Time Series Fundamentals: Reading the Story of Time 📅
Imagine you’re a detective with a magical journal that records everything that happens, day by day. Time series is like reading that journal to understand patterns and predict what might happen tomorrow!
The One Big Idea 🎯
Time series is like watching a movie of numbers — instead of looking at a single photo, you see how things change over time. Just like you can predict the sun will rise tomorrow because it always has, time series helps us predict the future by learning from the past.
Time Series Concepts: What’s in Our Magical Journal?
What is a Time Series?
Think of your height measured every birthday. At age 5, you were this tall. At age 6, a bit taller. At age 7, even taller! That’s a time series — numbers recorded at regular time intervals.
Age 5 → 100 cm
Age 6 → 108 cm
Age 7 → 115 cm
Age 8 → 122 cm
Real Life Examples:
- Temperature every hour 🌡️
- Your heartbeat every second ❤️
- Ice cream sales every month 🍦
- Stock prices every day 📈
Why is Order Important?
Imagine shuffling the pages of your journal randomly. The story wouldn’t make sense! In time series, the order matters. Tuesday comes after Monday, and that sequence tells a story.
Trend Analysis: The Big Picture Story 📈
What is a Trend?
A trend is the general direction your numbers are heading over a long time — like a river flowing steadily in one direction.
Simple Example: Your savings account over 5 years:
- Year 1: $100
- Year 2: $150
- Year 3: $200
- Year 4: $250
- Year 5: $300
See how it keeps going UP? That’s an upward trend!
graph TD A["Year 1: $100"] --> B["Year 2: $150"] B --> C["Year 3: $200"] C --> D["Year 4: $250"] D --> E["Year 5: $300"] style E fill:#90EE90
Types of Trends
| Trend Type | What It Looks Like | Example |
|---|---|---|
| Upward | Going up ↗️ | World population |
| Downward | Going down ↘️ | CD sales |
| Flat | Staying same → | Body temperature |
Why Trends Matter
Finding the trend is like finding the main storyline in a messy book. It helps you see past the daily noise to understand what’s really happening.
Seasonality Analysis: The Repeating Dance 🔄
What is Seasonality?
Seasonality is when patterns repeat like clockwork — think of the seasons repeating every year!
Simple Example: Ice cream shop sales:
- Summer: HIGH 🔥
- Winter: LOW ❄️
- Summer: HIGH 🔥
- Winter: LOW ❄️
Every year, the same pattern repeats!
Finding the Pattern
Imagine a Ferris wheel going round and round:
graph TD A["January: Low"] --> B["April: Rising"] B --> C["July: Peak!"] C --> D["October: Falling"] D --> A
Real World Seasonality
| What | Seasonal Pattern |
|---|---|
| Umbrella sales | Peak in rainy season |
| Toy stores | Peak in December |
| Gym memberships | Peak in January |
| Beach visits | Peak in summer |
Seasonality vs Trend
- Trend: The river flowing one direction
- Seasonality: The waves going up and down as it flows
Both can happen at the same time! 🌊
Stationarity: When Things Stay Calm 🧘
What is Stationarity?
A stationary time series is like a calm lake — it might have small ripples, but the overall level stays the same. The water doesn’t gradually rise or fall.
Think of it this way:
- Stationary: Your resting heart rate (stays around 70 bpm)
- Non-stationary: A balloon being inflated (keeps getting bigger)
The Three Rules of Stationarity
For data to be “calm” (stationary), it needs:
- Same average over time — not trending up or down
- Same wiggliness over time — consistent spread
- Patterns don’t depend on when you look
Why Does This Matter?
Most time series tools work best with calm, stationary data. If your data is going wild, you first need to calm it down!
Making Data Stationary:
Wild data → Take differences → Calm data
Day 1: 10
Day 2: 12 → (12-10) = 2
Day 3: 15 → (15-12) = 3
Day 4: 17 → (17-15) = 2
Now instead of rising numbers, we have stable differences!
Autocorrelation: Talking to Your Past Self 🗣️
What is Autocorrelation?
Auto = self, Correlation = relationship
Autocorrelation asks: “Does today’s number relate to yesterday’s number?”
Simple Example: If it’s hot today, tomorrow is probably hot too. Today’s temperature is correlated with tomorrow’s!
