Textbook

1. Goals and decisions of an organization

2. The market system

3. The domestic economy

4. Macroeconomics – The international economy

5. Macroeconomics – Index numbers

6. Introduction to the financial context of business entities

7. Foreign currencies

8. Investment appraisal

9. Summarizing and analyzing data

10. Inter-relationships between variables

11. Time series model

11.1 Fundamentals of time series model

11.2 Trendline calculation methods

11.3 Seasonal variation and forecasting methods

Wrapping up

11.2 Trendline calculation methods

CGMA BA1

11. Time series model

Our CGMA course is currently in development and is a work-in-progress.

Trendline calculation methods

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Calculating trendline

There are two methods used to calculate the trendline:

linear regression
moving average

Linear regression

You’ve already explored this formula in the previous chapter:

$Y = a + b x$

If you don’t remember how to use it, review the previous chapter before continuing.

Example 1

KTA is forecasting its sales using the trendline formula:
$Y = 2000 + 20 x$ , where $x$ represents the period number in months. January 2024 is period 1 and December 2024 is period 12. What is the forecasted trend for December 2025?

Solution

(spoiler)

December 2025 is period 24.

$Y Y = 2000 + 20 (24) = 2480$

The trend for December 2025 is $2,480.

The moving average

To understand this better, let us use an example.

Example 2

KTA has the following sales data from the past 3 years.

Year	Quarter	Sales
2022	Q1	1,020
	Q2	1,300
	Q3	1,100
	Q4	1,400
2023	Q1	1,400
	Q2	1,900
	Q3	1,700
	Q4	2,150
2024	Q1	1,700
	Q2	2,500
	Q3	2,100
	Q4	2,790

Solution

(spoiler)

Year	Quarter	Sales	Four-quarter total	8-quarter total	Trend
2022	Q1	1,020
	Q2	1,300		4,820
	Q3	1,100	5,200	10,020	1,252.5
	Q4	1,400	5,800	11,000	1,375
2023	Q1	1,400	6,400	12,200	1,525
	Q2	1,900	7,150	13,550	1,693.75
	Q3	1,700	7,450	14,600	1,825
	Q4	2,150	8,050	15,500	1,937.5
2024	Q1	1,700	8,450	16,500	2,062.5
	Q2	2,500	9,090	17,540	2,192.5

Four-quarter total: Add four consecutive quarters (for example, Q1 to Q4) and place the result in the middle of those four quarters (between Q2 and Q3). Repeat for the next set of four quarters (Q2 to Q5) and place that total between Q3 and Q4.

8-quarter total: Add two consecutive four-quarter totals and place the result as shown in the table. For example:

$4, 820 + 5, 200 5, 200 + 5, 800 = 10, 020 = 11, 000$

Trend: Divide the 8-quarter total by 8. For example:

$10, 020 \div 8 = 1, 252.5 (trend for Q3 2022)$

The examiner will not require you to complete the full table. Instead, you may be asked to fill in missing values or identify the trend for a specific season.

Calculating trendline

Two main methods: linear regression and moving average
Linear regression formula: $Y = a + b x$
Moving average: averages over set periods to smooth data

Linear regression

Uses formula $Y = a + b x$ to forecast future values
$x$ = period number (e.g., months or quarters)
Example: For period 24, $Y = 2000 + 20 (24) = 2480$

Moving average

Sums sales over consecutive periods (e.g., 4 quarters), places total between periods
8-quarter totals: sum two consecutive 4-quarter totals, divide by 8 for trend
Used to identify underlying trend by smoothing out fluctuations

Seasonal variations

Two models: multiplicative ( $S = Y / T$ ) and additive ( $S = Y - T$ )
Multiplicative: seasonal factors should sum to number of periods (e.g., 4 for quarters)
- Adjust factors equally if sum ≠ 4
Additive: seasonal factors should sum to zero
- Adjust averages equally if sum ≠ 0

Calculating seasonal variation (multiplicative model)

$S = Y / T$ for each period
Average each quarter’s factors across years
Adjust so total equals number of periods (e.g., 4 for quarters)
Forecast: $Y = T \times S$

Calculating seasonal variation (additive model)

$S = Y - T$ for each period
Average each quarter’s values across years
Adjust so total equals zero
Forecast: $Y = T + S$

Seasonally adjusted figures

Multiplicative: $T = Y / S$
Additive: $T = Y - S$
Seasonally adjusted = trend value (removes seasonal effects)

Choosing model

Use multiplicative if seasonal factor is a multiplier
Use additive if seasonal factor is a real value (added/subtracted)
Exam questions may specify which model to use or provide clues based on data format

Next | 11.3 Seasonal variation and forecasting methods

Trendline calculation methods

Calculating trendline

There are two methods used to calculate the trendline:

linear regression
moving average

Linear regression

You’ve already explored this formula in the previous chapter:

$Y = a + b x$

If you don’t remember how to use it, review the previous chapter before continuing.

