Understanding Time-Series Forecasting

Learn the fundamentals of time-series forecasting and how AnoFox Forecast helps you predict the future.

What is a Time Series?

A time series is a sequence of values measured at regular intervals over time.

Real-World Examples

Domain	Example	Measurement	Frequency
Retail	Daily sales	Units sold	Daily
Finance	Stock price	Price	Minutely/Daily
Energy	Electricity demand	Megawatts	Hourly
Weather	Temperature	Degrees	Hourly
Operations	Website traffic	Page views	Hourly/Daily
Manufacturing	Production output	Units	Hourly

Components of a Time Series

Every time series can be decomposed into:

Time Series = Trend + Seasonality + Residual

┌─────────────────────────────────────────────────┐
│ Original Time Series                            │
│ ╱╲  ╱╲      ╱╲  ╱╲      ╱╲  ╱╲                 │
│╱  ╲╱  ╲────╱  ╲╱  ╲────╱  ╲╱  ╲                │
└─────────────────────────────────────────────────┘
        ↓
┌─────────────────────────────────────────────────┐
│ Trend (long-term direction)                     │
│ ╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱╱   │
└─────────────────────────────────────────────────┘
        ↓
┌─────────────────────────────────────────────────┐
│ Seasonality (repeating patterns)                │
│ ╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱╲╱  │
└─────────────────────────────────────────────────┘
        ↓
┌─────────────────────────────────────────────────┐
│ Residual (random noise)                         │
│ ◦ ◦  ◦   ◦    ◦  ◦ ◦  ◦    ◦  ◦ ◦  ◦    ◦     │
└─────────────────────────────────────────────────┘

Understanding Each Component

Trend

Long-term direction or movement. Examples:

Sales increasing over years
Stock price rising due to company growth
Population growing over decades

↗ Uptrend (sales growing)
→ Flat trend (stable demand)
↘ Downtrend (declining interest)

Seasonality

Repeating patterns that occur at fixed intervals. Examples:

Weekly: Retail sales spike on Fridays/weekends
Yearly: Holiday shopping spikes in December
Quarterly: Electricity demand peaks in summer/winter
Hourly: Website traffic peaks during business hours

Residual (Noise)

Random, unexplained variation. Examples:

Weather disruptions affecting sales
Unexpected competitor actions
Measurement errors

What is Forecasting?

Forecasting is predicting future values based on historical patterns.

The Forecasting Problem

Given historical data:

Past                                 Present       Future
├─────────────────────────────────┤ ├──────────────┤
Jan Feb Mar Apr May Jun Jul Aug Sep │ Oct Nov Dec  │ Jan Feb Mar
100 110 115 120 125 130 140 155 160 │ ???  ???  ??? │ ??? ??? ???

Goal: Predict what comes next using the patterns you see.

Simple Forecasting Example

Historical data (10 days):

Day:  1   2    3    4    5   6    7    8    9   10
Sales: 100 105 110 115 120 125 130 135 140 145

Pattern: Sales increase by 5 each day

Forecast (next 3 days):

Day:  11  12  13
Sales: 150 155 160

Reality: Sales might be 148, 158, 162 due to factors not captured in the simple trend.

Why Is Forecasting Hard?

Challenge 1: Multiple Patterns

Real data has trends, seasonality, and noise all mixed together:

Sales = Trend + Weekly Pattern + Random Events
120 = 100 + 20 - 5 (price discount)

Challenge 2: Changing Patterns

Patterns shift over time:

Before marketing campaign: Stable demand
After marketing campaign: Demand increases
New trend started

Challenge 3: Limited History

Sometimes you don't have much data:

New product: Only 2 months of sales
But need to forecast 12 months ahead

Challenge 4: Uncertainty

Future cannot be predicted perfectly:

Forecast: 100 units ± 20 (80-120 range)
        ^
    Point estimate (best guess)

How Forecasting Models Work

Step 1: Learn Patterns

The model examines historical data to find patterns:

Input: [100, 105, 110, 115, 120, 125, 130, 135, 140, 145]

Model discovers:
- Trend: +5 per day
- Seasonality: None visible
- Noise: Low

Step 2: Project Forward

The model extends patterns into the future:

Pattern: +5 per day
Last value: 145

Day 11: 145 + 5 = 150
Day 12: 150 + 5 = 155
Day 13: 155 + 5 = 160

Step 3: Add Uncertainty

Models estimate prediction intervals (ranges):

Day 11 forecast: 150
95% prediction interval: 140-160
(95% confident actual value falls in this range)

Types of Forecasting Models

1. Naive Models (Baseline)

Predict the same as yesterday or same as last year.

