Time Series

1. Aggregate Data

2. Aggregate and Reshape

Aggregate the data by Store_ID and generate time-series features:

• Group by Store_ID.

• Generate features for each store based on the time series.

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3. Feature Engineering

a. Sales Statistics

Compute aggregate statistics for each store:

• Mean sales

• Median sales

• Standard deviation

• Min and max sales

• Coefficient of variation (std/mean)

b. Temporal Trends

Extract temporal trends:

• Seasonality: Average sales by day of the week, month, or season.

• Growth/Decline: Sales trend (slope) over time.

• Autocorrelation: Correlation between lagged sales.

c. Distribution Features

Analyze sales distribution:

• Percentiles (e.g., 25th, 50th, 75th percentiles)

• Skewness and kurtosis

d. Time-Based Features

Capture periodic patterns:

• Ratio of weekend sales to weekday sales

• Sales spikes (e.g., max sales deviation from average)

e. Missing Data

Handle and feature missing data:

• Count or percentage of missing sales values

• Fill missing values using interpolation or a constant.

f. Derived Metrics

Derive additional metrics:

• Rolling averages (e.g., 7-day or 30-day moving averages)

• Rolling standard deviation

• Ratio of sales to previous periods (e.g., week-over-week or month-over-month growth)

g. External Factors (Optional)

Incorporate external data:

• Holidays (binary feature: 1 if the date is a holiday, 0 otherwise)

• Local weather conditions (average temperature, precipitation)

• Macroeconomic indicators (CPI, local unemployment rate)

3. Autocorrelation

For autocorrelation:

• Compute the autocorrelation for each store over the entire time series.

• Use this single autocorrelation value as a feature.

Example (Python)

def compute_autocorr(series, lag=1):
    return series.autocorr(lag=lag)

data['autocorr'] = data.groupby('Store_ID')['Sales'].transform(lambda x: compute_autocorr(x, lag=1))

autocorr_features = data.groupby('Store_ID').agg(
    autocorr_mean=('autocorr', 'mean')
)

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4. Growth/Decline

Growth/decline trends can be summarized using:

• Slope of the linear trend: Fit a line to the sales data and use its slope.

• Percentage change: Compare the first and last sales values.

• Compound annual growth rate (CAGR): Measure overall growth.

Example (Python)

def compute_trend(series):
    if len(series) > 1:
        return np.polyfit(range(len(series)), series, 1)[0]  # Slope of trend line
    return 0

data['sales_trend'] = data.groupby('Store_ID')['Sales'].transform(compute_trend)

trend_features = data.groupby('Store_ID').agg(
    sales_trend_mean=('sales_trend', 'mean')
)