Perplexity vs Kimi for Data Analysis

No sales dataset was provided in the query, so a direct analysis cannot be performed. However, standard methods from time series analysis can identify seasonal trends, calculate year-over-year (YoY) growth rates, and flag outliers, as outlined below using established techniques from relevant sources[1][2][3].

Identifying Seasonal Trends

Seasonal trends involve predictable, recurring patterns tied to holidays, weather, or calendars, separable from noise and trends via decomposition[1][2].

• Time series decomposition: Manually compute monthly indices in Excel by comparing each month's demand to the yearly median; if indices match or are close for >75% of the year, seasonality is present. Use Holt-Winters filtering to confirm repeating coefficients at consistent intervals (e.g., yearly cycles)[1].
• Visualization tools: Plot sales trend charts, heat maps, or calendar views to spot peaks (e.g., holiday spikes); segment products into high-season (e.g., holiday-tied) vs. evergreen SKUs[2].
• Advanced steps: Deseasonalize data by dividing by seasonal indices, then fit linear trends; compare triple exponential smoothing forecasts against moving averages (e.g., 6-month) for validation[1][4].

In analyzed examples, ~30% of product groups showed consistent 36-month cycles[1].

Calculating Year-Over-Year (YoY) Growth Rates

YoY growth compares performance across similar periods to highlight demand shifts[2][3].

• Formula: For month $m$ in year $y$, compute $\frac{\text{Sales}_{y,m} - \text{Sales}_{y-1,m}}{\text{Sales}_{y-1,m}} \times 100\%$.
• Process: Aggregate sales by month/quarter over ≥12-36 months; plot line charts or moving averages to smooth noise and reveal patterns (e.g., consistent August dips indicate rhythm, not trend)[3].
• Comparative analysis: Use historical data with external factors (e.g., weather, marketing) for context; AI tools automate for real-time insights[2][3].

Flagging Statistical Outliers

Outliers may signal data errors or events (e.g., market shocks); detect via residuals post-decomposition or filtering[1][3].

• Methods:

  Technique	Description	Tools
  Residual analysis	After decomposition/Holt-Winters, flag points >2-3 standard deviations from smoothed series[1]	Excel, R forecasting package
  Visual smoothing	Use moving averages on line charts; spikes/dips beyond pattern indicate outliers[3]	Charts, AI platforms
  Pattern breaks	Compare YoY; sudden shifts vs. historical norms flag issues[2]	Heat maps, simulations

• Validate with "what-if" simulations (e.g., uniform distributions from historical min/max) to test if outliers fit seasonal models[1].
• Non-quantitative checks: Cross-reference customer/market factors[1].

Apply these to your dataset in R/Excel (e.g., decompose() or HoltWinters() in R); upload data for specific analysis if needed[1][5]. Limitations: Short datasets (<24 months) may confuse noise with seasonality[1].

I'll provide a comprehensive analysis framework. Since you didn't attach the dataset, I'll demonstrate the methodology using a realistic synthetic example that you can adapt to your actual data.

Complete Sales Analysis Pipeline

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
from statsmodels.tsa.seasonal import seasonal_decompose
import warnings
warnings.filterwarnings('ignore')

# ============================================
# 1. DATA GENERATION (Replace with your data)
# ============================================
def generate_sample_data(start_date='2020-01-01', periods=48):
    """Generate realistic sales data with trend, seasonality, and outliers"""
    dates = pd.date_range(start=start_date, periods=periods, freq='MS')
    
    # Components
    trend = np.linspace(1000, 2500, periods)  # Growth trend
    seasonal = 500 * np.sin(2 * np.pi * np.arange(periods) / 12) + 300  # Monthly seasonality
    noise = np.random.normal(0, 150, periods)
    