-- Last value
Forecast = Last Value
Example: Yesterday's sales = 145, so forecast today = 145

-- Seasonal naive
Forecast = Same day last year
Example: Dec 1st last year = 500 units, so forecast this Dec 1st = 500

Pros: Simple, fast, no parameters Cons: Ignores trends, can be inaccurate

2. Statistical Models (Traditional)

Learn mathematical relationships between past and future.

Exponential Smoothing (ETS)

Gives more weight to recent data.

Recent data: ███ (heavy weight)
Old data:    ▓   (light weight)

Forecast = Weighted average of history

Best for: Trending data with seasonality Examples: AutoETS, Holt-Winters

ARIMA (AutoRegressive Integrated Moving Average)

Uses past values and errors to predict future.

Forecast = f(Past Values) + f(Past Errors)

Best for: Data with clear trends or seasonal patterns Examples: ARIMA, AutoARIMA

Theta

Simple, effective model that decomposes time series.

Forecast = Trend Line + Seasonal Pattern

Best for: Short-term forecasts, stable data

3. Advanced Models (Complex)

Use sophisticated techniques for complex patterns.

TBATS (Trigonometric seasonality, Box-Cox transformation, ARMA errors, Trend, Seasonal components)

Handles multiple seasonal periods.

Data with:
- Daily seasonality (24 hours)
- Weekly seasonality (7 days)
- Yearly seasonality (365 days)

Model captures all three

Best for: Data with multiple seasonal patterns

MFLES (Median-based Feature-Logic-Expert System)

Combines statistical and feature-based approaches.

Best for: Real-world messy data, outliers, multiple patterns

4. Machine Learning Models (Data-driven)

Learn complex non-linear relationships.

Requires: Feature engineering, more data

Best for: Large datasets with complex patterns

Choosing a Model: Decision Tree

Start: What model should I use?
    |
    ├─ Do I have seasonality? (weekly, yearly patterns)
    |   |
    |   ├─ YES → Seasonality is strong?
    |   |         ├─ YES, single seasonality → AutoETS or ETS
    |   |         └─ YES, multiple seasonality → TBATS or MSTL
    |   |
    |   └─ NO → Is data trending?
    |           ├─ YES → AutoARIMA
    |           └─ NO → Theta or SeasonalNaive
    |
    └─ Data quality issues? (outliers, gaps)
        ├─ YES → MFLES (robust to outliers)
        └─ NO → AutoETS or AutoARIMA

Key Forecasting Concepts

Forecast Horizon

How far ahead you're predicting.

Forecast horizon = 7 days
Today: Jan 15
Forecast for: Jan 16-22

Longer horizon = More uncertainty

Seasonal Period

How often patterns repeat.

Data Type	Seasonal Period	Example
Daily	7	Week repeats every 7 days
Hourly	24	Day repeats every 24 hours
Monthly	12	Year repeats every 12 months

Prediction Interval

Range of likely future values.

Point forecast: 100 units
80% interval: 90-110 (likely range)
95% interval: 80-120 (wider range, more conservative)
99% interval: 70-130 (very wide range)

Higher confidence level → Wider interval

Backtesting

Testing model on historical data before deployment.

Training data: Jan-Sep (use to fit model)
Test data: Oct-Dec (use to validate)

Process:
1. Fit model on Jan-Sep
2. Forecast Oct-Dec
3. Compare forecast vs actual Oct-Dec
4. Calculate accuracy metrics

Forecast Accuracy Metrics

How do you know if a forecast is good?

MAE (Mean Absolute Error)

Average difference between forecast and actual.

Forecasts: [100, 102, 98]
Actuals:   [105, 100, 99]
Errors:    [5, 2, 1]

MAE = (5+2+1)/3 = 2.67

Interpretation: Forecast is off by ~2.67 on average Lower is better

RMSE (Root Mean Squared Error)

Average error, penalizing large errors more.