Example 1

KTA is forecasting its sales using the trendline formula:
$Y = 2000 + 20 x$ , where $x$ represents the period number in months. January 2024 is period 1 and December 2024 is period 12. What is the forecasted trend for December 2025?

Solution

(spoiler)

December 2025 is period 24.

$Y Y = 2000 + 20 (24) = 2480$

The trend for December 2025 is $2,480.

The moving average

To understand this better, let us use an example.

Example 2

KTA has the following sales data from the past 3 years.

Year	Quarter	Sales
2022	Q1	1,020
	Q2	1,300
	Q3	1,100
	Q4	1,400
2023	Q1	1,400
	Q2	1,900
	Q3	1,700
	Q4	2,150
2024	Q1	1,700
	Q2	2,500
	Q3	2,100
	Q4	2,790

Solution

(spoiler)

Year	Quarter	Sales	Four-quarter total	8-quarter total	Trend
2022	Q1	1,020
	Q2	1,300		4,820
	Q3	1,100	5,200	10,020	1,252.5
	Q4	1,400	5,800	11,000	1,375
2023	Q1	1,400	6,400	12,200	1,525
	Q2	1,900	7,150	13,550	1,693.75
	Q3	1,700	7,450	14,600	1,825
	Q4	2,150	8,050	15,500	1,937.5
2024	Q1	1,700	8,450	16,500	2,062.5
	Q2	2,500	9,090	17,540	2,192.5

8-quarter total: Add two consecutive four-quarter totals and place the result as shown in the table. For example:

$4, 820 + 5, 200 5, 200 + 5, 800 = 10, 020 = 11, 000$

Trend: Divide the 8-quarter total by 8. For example:

$10, 020 \div 8 = 1, 252.5 (trend for Q3 2022)$

The examiner will not require you to complete the full table. Instead, you may be asked to fill in missing values or identify the trend for a specific season.

CGMA BA1

11. Time series model

Our CGMA course is currently in development and is a work-in-progress.

Trendline calculation methods

3 min read

Font

Discuss

Feedback

Calculating trendline

There are two methods used to calculate the trendline:

linear regression
moving average

Linear regression

You’ve already explored this formula in the previous chapter:

$Y = a + b x$

If you don’t remember how to use it, review the previous chapter before continuing.

Example 1

KTA is forecasting its sales using the trendline formula:
$Y = 2000 + 20 x$ , where $x$ represents the period number in months. January 2024 is period 1 and December 2024 is period 12. What is the forecasted trend for December 2025?

Solution

(spoiler)

December 2025 is period 24.

$Y Y = 2000 + 20 (24) = 2480$

The trend for December 2025 is $2,480.

The moving average

To understand this better, let us use an example.

Example 2

KTA has the following sales data from the past 3 years.

Year	Quarter	Sales
2022	Q1	1,020
	Q2	1,300
	Q3	1,100
	Q4	1,400
2023	Q1	1,400
	Q2	1,900
	Q3	1,700
	Q4	2,150
2024	Q1	1,700
	Q2	2,500
	Q3	2,100
	Q4	2,790

Solution

(spoiler)

Year	Quarter	Sales	Four-quarter total	8-quarter total	Trend
2022	Q1	1,020
	Q2	1,300		4,820
	Q3	1,100	5,200	10,020	1,252.5
	Q4	1,400	5,800	11,000	1,375
2023	Q1	1,400	6,400	12,200	1,525
	Q2	1,900	7,150	13,550	1,693.75
	Q3	1,700	7,450	14,600	1,825
	Q4	2,150	8,050	15,500	1,937.5
2024	Q1	1,700	8,450	16,500	2,062.5
	Q2	2,500	9,090	17,540	2,192.5

8-quarter total: Add two consecutive four-quarter totals and place the result as shown in the table. For example:

$4, 820 + 5, 200 5, 200 + 5, 800 = 10, 020 = 11, 000$

Trend: Divide the 8-quarter total by 8. For example:

$10, 020 \div 8 = 1, 252.5 (trend for Q3 2022)$

The examiner will not require you to complete the full table. Instead, you may be asked to fill in missing values or identify the trend for a specific season.