    # Add holiday spikes (Nov/Dec)
    seasonal[10::12] += 800  # November
    seasonal[11::12] += 1200  # December
    
    # Create outliers
    sales = trend + seasonal + noise
    
    # Inject data quality issues and anomalies
    sales[14] *= 2.5  # Massive one-time sale (outlier)
    sales[25] = -500  # Data error (negative value)
    sales[36] *= 0.1  # System outage (underreporting)
    
    df = pd.DataFrame({
        'date': dates,
        'sales': sales,
        'units': (sales / 50 + np.random.normal(0, 5, periods)).astype(int)
    })
    
    return df

# Load your actual data here:
# df = pd.read_csv('your_sales_data.csv', parse_dates=['date'])
df = generate_sample_data()

print(f"Dataset shape: {df.shape}")
print(f"Date range: {df['date'].min()} to {df['date'].max()}")
print("\nFirst few rows:")
print(df.head())

2. Data Quality Check & Outlier Detection

def comprehensive_outlier_analysis(df, sales_col='sales'):
    """Identify statistical outliers and data quality issues"""
    
    results = {
        'missing_values': df[sales_col].isnull().sum(),
        'negative_values': (df[sales_col] < 0).sum(),
        'zero_values': (df[sales_col] == 0).sum()
    }
    
    # Statistical Methods
    
    # A. Z-Score Method (>3 std deviations)
    z_scores = np.abs(stats.zscore(df[sales_col]))
    z_outliers = df[z_scores > 3].copy()
    z_outliers['method'] = 'Z-Score (>3σ)'
    
    # B. IQR Method (1.5 * IQR rule)
    Q1 = df[sales_col].quantile(0.25)
    Q3 = df[sales_col].quantile(0.75)
    IQR = Q3 - Q1
    lower_bound = Q1 - 1.5 * IQR
    upper_bound = Q3 + 1.5 * IQR
    
    iqr_outliers = df[(df[sales_col] < lower_bound) | (df[sales_col] > upper_bound)].copy()
    iqr_outliers['method'] = 'IQR Method'
    
    # C. Modified Z-Score (using MAD - more robust)
    median = df[sales_col].median()
    mad = np.median(np.abs(df[sales_col] - median))
    modified_z = 0.6745 * (df[sales_col] - median) / mad
    mad_outliers = df[np.abs(modified_z) > 3.5].copy()
    mad_outliers['method'] = 'Modified Z-Score (MAD)'
    
    # Combine unique outliers
    all_outliers = pd.concat([z_outliers, iqr_outliers, mad_outliers]).drop_duplicates(subset=['date'])
    
    print("=== DATA QUALITY FLAGS ===")
    print(f"Missing values: {results['missing_values']}")
    print(f"Negative values (potential errors): {results['negative_values']}")
    print(f"Zero values: {results['zero_values']}")
    print(f"\nStatistical outliers detected: {len(all_outliers)}")
    
    if len(all_outliers) > 0:
        print("\nDetailed outlier report:")
        display_cols = ['date', sales_col, 'method']
        print(all_outliers[display_cols].sort_values('date'))
        
        # Context analysis
        print("\n=== OUTLIER CONTEXT ===")
        for idx, row in all_outliers.iterrows():
            date = row['date']
            context = df[(df['date'] >= date - pd.Timedelta(days=60)) & 
                        (df['date'] <= date + pd.Timedelta(days=60))]
            local_mean = context[context.index != idx][sales_col].mean()
            deviation = ((row[sales_col] - local_mean) / local_mean) * 100
            print(f"{date.strftime('%Y-%m')}: {row[sales_col]:,.0f} ({deviation:+.1f}% vs local avg)")
    
    return all_outliers, results

outliers, quality_metrics = comprehensive_outlier_analysis(df)

3. Seasonal Trend Analysis

def analyze_seasonality(df, date_col='date', sales_col='sales'):
    """Decompose time series into trend, seasonal, and residual components"""
    
    # Prepare time series
    df_ts = df.set_index(date_col)[sales_col].asfreq('MS')
    
    # Handle missing values if any
    df_ts = df_ts.interpolate(method='linear')
    
    # Decomposition (Multiplicative if variance increases with level, else Additive)
    # Test for multiplicative vs additive
    cv = df_ts.std() / df_ts.mean()  # Coefficient of variation
    model_type = 'multiplicative' if cv > 0.3 else 'additive'
    
    decomposition = seasonal_decompose(df_ts, model=model_type, period=12)
    
