forecasting - statistical techniques

Question 1

What are the three main quantitative techniques used to improve budget accuracy?

Answer 1

The three techniques are:

• Time series analysis: identifies patterns over time to make future predictions.
• Linear regression: estimates relationships between variables.
• Index numbers: track relative changes over time, useful in comparing data points.

These methods help refine budgets by using historical data to make more accurate forecasts.

Question 2

What is a time series, and how can it help in budgeting?

Answer 2

A time series is a sequence of data points recorded over time, such as monthly sales over several years. By identifying patterns (e.g., trends or seasonal changes), we can make predictions about future performance.

Recognizing trends in a time series allows for more accurate forecasting, benefiting budget planning and adjustments.

Question 3

What are the four main components of a time series?

Answer 3

The four components are:

• Trend (T): long-term, consistent direction in data.
• Seasonal Variation (SV): short-term, recurring fluctuations (e.g., high summer ice cream sales).
• Cyclical Variation (CV): long-term fluctuations related to economic cycles.
• Random Variation (RV): unpredictable changes due to events like natural disasters.

Understanding each component allows us to separate predictable patterns from random events when forecasting.

Question 4

How is the additive model used in time series forecasting?

Answer 4

The additive model combines the trend and seasonal variation by addition:

• Formula: TS = T + SV
• A positive SV means sales are typically above the trend in that period; a negative SV means sales are typically below the trend.
• Example: If the trend for sales in Q2 is 10,000 and SV is -200, the forecast is:
  TS = 10,000 - 200 = 9,800.

The additive model is useful when the trend and seasonal impacts are linear

Question 5

How is the multiplicative model applied in forecasting?

Answer 5

The multiplicative model combines the trend and seasonal variation by multiplication:

• Formula: TS = T × SV
• Seasonal variation is a percentage or fraction of the trend; values above 100% mean higher-than-trend, and values below 100% mean lower-than-trend.
• Example: If the trend is £12,000 and SV for Q3 is 120% (or 1.2), forecasted sales are: TS = 12,000 × 1.2 = 14,400.

The multiplicative model is ideal for situations where the trend and seasonal impacts are proportional.

Question 6

How can a time series graph aid in forecasting?

Answer 6

A time series graph plots historical data, showing both the trend (as a straight line) and seasonal variations (as fluctuations). It helps visualize patterns and seasonal cycles, supporting better future projections.

Example: If sales increase yearly, with Q1 always lowest and Q4 highest, the graph shows a rising trend with predictable seasonal lows and highs.

Visualizing data trends on a graph enhances forecasting accuracy by making patterns clearer.

Question 7

What is the purpose of de-seasonalizing data?

Answer 7

De-seasonalizing removes seasonal variations to isolate the underlying trend. This helps in understanding the consistent direction of data without seasonal impacts.

Question 8

How is the trend calculated in de-seasonalizing with a multiplicative model?

Answer 8

For the multiplicative model:

• Formula: T = TS/SV
• Example: If sales (TS) are £120,000 in January, and January’s SV is 120%, then: T = £120,000/1.2 = £100,000

Question 9

How do you de-seasonalize data using the additive model?

Answer 9

In the additive model, subtract the seasonal variation from the time series to find the trend.

• Formula: T = TS - SV
• Example: If Sales (TS) are £140,000 in February and SV is +£15,000, then: T = £140,000-£15,000 = £125,000

Question 10

How do moving averages help in identifying trends in time series data?

Answer 10

Moving averages smooth out short-term seasonal variations, revealing the underlying trend by averaging data points over a set period.

Question 11

How do you calculate a 3-period moving average?

Answer 11

Average three consecutive data points:
* Example: For data values 120,74, and 55: 120+74+55/3 = 83

Place the average alongside the middle data point in the period.

Question 12

How do you calculate the trend increase per period?

Answer 12

Find the difference in trend values over a number of periods and divide by the number of steps.
* Example: From Tuesday week 1 (83) to Tuesday week 3 (107) over 6 steps: 107-83/6 = 4

Question 13

How do you calculate seasonal variation for a period?

Answer 13

Subtract the trend from the time series (TS) value for that period. A positive result indicates above-trend performance; a negative result indicates below-trend.
* Example: If TS is 74 and trend (T) is 83, then: SV = 74-83 = -9

Question 14

How do you calculate the average seasonal variation for each day?

