Forecasting Methods Overview

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Questions and Answers

What is the primary purpose of Causal Models in forecasting?

To identify historical patterns for future predictions.

To establish a linear relationship between forecasts and influencing factors. (correct)

To analyze the competitive environment for similar services.

To interpret expert opinions on likely future events.

Which statement accurately describes Econometric Models?

They use simultaneous equations involving multiple independent variables. (correct)

They consist of one equation representing a dependent variable.

They are primarily used for short-term forecasts.

They require minimal data collection and analysis.

In Simple Linear Regression, what does the symbol $Y$ represent?

An independent variable influencing the forecast.

The dependent variable being predicted. (correct)

A hidden variable affecting the growth pattern.

The constant term in the regression equation.

What is a common use of Historical Analogy in forecasting?

To predict market penetration based on similar products. Signup and view all the answers

Which part of the regression equation $Y = a_0 + a_1 X_1 + a_2 X_2 + ... + a_n X_n$ is $a_0$?

The intercept of the regression line. Signup and view all the answers

What is a major limitation of using Historical Analogy for forecasting?

It assumes future patterns will be identical to past patterns. Signup and view all the answers

What do Econometric Models require for accurate forecasting?

Advanced data collection and sophisticated analysis techniques. Signup and view all the answers

Which forecasting method is primarily based on expert opinions?

Cross Impact Analysis Signup and view all the answers

What does the equation $y = mx + b$ represent in a simple linear regression model?

The relationship between the dependent and independent variables Signup and view all the answers

In the context of the train cost model, what does the value 17.8594 represent?

The slope of the regression line indicating how cost changes with the number of trains Signup and view all the answers

Which value measures the reliability of the linear relationship in a simple linear regression model?

$r$ (correlation coefficient) Signup and view all the answers

How is the coefficient of determination ($r^2$) interpreted in the train cost model?

It represents the percentage of variation in cost explained by the number of trains Signup and view all the answers

What does a correlation coefficient ($r$) value close to 1 indicate?

There is a strong positive linear relationship between the variables Signup and view all the answers

Which of the following statements about simple linear regression is true?

It only examines linear relationships Signup and view all the answers

What is the purpose of finding the regression equation in the context of train costs?

To predict future costs based on the number of trains Signup and view all the answers

If the number of trains increases but shows a decrease in cost after a certain point, which aspect of regression analysis is being violated?

Linearity assumption Signup and view all the answers

What is the formula for calculating the forecast using moving averages for three periods?

$F_t = \frac{A_{t} + A_{t-1} + A_{t-2}}{3}$ Signup and view all the answers

In exponential smoothing, how is the new smoothed value expressed mathematically?

$S_t = \alpha A_t + (1 - \alpha) S_{t-1}$ Signup and view all the answers

What does the cumulative forecast error (CFE) measure?

Difference between actual values and forecasted values Signup and view all the answers

Which statement about exponential smoothing is true?

Exponential smoothing allows old data to progressively lose significance. Signup and view all the answers

What is the primary disadvantage of using older data in forecasting models?

Older data may no longer reflect current trends. Signup and view all the answers

What role does the parameter ( \alpha ) play in exponential smoothing?

Indicates the weight given to the most recent observation Signup and view all the answers

What outcome should cumulative forecast errors (CFE) aim for?

A sum that tends to zero Signup and view all the answers

Using three previous periods, if the actual values are 79, 84, and 83, what is the forecast for the next period?

82 Signup and view all the answers

Study Notes

### Expensive & Time Consuming

A forecasting method that is very expensive and time consuming
Practical only for long-term forecasting

### Subjective Models

Cross Impact Analysis:
- Assumes future events are related to the occurrence of earlier ones
- Uses a conditional probability matrix
- Requires expert input
Historical Analogy
- Assumes new services follow the introduction and growth patterns of similar services
- Frequently used to predict market penetration and product life cycles
- Can be unreliable and questionable

### Causal Models

Data follows an identifiable pattern over time
There's an identifiable relationship between the information to be forecasted and other factors
Regression Analysis: Uses a linear relationship between independent and dependent variables to form a regression model:
- Dependent variable (Y): the factor being forecasted
- Independent variables (Xi): the factors that determine the value of Y
- Formula: 𝑌 = 𝑎0 + 𝑎1 𝑋1 + 𝑎2 𝑋2 + …..+ 𝑎!𝑋𝑛
Econometric Models:
- A version of regression models
- Consists of a set of simultaneous equations that express a dependent variable in terms of multiple independent variables
- Requires extensive data collection and sophisticated analysis
- Suitable for long-range forecasting

### Causal Models - Regression Models - Simple Linear Regression

Given n data points (xi, yi), i = 1, … , 𝑛
The function describing the relationship between x and y is: 𝑦" = 𝑚𝑥" + 𝑏
The aim is to find the equation of the straight line: 𝑦 = 𝑚𝑥 + 𝑏
Solution
- Use 𝑥̅ = ∑𝑥/n, 𝑦1 = ∑𝑦/n, 𝑥𝑦 = ∑𝑥𝑦/n
- 𝑚 = (∑𝑥𝑦 − 𝑥̅ 𝑦1) / (∑𝑥² − 𝑥̅²)
- 𝑏 = 𝑦1 − 𝑚𝑥̅
Correlation Coefficient (r):
- A measure of the reliability of the linear relationship between x and y values
- Values close to 1 indicate an excellent linear relationship
Coefficient of Determination (r²):
- A measure of the percentage of variation in y explained by x

Train Cost Model Example

10 weeks of data on the number of trains produced and their production cost
Simple Linear Regression Model: cost = 17,8594 * (number of trains) + 164,8651

Time Series Models - Exponential Smoothing

Variables:
- St: Smoothed value at the end of period t
- At: Actual observation for period t
- F(t+1): Forecast for period t + 1
Formula:
- New value (St) = Old value (St-1) + α [observed error]
- St = αAt + (1 - α) St-1
- F(t+1) = St
Benefits:
- Smooths out blips in data
- Older data are given progressively less weight
- Simple calculation, requiring only recent data

Time Series Models - Exponential Smoothing - Weights of Past Demand

Formula: St = aAt + a (1 - a ) At -1 + a (1 - a ) 2 At - 2 +.....+ a (1 - a )t -1 A1 + (1 - a )t S 0
The weights a, a(1-a), a(1-a)², a(1-a)³... sum up to 1. This means the weight of each past demand is discounted by a factor of (1-a).
Formula shows that a lot of past information is used to estimate the present, but older data are given progressively less weight.

Forecast Error

Formula: 𝐴( ) − 𝐹( )
Cumulative Forecast Error (CFE) = ∑)&'((𝐴& − 𝐹& )
- The sum of forecast errors should tend to zero
- Measures the sum of forecast errors
Mean Absolute Error (MAE): Calculates the average magnitude of the error by summing the absolute difference between forecast and actual value over a period.
Mean Squared Error (MSE): Calculates the average of the squared error which emphasizes large errors.
Root Mean Squared Error (RMSE): The square-root of the mean squared error, which gives the error in the same unit as the original data.

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Description

This quiz covers various forecasting methods including expensive and time-consuming approaches, subjective models like Cross Impact Analysis and Historical Analogy, as well as causal models such as Regression Analysis. Each method is explored in terms of its practicality, assumptions, and application in forecasting.