Calculating trendline

Two main methods: linear regression and moving average
Linear regression formula: $Y = a + b x$
Moving average: averages over set periods to smooth data

Linear regression

Uses formula $Y = a + b x$ to forecast future values
$x$ = period number (e.g., months or quarters)
Example: For period 24, $Y = 2000 + 20 (24) = 2480$

Moving average

Sums sales over consecutive periods (e.g., 4 quarters), places total between periods
8-quarter totals: sum two consecutive 4-quarter totals, divide by 8 for trend
Used to identify underlying trend by smoothing out fluctuations

Seasonal variations

Two models: multiplicative ( $S = Y / T$ ) and additive ( $S = Y - T$ )
Multiplicative: seasonal factors should sum to number of periods (e.g., 4 for quarters)
- Adjust factors equally if sum ≠ 4
Additive: seasonal factors should sum to zero
- Adjust averages equally if sum ≠ 0

Calculating seasonal variation (multiplicative model)

$S = Y / T$ for each period
Average each quarter’s factors across years
Adjust so total equals number of periods (e.g., 4 for quarters)
Forecast: $Y = T \times S$

Calculating seasonal variation (additive model)

$S = Y - T$ for each period
Average each quarter’s values across years
Adjust so total equals zero
Forecast: $Y = T + S$

Seasonally adjusted figures

Multiplicative: $T = Y / S$
Additive: $T = Y - S$
Seasonally adjusted = trend value (removes seasonal effects)

Choosing model

Use multiplicative if seasonal factor is a multiplier
Use additive if seasonal factor is a real value (added/subtracted)
Exam questions may specify which model to use or provide clues based on data format

Next | 11.3 Seasonal variation and forecasting methods

Trendline calculation methods

Calculating trendline

There are two methods used to calculate the trendline:

linear regression
moving average

Linear regression

You’ve already explored this formula in the previous chapter:

$Y = a + b x$

If you don’t remember how to use it, review the previous chapter before continuing.

Example 1

KTA is forecasting its sales using the trendline formula:
$Y = 2000 + 20 x$ , where $x$ represents the period number in months. January 2024 is period 1 and December 2024 is period 12. What is the forecasted trend for December 2025?

Solution

(spoiler)

December 2025 is period 24.

$Y Y = 2000 + 20 (24) = 2480$

The trend for December 2025 is $2,480.

The moving average

To understand this better, let us use an example.

Example 2

KTA has the following sales data from the past 3 years.

Year	Quarter	Sales
2022	Q1	1,020
	Q2	1,300
	Q3	1,100
	Q4	1,400
2023	Q1	1,400
	Q2	1,900
	Q3	1,700
	Q4	2,150
2024	Q1	1,700
	Q2	2,500
	Q3	2,100
	Q4	2,790

Solution

(spoiler)

Year	Quarter	Sales	Four-quarter total	8-quarter total	Trend
2022	Q1	1,020
	Q2	1,300		4,820
	Q3	1,100	5,200	10,020	1,252.5
	Q4	1,400	5,800	11,000	1,375
2023	Q1	1,400	6,400	12,200	1,525
	Q2	1,900	7,150	13,550	1,693.75
	Q3	1,700	7,450	14,600	1,825
	Q4	2,150	8,050	15,500	1,937.5
2024	Q1	1,700	8,450	16,500	2,062.5
	Q2	2,500	9,090	17,540	2,192.5

8-quarter total: Add two consecutive four-quarter totals and place the result as shown in the table. For example:

$4, 820 + 5, 200 5, 200 + 5, 800 = 10, 020 = 11, 000$

Trend: Divide the 8-quarter total by 8. For example:

$10, 020 \div 8 = 1, 252.5 (trend for Q3 2022)$

The examiner will not require you to complete the full table. Instead, you may be asked to fill in missing values or identify the trend for a specific season.