    # Calculate seasonal strength
    var_residual = np.var(decomposition.resid.dropna())
    var_seasonal = np.var(decomposition.seasonal + decomposition.resid.dropna())
    seasonal_strength = 1 - (var_residual / var_seasonal)
    
    # Extract monthly patterns
    df['month'] = df[date_col].dt.month
    df['quarter'] = df[date_col].dt.quarter
    df['year'] = df[date_col].dt.year
    
    monthly_pattern = df.groupby('month')[sales_col].agg(['mean', 'std', 'min', 'max'])
    monthly_pattern['cv'] = monthly_pattern['std'] / monthly_pattern['mean']
    
    print(f"\n=== SEASONAL ANALYSIS ({model_type.upper()} model) ===")
    print(f"Seasonal strength: {seasonal_strength:.2%}")
    print(f"Peak months (top 3): {monthly_pattern['mean'].nlargest(3).index.tolist()}")
    print(f"Low months (bottom 3): {monthly_pattern['mean'].nsmallest(3).index.tolist()}")
    
    # Quarter analysis
    q_analysis = df.groupby('quarter')[sales_col].mean()
    q_analysis = q_analysis.sort_values(ascending=False)
    print(f"\nQuarter ranking: {dict(zip(q_analysis.index, ['Q'+str(x) for x in q_analysis.index]))}")
    
    # Visualization
    fig, axes = plt.subplots(4, 1, figsize=(12, 10))
    
    decomposition.observed.plot(ax=axes[0], title='Original Time Series')
    decomposition.trend.plot(ax=axes[1], title='Trend Component')
    decomposition.seasonal.plot(ax=axes[2], title='Seasonal Component')
    decomposition.resid.plot(ax=axes[3], title='Residual Component', style='o')
    
    plt.tight_layout()
    plt.show()
    
    return decomposition, monthly_pattern

decomp, monthly_stats = analyze_seasonality(df)

4. Year-over-Year Growth Analysis

def calculate_yoy_growth(df, date_col='date', sales_col='sales'):
    """Calculate YoY growth with proper period alignment"""
    
    df = df.copy()
    df['year_month'] = df[date_col].dt.to_period('M')
    
    # Pivot to wide format for easy YoY calculation
    pivot = df.pivot_table(
        values=sales_col, 
        index=df[date_col].dt.month, 
        columns=df[date_col].dt.year,
        aggfunc='sum'
    )
    
    print("=== YEAR-OVER-YEAR GROWTH ===")
    print("\nMonthly Sales by Year:")
    print(pivot.round(0))
    
    # Calculate YoY % change
    yoy_changes = pivot.pct_change(axis=1) * 100
    
    print("\nYoY Growth Rates (%):")
    print(yoy_changes.round(1))
    
    # Rolling 12-month growth (trailing TTM)
    df_monthly = df.groupby('year_month')[sales_col].sum().reset_index()
    df_monthly['date'] = df_monthly['year_month'].dt.to_timestamp()
    df_monthly['trailing_12m'] = df_monthly[sales_col].rolling(window=12).sum()
    df_monthly['yoy_ttm'] = df_monthly['trailing_12m'].pct_change(periods=12) * 100
    
    # Latest metrics
    if len(df_monthly) >= 13:
        latest_yoy = df_monthly['yoy_ttm'].iloc[-1]
        avg_growth = yoy_changes.mean().mean()
        
        print(f"\nKey Metrics:")
        print(f"Latest YoY growth (TTM): {latest_yoy:.1f}%")
        print(f"Average monthly YoY growth: {avg_growth:.1f}%")
        print(f"Volatility (std of YoY): {yoy_changes.std().mean():.1f}%")
    
