A Comprehensive Guide to Forecasting Techniques in Business

Posted on Sep 5, 2024 in Design and Engineering

Week 1 – Introduction to Forecasting

Forecasting is the prediction of future events or future outcomes of key variables. An accurate prediction of outcomes can provide improved certainty and assist in the decision-making and planning process.

The purpose of forecasting is to identify problems, opportunities, and threats before they happen. By being proactive, greater efficiency, profitability, and longevity can be achieved.

When forecasting, the assumption is that the conditions of the past will be similar to the conditions of the future apart from variables specifically recognized by the forecasting model.

Time Horizons:

  • Short-term → immediate strategies to meet the needs of the short-term (operational)
  • Medium-term → mix of operational and strategic forecasts of demand
  • Long-term → mostly strategic forecasts to set the general course for the organization

Different parts of the organization have different forecasting requirements and have different time horizons, importance, and variables. The methods will vary in each case.

Forecasting = what the future will look like

Vs.

Planning = what the future should look like

Data should be Consistent, Accurate, Reliable, Relevant, and Timely (CARRT) and can be from internal or external sources.

Steps in forecasting:

  1. Problem formulation and data collection
  2. Data manipulation and cleaning – making the data appropriate for the forecast
  3. Model building and evaluation – choosing the appropriate model for minimum error
  4. Model implementation (actual forecast)
  5. Forecast Evaluation – comparison of actual values and forecast values for historical periods to analyze errors


Week 2 – Forecasting Techniques

Quantitative Forecasting – the prediction is derived using some algorithm or mathematical technique based on quantitative data. Time series and Causal

Qualitative Forecasting – the prediction is based primarily on judgment or opinion.

Time Series – are methods that rely on past measurements of the variable of interest. Examples include moving averages, exponential smoothing, decomposition, and extrapolation.

Causal Methods – where the prediction of the target series or variable is linked to other variables or time series.

Examples include regression, correlation, and leading indicator methods.

Time series is a sequence of measurements taken at successive intervals of time

vs.

Cross-sectional is measurements at one point in time, spread across a population

Time Series patterns can either be:

  • Systematic – level, trend, season, or cycle
  • Non-systematic – random

Level – is the underlying value of the series for a time period. The level may be constant over time or experience changes due to other components. When it is relatively constant over time a horizontal pattern can be observed.

Trend – is the long-term component that represents the growth or decline in the time series over an extended period.

Cyclical Pattern – the wave-like fluctuation around the trend that is often affected by general economic conditions.

Seasonal Pattern – is a pattern of change that repeats itself year after year relevant to a specific time period. Generally, due to weather or industry-related seasons.

Random Component – cannot be predicted accurately and has effects on the time series that cannot be explained by the variables that influence the systematic components. The extent of the random variation in a series determines the maximum level of forecast accuracy possible.

Data Patterns

Autocorrelation – is the correlation between the elements of a time series at one or more lagged time periods and itself. The pattern can be identified by examining the autocorrelation coefficients at different time lags of a variable.

Week 3 – Judgmental Forecasting

Advantages of Quantitative Forecasting

Objective, consistent, capable of processing large amounts of data

Considers relationships between multiple variables

Disadvantages of Quantitative Forecasting

Only as good as the available data

Changes that occur in data are not incorporated into the model, leading to an inaccurate forecast

Advantages of Qualitative Forecasting

Useful when there is little or no numerical data or relevant historical data available

Useful when there are rapid changes in the market

  • Forecast made with up-to-date knowledge of current changes and events

Disadvantages of Qualitative Forecasting

Almost always biased

Not consistently accurate over time

Takes years of experience to learn to convert intuitive judgment into good forecasts

Judgmental Forecasting – is typically based on information relevant to the forecasting task other than the time series data (non-time series information)

Methodology Tree

Wisdom of the Crowd – is an unaided judgment that relies on many independent estimates. It requires independence, diversity of opinions, decentralization, and aggregation.

Wisdom of the Crowds is affected by:

  1. Social influence effect – diminish the diversity of the crowd
  2. Range reduction effect – range is set by the influence of external factors, less reliable
  3. Confidence effect – boosts individual confidence after the convergence of estimates

Role-Playing – involves the simulation of human behavior where individuals represent people in an actual situation.

