Time Series Forecasting 📈

Every time series can be decomposed into three signals:

1. Trend: The long-term direction. Anjali's shop grew 8% YoY.
2. Seasonality: Repeating patterns. Weekly (weekend spike), yearly (Diwali, Holi, Karva Chauth), and even hourly.
3. Residual: What's left after removing trend + seasonality. Often modelled as noise or with autoregression.

!pip install -q prophet

import pandas as pd
from prophet import Prophet
from prophet.make_holidays import make_holidays_df

# Load 3 years of daily ladoo sales
df = pd.read_csv("ladoo_sales.csv")  # columns: ds, y
df["ds"] = pd.to_datetime(df["ds"])

# Indian holidays — built-in support
holidays = make_holidays_df(year_list=[2023, 2024, 2025, 2026], country="IN")

# Add custom mithai-relevant events
custom = pd.DataFrame({
    "holiday": "raksha_bandhan_week",
    "ds": pd.to_datetime(["2024-08-19", "2025-08-09", "2026-08-28"]),
    "lower_window": -3, "upper_window": 1,  # spike starts 3 days before
})
holidays = pd.concat([holidays, custom])

m = Prophet(
    holidays=holidays,
    yearly_seasonality=True,
    weekly_seasonality=True,
    daily_seasonality=False,
    seasonality_mode="multiplicative",  # spikes scale with trend
    changepoint_prior_scale=0.05,       # default; raise to fit faster trend changes
)
m.fit(df)

future = m.make_future_dataframe(periods=60)        # 60-day forecast
forecast = m.predict(future)

# yhat = point estimate, yhat_lower / yhat_upper = 80% confidence interval
print(forecast[["ds", "yhat", "yhat_lower", "yhat_upper"]].tail(10))
m.plot(forecast)
m.plot_components(forecast)  # trend / weekly / yearly / holidays

!pip install -q neuralforecast

from neuralforecast import NeuralForecast
from neuralforecast.models import NBEATS

# Same dataframe but renamed to neuralforecast convention
df_nf = df.rename(columns={"ds": "ds", "y": "y"})
df_nf["unique_id"] = "ladoo"   # one series — could be many if multi-shop

model = NBEATS(
    h=60,                       # forecast horizon = 60 days
    input_size=180,             # use last 180 days as input
    max_steps=2000,
    stack_types=["trend", "seasonality"],
    n_blocks=[3, 3],
    mlp_units=[[256, 256], [256, 256]],
    learning_rate=1e-3,
    early_stop_patience_steps=20,
)
nf = NeuralForecast(models=[model], freq="D")
nf.fit(df_nf)

predictions = nf.predict()
print(predictions.head())

N-BEATS often beats Prophet on long, noisy series because it learns trend and seasonality basis functions directly from data rather than assuming a fixed parametric form.

Right metrics:

• MAPE (Mean Absolute Percentage Error): Most intuitive. "Forecast was off by 12% on average."
• MASE (Mean Absolute Scaled Error): Compares to a naive baseline (yesterday=today). MASE < 1 means you beat the baseline.
• Pinball loss (quantile loss): If you forecast a confidence interval, this scores it.

Drift handling: Retail patterns shift (new metro line opens, competitor closes). Anjali retrains weekly and runs a drift detector — if MAPE jumps 30% above baseline for 3 consecutive days, alert.

From forecast to inventory: Raw forecasts mislead. Anjali uses the upper 80% confidence interval for perishable items (better to slightly over-stock than stockout) and the lower 60% for non-perishable packaging (cash-flow optimisation). The forecast is one input — final order quantity also factors in: shelf life, safety stock, supplier lead time, cash on hand.