Analysis of Time Series

Components of Time Series

Definition:

A time series is a sequence of data points recorded at successive points in time. Common examples include monthly industrial production statistics, annual birth rates, and daily sales records.

Components of Time Series: 

Time series data can be decomposed into four main components:

1. Secular Trend (T):
   • This represents the long-term movement or direction in the data over a period of time, showing a general increase or decrease.
   • Examples include a steady growth in population or a gradual decline in manufacturing output.
2. Seasonal Variations (S):
   • These are periodic fluctuations that occur at regular intervals due to seasonal factors like weather, holidays, or customs.
   • Examples include higher retail sales during the festive season or increased agricultural output during the harvest season.
3. Cyclical Movements (C):
   • These are long-term oscillations around the trend line, often tied to the broader economic or business cycle, which include phases like expansion, recession, and recovery.
   • Unlike seasonal variations, cyclical movements do not occur at fixed intervals.
   • Examples include economic booms and busts.
4. Irregular Variations (I):
   • These are random or unpredictable fluctuations caused by unusual or unexpected events like natural disasters, wars, or sudden market crashes.
   • Examples include the impact of a major earthquake or a sudden financial crisis.

Mathematical Models:

Time series analysis often employs two main models to represent the data:

1. Multiplicative Model:
   • Assumes that the components multiply together to give the observed value. $O=T\times S\times C\times I$
2. Additive Model:
   • Assumes that the components add together to give the observed value. $O=T+S+C+I$

Importance of Decomposition:

• Analysis: Understanding the individual components helps in analyzing the underlying patterns and trends in the data.
• Forecasting: It aids in making more accurate forecasts by isolating and predicting each component separately.
• Business Planning: Helps businesses in planning and decision-making by anticipating seasonal demand, managing resources, and preparing for cyclical changes.

Additional Information:

Applications:

• Finance: Analyzing stock prices or economic indicators to make investment decisions.
• Retail: Forecasting sales and managing inventory based on seasonal trends.
• Agriculture: Planning crop production and marketing strategies according to seasonal patterns and long-term trends.

Time Series Analysis: Concept, Additive and Multiplicative Models

Concept of Time Series:

• Definition: A time series is a sequence of data points collected or recorded at successive time intervals. Examples include daily stock prices, monthly rainfall, and annual GDP growth rates.
• Applications: Used in various fields such as finance, economics, weather forecasting, engineering, and more.
• Visualization: Often plotted using line charts to identify trends, seasonal patterns, and other characteristics.

Time Series Analysis:

• Purpose: To analyze time series data to extract meaningful statistics, identify patterns, and forecast future values.
• Distinction: Unlike cross-sectional studies or spatial data analysis, time series analysis focuses on temporal ordering and the relationships between observations over time.