Role-Playing involves:

  1. Realistic casting
  2. Role instructions
  3. Description of the situation
  4. Administration – participants asked to act out responses
  5. Coding – role-players provide a perspective on the decision
  6. The number of sessions conducted if needed

Behavioral Intentions – personal intentions of plans, goals, or expectations regarding the future are measured to determine the likelihood of future actions.

Example: Juster 11 point (0→10) scale of likelihood

Delphi Method – is designed to determine a consensus from a group of experts in a structured and iterative manner. The steps involved are as follows:

  1. The problem is defined
  2. A panel of experts is assembled
  3. Forecasting tasks are set and distributed to experts
  4. Expert opinions are compiled and summarized then returned to experts
  5. Using feedback experts may alter their forecasts, iterated until consensus reached
  6. The final forecast is created using the aggregation of expert forecasts

Features of the Delphi Method:

  1. Experts remain anonymous and remove the influence of others
  2. Facilitator has a high level of control over feedback
  3. Consensus involves reaching a satisfactory level of variance among forecasts
  4. Usually 2-3 rounds of iteration are adequate, additional rounds lead to worse results

Conjoint Analysis – is a technique used to determine how people value different attributes that make up an individual product/service. Example: Airlines – High Price vs. Level of Service

Week 4 – Simple Naïve Forecasting

Forecast Error (Residual) is the difference between the actual value and forecast value

et = Yt – Ŷt

et = residual or forecast error

Yt = actual value

Ŷt = forecast value

Mean Percentage Error (MPE) =

MPE is used to determine if the forecasting method is biased.

If consistently large positive percentage → underestimating

If consistently large negative percentage → overestimating

Mean Average Percentage Error (MAPE):

Less than 10% = Highly Accurate

10 – 20% = Good

20 – 50% = Reasonable

Greater than 50% = Inaccurate

Mean Squared Error (MSE) – penalizes large forecasting errors

Root Mean Squared Error (RMSE) – one of the most commonly used measures


Naïve Method – is based solely on the most recent information available and is useful when there is stationary data with minimal changes.

Simple Naïve Method simply uses the previous time period data as the forecast for the following period.

Naïve Trend Method – adjusts for trend by adding the difference between this period and the last period.

Ŷt+1 = Yt – (Yt – Yt-1)

Naïve Seasonal Method – next period is the same as the respective period last season

Example: The forecast for March is the actual value for March last year

Naïve Trend and Seasonal Method – combining seasonal forecast with the difference between this period and the same period last season.

Example: The forecast for December is December last year PLUS the difference between November this year and the previous November.


Week 5 – Moving Averages and Exponential Smoothing

Moving Average formula: Ŷt+1 =

Ŷt+1 = forecast value for the next period

Yt = actual value at the current period

k = the number of terms in the moving average

In a moving average, equal weighting is applied for each recent observation, and each new data point is included in the average as it becomes available. The number of periods included will decide the ability of the method to respond to changes.

Simple Exponential Smoothing

New Forecast = [α (actual value of period t)] + (1-α) x (forecast for period t)

Alpha (α) = smoothing constant (01)>

Exponential Smoothing – provides an exponentially weighted moving average of all previously observed values. It applies the most weighting to recent observations while applying exponentially decreasing weight to past values. It does not handle trend and seasonality well and is therefore appropriate for stationary data.

Exponential smoothing continually revises a forecast in the light of more-recent experience

Holt’s Exponential Smoothing

This method allows for evolving linear trends because it adds a trend factor to the smoothing equation as a way of adjusting for the trend.

Exponentially smoothed series (current level):

Trend Estimate

Lt = the estimate of the level of the series at time t → usually the initial time series value

Alpha (α) = smoothing constant for trend

Beta (β) = smoothing constant for level

Yt = actual value of period t

Tt = the trend estimate → usually the average of change in the first few periods

p = periods to be forecast into the future

Winter’s Exponential Smoothing

Holt’s and Simple Exponential Smoothing do not consider seasonal patterns that can occur in a time series. Winter’s method uses one additional equation to estimate seasonality which is then considered in the forecast.

