import pandas as pd

def process_data(transactions):
    # Convert to DataFrame
    df = pd.DataFrame(transactions)
    
    if df.empty:
        return df
    
    # Ensure correct data types
    df["date"] = pd.to_datetime(df["date"])
    df["amount"] = df["amount"].astype(float)
    
    # Add time-based columns
    df["month"] = df["date"].dt.to_period("M")
    df["week"] = df["date"].dt.isocalendar().week
    
    return df