Time Series Problems 🧮

Here we will solve numerical problems covering Trend Analysis and Seasonal Variations.

Problem 1: Least Squares Method (Trend)

Data: Values: 80, 90, 92, 83, 94, 99, 92 Years: 2010 to 2016 (7 Years)

Find:

1. The linear trend equation.
2. Estimate value for 2018.

Solution: Least Squares Trend Analysis 💡

Step 1: Mid Year N = 7 (Odd). Mid year is 2013. X = Year - 2013.

Step 2: Calculation Table

Step 3: Constants

• a = ∑ Y / N = 630 / 7 = 90
• b = ∑ XY / ∑ X² = 56 / 28 = 2

Step 4: Equation

Yc = 90 + 2X

Step 5: Estimate for 2018 X for 2018 = 2018 - 2013 = 5. Yc = 90 + 2(5) = 90 + 10 = 100.

Problem 2: 3-Year Moving Average

Data: 2, 4, 5, 7, 8, 10, 13

Find: Trend values.

Solution: 3-Year Moving Average Calculation 💡

Problem 3: Sales Forecasting

If the seasonal index for Q4 is 150 and the desaeasonalised trend value for Q4 2024 is projected to be 2000 units, what will be the actual sales?

Solution: Sales Forecast Calculation 💡

We know: Deseasonalised = (Actual / SI) * 100 Therefore: Actual = (Deseasonalised * SI) / 100

Calculation: Actual Sales = (2000 * 150) / 100 Actual Sales = 3000 Units

Summary of Use Cases

1. Least Squares: Best for long term trend projection.
2. Moving Averages: Best for understanding cycles.
3. Seasonal Indices: Refining forecasts for specific months/quarters.