The document discusses time series analysis using secular or linear trend models. It describes time series data as observations recorded at regular time intervals that can be analyzed to forecast or predict future periods based on patterns from previous periods. It outlines different types of secular trend models including free hand curve, semi-average, moving average, and least squares methods. These models analyze long-term trends in time series data to make predictions.

1. Time Series Analysis by Using
Secular or Linear Trend Model
Presenter : Aamna Aamir
Roll #: 22011708-002
Subject: Advanced Quantitative Techniques
M.phil 1St Semester
Department of Geography

3. Time Series Analysis
• Time series data: data or observation recorded at regular time
intervals.
• Analysis of any variable measured “over time” called Time Series
Analysis.
• Time series is looking at the data overtime to FORECAST OR PREDICT
what will happen in the nest time period base on:
• Patterns and Recurring trends from previous time periods.
• E.g. Weather Data
• Seasonal sales revenue

4. Types of Secular or Linear Trend Model

5. Time Series Analysis
• e.g.
• Earning of a Firm We can say that Earning depends on:
• Sale
• Consumer Price Index
• GDP etc.

6. Time Series Analysis
• Similarly, Human Induced Activities can alter the climate:
• Fossil Fuels
• Aerosols
• GHG’s
• Ozone Molecules etc.

7. Time Series Analysis
• We can say in January 2023 the Sale was 88% and then Predict for
February 2023.
• Likewise, We can say in January 2023 the GHG’s Emission was 78%
and then Predict for February 2023.
• In Time Series (T.S) Model we look at the particular period of time.
• In T.S we take Variable depending on time.

8. Why Time Series Model different from other
Types Predictive Models
• T.S is based on Given time, and sequence of Observation over time.
• Normally, we could look at the a trend on a graph and take an
educated guess that ”Trend” will probably continue.
• Whereas, in T.S Forecast: can give us a better estimated figure for
how much Time it would continue.
• Example: “ within a specific period of time T.S Model Predicts
100,000 people to Login online ”
• “Prediction is based on Given time.”

9. Components of Time Series
• Secular Trend / Linear Trend
• Cyclic Variation Trend
• Seasonal Variation Trend
• Irregular Variation Trend

10. Components of Time Series

11. Secular Trend

12. Secular Linear Trend
25%

13. Secular / Non-Linear Trend

14. Cyclic Variation Trend

15. Seasonal Variation Trend

16. Irregular Variation Trend

17. Secular Trend / Linear Trend / Long Term Trend

18. Time Series Analysis
• Example:
• Sales of a Firm Vs.
• Germicide into Bacterial Culture (took 40 Observations in 8 minutes)

20. Types of Secular or Linear Trend Model
• Free Hand Curve method
• Semi Average Method
• Moving Average method
• Least Square Method

21. Types of Secular or Linear Trend Model

23. Draw Free Handily Straight
Line which Passes through the
Middle of our Actual Data

24. Draw Free Handily Straight
Line which Passes through the
Middle of our Actual Data

25. Free Hand Curve
• Limitation:
• Different people may have different trend Line due to Free Hand way.

27. Entire Data set Divided into 2 Equal Parts
Sum Average

31. Semi Average Graphic method
• Benefit:
• Everyone would have same trend line.
• But data odd then ignore central / Middle value.
• And make groups of remaining data.

32. If Total “ODD” numbers

35. Moving Average Method
• Make group and then find average.
• Series of data may be of odd or even nature.

36. Make combination of “Three” numbers
Sum
Where to write Average in font of
Middle year

38. Least Square Method
• Formula
• Y= Dependent Variable
• X= independent variable
• a= alpha
• b= Beta (co-efficient of X)