Understanding Lags
A lag is how far back we look:
- Lag 1 = Yesterday
- Lag 7 = One week ago
- Lag 365 = One year ago
Today vs Yesterday (Lag 1):
Hot → Hot ✓ Related!
Today vs Last Week (Lag 7):
Hot → Cold ✗ Less related
Today vs Last Year Same Day (Lag 365):
Hot → Hot ✓ Related again!
Why Autocorrelation is Powerful
If we know data is related to its past, we can use the past to predict the future!
ACF and PACF Plots: The Detective’s Tools 🔍
ACF: Autocorrelation Function
ACF shows you how each lag is related to the current value. It’s like a report card showing which past days matter.
ACF Plot:
Lag 1: ████████░░ Strong!
Lag 2: ██████░░░░ Medium
Lag 3: ████░░░░░░ Weaker
Lag 4: ██░░░░░░░░ Weak
PACF: Partial Autocorrelation Function
PACF is sneakier — it shows the direct relationship only, removing the middle connections.
Think of it like this:
- ACF: “Your grandma affects you” (true, through your mom)
- PACF: “Your grandma affects you DIRECTLY” (just the direct link)
Reading the Plots
| Pattern | What It Means |
|---|---|
| Bars slowly shrinking | Data might have a trend |
| Bars cutting off suddenly | Useful for model selection |
| Bars at regular intervals | Seasonality present! |
Why Two Plots?
Together, ACF and PACF help you choose the right prediction model. They’re like two clues that solve the mystery!
ARIMA Models: The Crystal Ball 🔮
What is ARIMA?
ARIMA = AutoRegressive Integrated Moving Average
Don’t let the big name scare you! It’s made of three simple friends:
The Three Friends
AR (AutoRegressive) = Using past values
“Tomorrow’s weather depends on today’s weather”
I (Integrated) = Making data calm
“Take differences until data stops trending”
MA (Moving Average) = Using past mistakes
“Learn from yesterday’s prediction errors”
The Magic Formula: ARIMA(p, d, q)
Three numbers control everything:
| Letter | What It Does | How to Find It |
|---|---|---|
| p | How many past values to use | Look at PACF |
| d | How many times to calm data | Test stationarity |
| q | How many past errors to use | Look at ACF |
Simple Example
Imagine predicting tomorrow’s temperature:
ARIMA(1, 0, 1) means:
- Use 1 past day (p=1)
- Data is already calm (d=0)
- Use 1 past error (q=1)
Prediction:
Tomorrow = 0.8×(Today) + 0.3×(Yesterday's Error)
Choosing p, d, q
graph TD A["Is data stationary?"] -->|No| B["Take differences d=1"] A -->|Yes| C["d=0"] B --> D["Check ACF for q"] C --> D D --> E["Check PACF for p"] E --> F["Build ARIMA model!"] style F fill:#FFD700
Putting It All Together 🧩
The Complete Detective Process
- Look at your data — Plot it! See the story.
- Find the trend — Is it going up, down, or flat?
- Spot seasonality — Are there repeating patterns?
- Check stationarity — Is the data calm enough?
- Calculate autocorrelation — How does past relate to present?
- Use ACF/PACF — Get clues for your model
- Build ARIMA — Make predictions!
Real World Story
The Coffee Shop Example:
Your coffee shop tracks daily sales:
- Trend: Sales growing 5% yearly (business is booming!)
- Seasonality: Mondays are slow, Fridays are busy
- Stationarity: After removing trend + season, data is calm
- Autocorrelation: Today’s sales relate to yesterday’s
- ARIMA(1,1,1): Use this to predict next week’s sales!
Key Takeaways 🎯
| Concept | One-Line Summary |
|---|---|
| Time Series | Numbers recorded over time, order matters |
| Trend | The long-term direction (up/down/flat) |
| Seasonality | Repeating patterns (daily, weekly, yearly) |
| Stationarity | Data that stays “calm” with no trend |
| Autocorrelation | How past values relate to current value |
| ACF | Shows total correlation at each lag |
| PACF | Shows direct correlation only |
| ARIMA | Prediction model using AR + I + MA |
You’ve Got This! 🚀
Time series might seem complex, but remember:
- It’s just reading the story of numbers over time
- Patterns repeat — find them and you can predict!
- Start simple — look at your data before doing math
- Practice — every dataset has a story waiting to be discovered
You’re now ready to read the stories hidden in time! ⏰✨