L1 Time Series Intro

Difference between
- \(X_{1},X_{2}\dots,X_{100}\) dice roll in 100 rounds (IID random)
- \(X_{1},X_{2}\dots,X_{100}\) closing prices of stock for 100 consecutive days (autocorrelated random)
What exactly is time series?
- Classical inference (IID¹)
- Time Series (Ordered by time, chronological)
- Thus, time series data is not independent!
Data Types
- Cross-sectional data
  - Different individuals
  - at a SINGLE POINT OF TIME
  - Eg.
    - Max humidity at 20 diff locations
    - 20 stocks ka closing price on a particular day
    - Heights of students, on a particular day
  - Several variables at a single point of time
- Time series data
  - For a particular individual/entity (fixed)
  - over DIFFERENT POINTS OF TIME
  - Eg. (transition the time point over a month)
    - Max HUMIDITY level for a month
    - Closing stock price of a (single) STOCK over 6 months
    - Quarterly student enrolment in a COLLEGE over 5 years.
  - Same variable over a period of time
- Panel/Longitudinal
  - Observations on different cross-sections over a time
  - E.g.
    - Annual cancer mortality rates of different Indian states during 2015-2023
      - Delhi, Jharkhand, Maharashtra…
      - for each of these 2015-2023
    - Yearly sales of 10 companies over 10 years
      - Multiple companies
      - Multiple years
Steps in Time Series Analysis
1. Plotting data
2. Study past behavior
3. Identify underlying patterns and trends²
4. Use past data for forecasting
Application Areas
- Retail stores → sales
- Energy company → reserves, production, demand, price
- Education → enrollment
- Intl. Fin Orgs (World Bank, IMF) → Inflation, econ activity
- Transportation → Future travel
- Banks → New home purchases

IID means, Identical observations (random variable) come from some distribution and Independent observations (doesn't depend on observations) ↩
Trend = upward or downward movement of an entity ↩