

A static Standard Deviation metric fails to capture this. Instead, we modeled Rolling Volatility (30-Day Standard Deviation). This creates a dynamic "Fear Gauge" that evolves over time. By visualizing this alongside returns, we can mathematically identify "Stress Regimes" where the asset becomes statistically unstable.

analysis/volatility.py

# Quantify local uncertainty over a 30-day window
df["Volatility_30D"] = df["Daily_Return"].rolling(window=30).std()

# Visualization Logic
plt.plot(df["Volatility_30D"], color='red', label='Risk Regime')

Exploratory Data Analysis (Distributional Physics)

We validated the statistical properties of the asset using Histograms and Kernel Density Estimation (KDE).

While financial theory often assumes a Normal (Gaussian) distribution, our EDA revealed "Fat Tails" (Kurtosis). This means extreme events (crashes and moonshots) happen far more often than a standard bell curve predicts. Recognizing this is critical for stress-testing any investment thesis.

Performance Evaluation: The Drawdown Test

Volatility describes the "bumpiness" of the ride, but Drawdown describes the risk of ruin.

We calculated the Maximum Drawdown curve to visualize the "Underwater Period"—how long an investor would have to wait to break even if they bought at the absolute peak. This metric separates resilient assets (which recover quickly) from speculative bubbles (which may never recover).

Final Metrics:

Sharpe Ratio: Reward per unit of risk.
Max Drawdown: Worst-case scenario depth.
Compound Annual Growth Rate (CAGR): The geometric mean return.

metrics/risk.py

# Sharpe Ratio Calculation (Risk-Adjusted Return)
mean_return = df["Daily_Return"].mean()
std_dev = df["Daily_Return"].std()

# Annualize the daily metrics (252 trading days)
annualized_sharpe = (mean_return / std_dev) * np.sqrt(252)

print(f"Efficiency Score: {annualized_sharpe:.2f}")