The formula for WES

Ŷt+p = Forecast for p periods into the future

Lt = level estimate

Tt = trend estimate

p = number of periods to be forecast into the future

St = seasonal estimate

s = number of periods (length) of the season

Alpha (α) = smoothing constant for level

Beta (β) = smoothing constant for trend

Gamma (γ) = smoothing constant for seasonality


Week 6 – Time Series and Their Components

Time series require special methods for their analysis and are typically related to each other. This means that patterns of variability can be used to forecast future values and assist in the management of business operations. It is important for managers to understand the past historical data to make sound judgments and intelligent plans to meet future needs.

Decomposition methods involve identifying the component factors that influence each of the values in a series. The four components of a time series are Trend, Cyclical, Seasonal, and Random (Irregular).

Additive Approach

  • when fluctuations are fairly consistent in size throughout the time series
  • time series needs to be linear in trend and seasonality
  • seasonal fluctuations must be constant over all seasonal cycles

Multiplicative Approach

  • when the variability of the time series increases with the level
  • the amplitude of the seasonal component will not be constant

Steps in Decomposition

  1. Season/Random components identified and removed
  2. Seasonal index estimation and deseasonalisation
  3. Cycle and Trend Separation
  4. Forecasting (Recomposing)

The length of Moving Average depends on the period of the season (e.g. Quarterly = MA4)

Centred Moving Average (CMA) is able to summarise the variation in a time series that can be attributed to seasonality and/or random variation.

Additive Seasonal Relative = Time Series (Y) – CMA

Multiplicative Seasonal Relative = Time Series (Y)/CMA

If the seasonal relative is > 1 then when using MA seasonal variation has been overstated

If the seasonal relative is < 1 then seasonal variation has been understated

The seasonal index is the average of seasonal relatives. The sum of all the seasonal indices should be equal to the periodicity (e.g. Quarterly should equal 4)

For the Additive method, the adjusted seasonal index (ASI) = Seasonal Index – Mean Seasonal Index

Deseasonalised data is estimated by the ratio of actual observation to the adjusted seasonal index. Formula = (Yt / ASI)

Once the data is deseasonalised the trend can be separated using the formula:

The additive or multiplicative formula can be used to forecast

Week 7 – Simple Linear Regression

Correlation Coefficient (r):

  • less than 0 = negative (inverse)
  • correlation, 0 = no correlation
  • more than 0 = positive correlation

Least Squares Line (fitted regression) – the line that best fits a collection of X-Y data points is the line that minimizes the sum of the squared distances (SSE) from the points to the line as measured in the vertical direction.

SSE = Σ (Y – Ŷ)Σ (Y – b0 – b1X)2

Fitted Straight Line→Ŷ = b0 + b1X

b0 = y-intercept (value of Y when x=0)

b1 = slope that indicated how much of the value of Y changes when the value of X changes by one

X = Independent variable

Standard Error of the Estimate (SEE) – measures the amount by which the actual Y values differ from the estimated or Ŷ values. It is the measure of accuracy for predictions and measures the vertical spread of data points about the fitted line. SEE is the standard deviation of the errors.

σ2 is the estimated average squared residual

A simple regression analysis gives the ability to estimate the mathematical relationship between a dependent variable (Usually = Y) and an independent variable (Usually = X). The dependent variable (Y) is the variable that we want to make a prediction about while the independent variable (X) is used as a predictor.


Testing for goodness of fit

F Test → shows if there is a relationship between all the X variables considered together and Y. If equal to 0 there is no relationship any other number means that the independent variable affects Y. If the significance level is more than 5% there is insufficient evidence of a relationship between the independent and dependent variable.

T-Test → for individual variable significance

Coefficient of Determination R2→ is the percentage of variance in Y explained by X.

R2 is between 0 and 1; the closer it is to 1 the better the estimated model fits the data.

R2 = Regression Sum of Squares/Total Sum of Squares = SSR/SST

e.g. 79.5% of the variation in Sales (Y) is explained by the variation in Advertising (X) exp.

Total Variation in Y = Variation explained by regression + remaining variation after regression

SST = SSR + SSE