Answer 14

Add the seasonal variations across periods for each day, then divide by the number of periods.

Question 15

How do you forecast future values using the trend and seasonal variation?

Answer 15

Extend the trend, then add the average seasonal variation.

• Example: If the last trend is 107 and the increase per day is 4, then for 2 periods ahead: Trend = 107+(24) = 115
• Adding seasonal variation for Monday (+41): TS = 115

Question 16

How do you calculate forecast sales revenue per quarter using seasonal variations?

Answer 16

Adjust the total sales forecast by seasonal variation.

• Example: Last year’s sales were £720,000 with a 12% growth rate, so next year’s total = £720,000 x 1.12 = £806,400.

Question 17

What is linear regression, or the method of least squares, used for in forecasting?

Answer 17

Linear regression is used to forecast future costs or sales based on historical data, assuming a linear relationship between variables (e.g., as production output increases, so do production costs).

Question 18

How is the “line of best fit” determined in linear regression?

Answer 18

The line of best fit is the line that best represents the relationship between variables on a graph. It’s expressed as the regression equation y = a + bx.

Question 19

In the regression equation y = a + bx, what do each of the variables represent?

Answer 19

• y: Total costs (on the y-axis).
• x: Volume of production output (on the x-axis).
• a: Fixed cost, where the line intersects the y-axis.
• b: Variable cost per unit, or the slope of the line.

Example: If a = £20,000 and b = £5, then for 1,000 units:
Total cost = 20,000 + (5 × 1,000) = £25,000 = 20,000 + (5 × 1,000) = £25,000.

Question 20

What are some limitations of using historical data to forecast trends?

Answer 20

• Observations may not reflect typical behavior, especially if they are limited.
• Assumes a linear relationship, which may not always be accurate.
• Predictions outside data range are less reliable.
• External factors (e.g., inflation) can impact results beyond the linear trend.

Question 21

How is an Expected Value (EV) calculated?

Answer 21

EV is the weighted average of possible outcomes, calculated by multiplying each outcome by its probability and summing the results (∑px).

Question 22

What are limitations of using Expected Value in decision-making?

Answer 22

• EV is less relevant in one-off situations, as it reflects a long-run average.
• It doesn’t consider the spread or risk of outcomes.
• The reliability of EV depends on accurate probabilities.

Question 23

What does sensitivity analysis assess?

Answer 23

Sensitivity analysis determines how changes in variables (e.g., costs or revenues) impact a decision, often calculating the maximum change allowed before profitability is affected.

Question 24

How is the sensitivity percentage calculated?

Answer 24

Sensitivity % = Profit level/Variable (Revenue or Cost) x 100%

Question 25

What is the purpose of index numbers?

Answer 25

Index numbers measure changes in value or volume over time, making it easier to track relative changes (e.g., inflation or stock indices).

Question 26

How is an index number calculated for a period?

Answer 26

Formula: Currentperiodfigure x 100/Base period figure

Question 27

How can real wages be calculated to adjust for inflation?

Answer 27

Real Wage = Weekly Wage x Base Year Index/Current Year Index

Example: For a wage of £153 in 2011 with an RPI increase from 100 to 102: Real Wage = 153 x 100/102 = £150

Question 28

What methods help manage uncertainty in forecasting?

Answer 28

• Flexible Budgets: Prepare budgets for different activity levels.
• Rolling Budgets: Regularly update budgets to adjust for changing conditions.
• Planning Models: Use software to predict a range of outcomes.

Question 29

What are the stages of the product life cycle?

Answer 29

1. Development: High costs, no revenue.
2. Introduction: Low revenue, high marketing costs.
3. Growth: Rapid sales growth, lower production costs.
4. Maturity: High sales, competitive pressure, highest profits.
5. Decline: Falling demand, reduced market share.

Forecasts should adjust based on the life cycle stage, anticipating slower growth or decline as the product matures

Question 30

What factors affect the reliability of forecasts?

Answer 30

• Data Volume: More data improves reliability.
• Data Quality: Reliable, consistent data improves accuracy.
• Unexpected Events: These can disrupt forecasts and assumptions.