Time Series & Forecasting

Time Series & Forecasting#

“Because even your boss wants to know what happens next.” 🔮📈

🎯 Chapter Goal#

In this chapter, you’ll learn how to predict the future — not with tarot cards or crystal balls 🧙‍♂️, but with Time Series Models that actually make sense to CFOs. 💼

You’ll move from:

“Let’s guess next quarter’s revenue.” to “According to our ARIMA(1,1,1), we’ll hit ₹3.2M ± 5%.” 😎

🧠 Why Time Series?#

Because time doesn’t stop. Sales, stock prices, website traffic — they all depend on their past selves, just like your caffeine habit. ☕

ML for time series helps businesses:

  • Forecast demand 🏪

  • Plan inventory 🧺

  • Allocate budgets 💰

  • Detect anomalies 🚨

In short: it’s how businesses time-travel responsibly.

🧩 What You’ll Learn#

Section

Concept

Comedy Tag

Stationarity & Differencing

How to calm your chaotic data

“Because trends are cute until they break your model.” 📉

ARIMA / SARIMA

Classic forecasting workhorses

“The economists’ version of comfort food.” 🍛

Prophet

Facebook’s easy-to-love forecaster

“For those who prefer drag-and-drop time travel.” 🧙‍♀️

Backtesting & KPIs

Measuring forecast success

“Because even fortune tellers need validation.” 🔍

Case Study – Inventory Planning

Hands-on business scenario

“When your warehouse finally thanks you.” 🏭

🧮 Forecasting 101#

Definition: A time series is a sequence of data points collected over time — e.g. daily sales, monthly revenue, hourly heart rate during exams 🫀.

You model it by separating three secret ingredients: [ \text{Time Series} = \text{Trend} + \text{Seasonality} + \text{Noise} ]

Trend = long-term direction Seasonality = repeating pattern (weekly, yearly, etc.) Noise = life’s chaos 💥

🔍 Key Concepts You’ll Master#

1. Stationarity#

Your data must behave consistently over time — same mean, same variance, no drama. If it doesn’t, we difference it until it learns discipline.

2. Autocorrelation & Lag#

Autocorrelation tells you how much today’s value depends on yesterday’s. (For sales teams, it’s usually a lot — hangovers from Black Friday deals are real. 🛍️)

You’ll meet tools like:

  • ACF (AutoCorrelation Function)

  • PACF (Partial AutoCorrelation Function)

Think of them as your data’s “trust issues” — which past values influence the present?

3. ARIMA / SARIMA#

The OGs of forecasting:

  • AR (AutoRegressive): past values predict future ones

  • I (Integrated): handle non-stationarity

  • MA (Moving Average): handle shocks or randomness

SARIMA adds Seasonality, for when your sales rise and fall like coffee prices ☕📉📈.

4. Prophet (by Facebook/Meta)#

For those who love intuitive forecasting without wrestling math. It handles:

  • Seasonality (daily, weekly, yearly)

  • Holidays 🏖️

  • Trend changepoints

  • Outliers (we all have them)

Prophet = “The data scientist’s emotional support forecaster.” 🐶

5. Backtesting & Forecast KPIs#

Unlike regular ML, you can’t randomly shuffle time data (unless you want chaos). So we backtest — simulate the past to see how your forecast would’ve done in reality.

KPIs to know:

  • MAE (Mean Absolute Error)

  • RMSE (Root Mean Squared Error)

  • MAPE (Mean Absolute Percentage Error)

  • WAPE (Weighted Absolute Percentage Error)

If MAPE = 10%, your forecast is 90% less embarrassing. 🎯

🏢 Business Use Cases#

Domain

Forecast Example

Impact

Retail

Sales forecasting

Prevent overstocking / shortages

Finance

Stock / portfolio forecasting

Optimize trading strategies

Logistics

Delivery demand

Optimize fleet and staffing

Energy

Power usage

Balance supply vs demand

SaaS

Subscription renewals

Plan server capacity

🧪 Hands-On Forecasting Flow#

  1. Visualize the series

    • Check trends, spikes, and seasonal effects

  2. Check stationarity with ADF test

  3. Apply differencing (if needed)

  4. Fit ARIMA or Prophet model

  5. Forecast ahead & plot confidence intervals

  6. Backtest with rolling windows

  7. Compare models using RMSE & MAPE

🧰 Tools You’ll Use#

  • pandas → Time indexing and rolling windows

  • statsmodels → ARIMA, ADF test

  • prophet → Quick forecasts, trends & holidays

  • matplotlib / plotly → Trend and error visualization

⚙️ Example Snippet#

from statsmodels.tsa.arima.model import ARIMA
import pandas as pd

df = pd.read_csv("sales_data.csv", parse_dates=["date"], index_col="date")
model = ARIMA(df["sales"], order=(1,1,1))
result = model.fit()

print(result.summary())
df["forecast"] = result.predict(start="2024-01-01", end="2024-12-31", dynamic=True)
df[["sales", "forecast"]].plot(title="Sales Forecast vs Actuals")

Spoiler: If your forecast line looks too perfect, you probably peeked into the future. 🚫🔮

💬 Business Translation#

CFO: “Can we trust this forecast?” You: “With 95% confidence, yes — unless it rains on a public holiday again.” ☔📉

Machine learning helps predict the future, but business context tells you whether it’s worth acting on.

🎓 Takeaways#

✅ Time Series ≠ Random Guessing ✅ Always validate forecasts (don’t overtrust your ARIMA) ✅ Seasonality matters — Mondays are not Fridays ✅ Translate metrics → dollars, not decimals

🧪 Lab Preview#

In the Inventory Planning Case Study, you’ll:

  • Forecast demand using ARIMA and Prophet

  • Compare forecast KPIs (RMSE, MAPE)

  • Optimize reorder points

  • Visualize cost savings from smarter predictions 💰

“Forecasting is like weather prediction — everyone complains when it’s wrong, no one thanks you when it’s right.” 🌦️

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