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Introduction to Time Series ⏳

A Time Series is a set of statistical observations arranged in chronological order. Examples:

  • Population of India from 1950 to 2024.
  • Daily closing price of a Stock.
  • Annual rainfall in a city for the last 10 years.

Importance of Time Series 🌟

  1. Understanding Past Behavior: It helps in analyzing how a variable has behaved in the past.
  2. Forecasting: The main objective is to predict future values based on past trends.
  3. Evaluation of Performance: Comparing actual performance with expected performance.
  4. Planning: Essential for business budgeting and policy making.

Components of Time Series 🧩

There are four main components that affect a time series.

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1. Secular Trend (T) 📈

The general tendency of the data to increase or decrease over a long period.

  • Example: Population growth, increase in literacy rate, decline in death rate.
  • It is smooth, regular, and long-term.

2. Seasonal Variations (S) 🌤️

Short-term fluctuations that repeat in a regular pattern typically within a year.

  • Example: Sales of umbrellas in monsoon, woolens in winter, ice-creams in summer.
  • Caused by climate, festivals, and customs.

3. Cyclical Variations (C) 🔄

Long-term oscillations occurring over a period of more than one year.

  • Example: Business Cycles (Boom, Recession, Depression, Recovery).
  • These are wave-like movements commonly found in economic and business data.

4. Irregular / Random Variations (I) 🎲

Unpredictable, accidental, or erratic changes.

  • Example: Stock market crash due to a war, sales drop due to a strike, flood, or earthquake.
  • These cannot be predicted.

Mathematical Models 📐

How do these components combine?

1. Additive Model

Used when components are independent.

Y = T + S + C + I

2. Multiplicative Model (Most Common)

Used when components are dependent on each other.

Y = T * S * C * I

Summary

  • Time Series = Data ordered by time.
  • Trend (T): Long-term direction.
  • Seasonal (S): predictable, short-term (< 1 year).
  • Cyclical (C): Wave-like, long-term (> 1 year).
  • Irregular (I): Random, unpredictable.

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