    # CAGR Calculation
    years = df[date_col].dt.year.max() - df[date_col].dt.year.min()
    if years > 0:
        start_val = df.groupby(df[date_col].dt.year)[sales_col].sum().iloc[0]
        end_val = df.groupby(df[date_col].dt.year)[sales_col].sum().iloc[-1]
        cagr = ((end_val / start_val) ** (1/years) - 1) * 100
        print(f"CAGR ({years} years): {cagr:.1f}%")
    
    # Visualization
    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 8))
    
    # Heatmap of YoY
    sns.heatmap(yoy_changes, annot=True, fmt='.1f', cmap='RdYlGn', center=0, ax=ax1)
    ax1.set_title('YoY Growth Heatmap by Month')
    
    # TTM Trend
    if 'yoy_ttm' in df_monthly.columns:
        df_monthly.dropna().plot(x='date', y='yoy_ttm', ax=ax2, marker='o')
        ax2.axhline(y=0, color='r', linestyle='--', alpha=0.5)
        ax2.set_title('Trailing 12-Month YoY Growth Rate')
        ax2.set_ylabel('Growth %')
    
    plt.tight_layout()
    plt.show()
    
    return yoy_changes, df_monthly

yoy_results, monthly_trends = calculate_yoy_growth(df)

5. Executive Summary Report

def generate_executive_summary(df, outliers, yoy_data):
    """Generate automated insights"""
    
    print("\n" + "="*50)
    print("EXECUTIVE SUMMARY")
    print("="*50)
    
    # Overall performance
    latest_month = df['date'].max()
    latest_sales = df[df['date'] == latest_month]['sales'].values[0]
    
    print(f"\nCurrent Status (as of {latest_month.strftime('%Y-%m')}):")
    print(f"Latest monthly sales: ${latest_sales:,.0f}")
    
    # Data quality warning
    if len(outliers) > 0:
        print(f"\n⚠️  ALERT: {len(outliers)} anomalous data points detected")
        print("   Review outliers for data entry errors or one-time events")
    
    # Seasonality insight
    peak_month = df.groupby(df['date'].dt.month)['sales'].mean().idxmax()
    month_names = {1:'Jan', 2:'Feb', 3:'Mar', 4:'Apr', 5:'May', 6:'Jun',
                   7:'Jul', 8:'Aug', 9:'Sep', 10:'Oct', 11:'Nov', 12:'Dec'}
    print(f"\n📊 Seasonal Pattern: Peak sales typically occur in {month_names[peak_month]}")
    
    # Growth trajectory
    if isinstance(yoy_data, pd.DataFrame) and 'yoy_ttm' in yoy_data.columns:
        recent_growth = yoy_data['yoy_ttm'].dropna().iloc[-1]
        if recent_growth > 20:
            status = "🚀 Accelerating"
        elif recent_growth > 0:
            status = "📈 Growing"
        elif recent_growth > -10:
            status = "⚖️ Stable/Declining"
        else:
            status = "📉 Concerning"
        print(f"\n{status} ({recent_growth:+.1f}% YoY)")

# Run the report
generate_executive_summary(df, outliers, monthly_trends)

Key Interpretation Guidelines

Outlier Classification:

• Data Errors: Negative values, extreme deviations (>500%), zero values in high-volume periods
• Market Events: Sudden spikes (viral marketing, bulk orders), drops (inventory outages, economic shocks)
• Natural Variance: Random noise within 2-3 standard deviations

Seasonal Insights to Look For:

• Multiplicative vs Additive: If December is +$1000 when baseline is $5000, but +$2000 when baseline is $10000, use multiplicative models
• Shift Detection: If seasonality peaks drift (e.g., Black Friday moving earlier), check for calendar effects or market changes

YoY Nuances:

• Align fiscal calendars correctly (52/53-week years can distort comparisons)
• Distinguish between calendar effects (extra weekend days) vs true demand changes
• Check for COVID-19 or other structural breaks in your date range

Would you like me to:

1. Analyze your specific dataset (upload the CSV/Excel file)?
2. Deep-dive into any specific component (e.g., anomaly detection algorithms)?
3. Add forecasting capabilities to predict next quarter's performance?