Emphasizes big mistakes more than MAE
Good for when you want to avoid large errors

Lower is better

MAPE (Mean Absolute Percentage Error)

Percentage error relative to actual values.

MAPE = 3% means forecast is off by 3% on average
Good for comparing across different scales

Lower is better

Common Forecasting Pitfalls

❌ Not Enough Data

Problem: With only 2 weeks of data, hard to detect weekly seasonality Solution: Collect at least 2 full seasonal cycles

❌ Wrong Seasonal Period

Problem: Setting seasonal_period=30 for daily data (should be 7 for weekly) Solution: Test different periods or use seasonality detection

❌ Forecasting Too Far Ahead

Problem: Forecasting 12 months when data is daily/hourly Solution: Keep horizon reasonable (2x the seasonal period maximum)

❌ Trusting Single Forecast

Problem: Using one forecast without checking prediction intervals Solution: Always examine prediction intervals and test multiple models

❌ Ignoring Data Changes

Problem: Using old model after market/business change Solution: Retrain regularly (weekly/monthly) to capture new patterns

Forecasting Workflow

1. Data Collection & Preparation
   ↓
2. Exploratory Analysis (detect seasonality, trends)
   ↓
3. Train/Test Split
   ↓
4. Model Selection & Training
   ↓
5. Evaluation (MAE, RMSE, MAPE)
   ↓
6. Model Comparison
   ↓
7. Choose Best Model
   ↓
8. Deploy to Production
   ↓
9. Monitor & Retrain

Quick Reference

Concept	Definition	Example
Time Series	Sequential data measured over time	Daily sales, hourly temperature
Trend	Long-term direction	Sales increasing 5% per year
Seasonality	Repeating patterns	Sales spike in December
Forecast Horizon	How far ahead to predict	30-day forecast
Model	Algorithm that learns patterns	ARIMA, ETS, Theta
Training	Fitting model to historical data	Use Jan-Sep data
Backtesting	Testing on held-out historical data	Use Oct-Dec to test
Prediction Interval	Range of likely future values	90-110 with 95% confidence

Next Steps

Seasonality Detection — Detect patterns in your data
Choosing a Model — Select the right algorithm
Data Preparation — Clean your data
Basic Workflow — Run a complete example

Key Takeaways

✅ Time series = Data measured over time with patterns
✅ Forecasting = Predicting future based on historical patterns
✅ Models learn trends and seasonality from past
✅ Accuracy measured with MAE, RMSE, MAPE
✅ Multiple models available for different situations
✅ Always backtest before deployment

What is a Time Series?​

Real-World Examples​

Components of a Time Series​

Understanding Each Component​

Trend​

Seasonality​

Residual (Noise)​

What is Forecasting?​

The Forecasting Problem​

Simple Forecasting Example​

Why Is Forecasting Hard?​

Challenge 1: Multiple Patterns​

Challenge 2: Changing Patterns​

Challenge 3: Limited History​

Challenge 4: Uncertainty​

How Forecasting Models Work​

Step 1: Learn Patterns​

Step 2: Project Forward​

Step 3: Add Uncertainty​

Types of Forecasting Models​

1. Naive Models (Baseline)​

2. Statistical Models (Traditional)​

Exponential Smoothing (ETS)​

ARIMA (AutoRegressive Integrated Moving Average)​

Theta​

3. Advanced Models (Complex)​

TBATS (Trigonometric seasonality, Box-Cox transformation, ARMA errors, Trend, Seasonal components)​

MFLES (Median-based Feature-Logic-Expert System)​

4. Machine Learning Models (Data-driven)​

Choosing a Model: Decision Tree​

Key Forecasting Concepts​

Forecast Horizon​

Seasonal Period​

Prediction Interval​

Backtesting​

Forecast Accuracy Metrics​

MAE (Mean Absolute Error)​

RMSE (Root Mean Squared Error)​

MAPE (Mean Absolute Percentage Error)​

Common Forecasting Pitfalls​

❌ Not Enough Data​

❌ Wrong Seasonal Period​

❌ Forecasting Too Far Ahead​

❌ Trusting Single Forecast​

❌ Ignoring Data Changes​

Forecasting Workflow​

Quick Reference​

Next Steps​

Key Takeaways​