# Forecasting

Basic Forecasting Concepts

Forecasting

Look at the Historical Data

Analyze the variation in the data which happened in the past

Develop a rule or explanation of why the data elements changed in the past

Check to see if the rule or explanation is acceptable.

If acceptable, project future using the same rule or explanation.

Forecasting Techniques

Persistence

Qualitative Techniques (includes Delphi Methods, Expert Opinion, Sales Force Composite, Market Surveys)

Time Series Analysis (also known as Variation Analysis, Technical Analysis, Trend Analysis – Regression with time as the only Independent Variable.

Causal Techniques (also known as Forces at Work, Regression/Correlation, Fundamental Analysis

Persistence

Persistence is the most widely used technique for very short-term decisions (e. g. which bus or train to take, which route to take to drive)

One of the time series forecasting techniques also knows as Naïve Method #1 is based on Persistence. Whatever happened in this period will happen in the following period.

Forecasted Sales for period t+1 = Ycap(t+1) will be actual sales for period t = Y(t)

Qualitative Methods

Delphi Method – Iterative group process, Respondents provide input to decision makers, Repeated until consensus is reached

Expert Opinion — Collect opinions of a small group of known experts, Use statistical techniques to analyze the results

Sales Force Composite – Collect estimates of individual salespersons, adjust data for reasonableness, Consolidate results as necessary

Consumer Market Survey — Information on purchasing plans solicited from customers or potential customers — Used in forecasting, product design, new product planning

Time Series Analysis Quantitative Methods

Historical data about the variable (e. g. Sales) is collected over time.

The variation in data may be the result of four types of variations: Cyclical, Seasonal, Trend, and Random.

Cyclical variation is often ignored in most business situations since the data form several decades ago is no longer relevant.

Seasonal variation (changes occurring with frequency of less than one year) is easy to adjust in any data set. We will generally work with seasonally adjusted data which means that seasonal variation has been eliminated.

The data we will work with, will have two types of variations: Trend and Random. Our goal will be to devlop models where the random variation can be reduced as much as possible.

Cyclical and Random Variation

Types of Variation

Forecasting — Time Series

Example 1 – Sales for last 7 periods 5,5,5,5,5,5,5: Forecast for period 8. Actual sales Y(1) = Y2) = … =Y(7) = 5. The data shows no variation in the past hence the forecast Ycap(8) = 5. No random variation remaining or Residual (unexplainable variation is Zero) . This is a perfect model.

Example 2 – Sales for last 7 periods 6,8,10,12,14,16,18: Forecast for period 8. Simple to make a rule or Regression equation which is Ycap = 4 + 2 x (period #). For period 8 the forecast Ycap(8) = 4 + 2 x( 8) = 20. What was the original variation and the residual variation after using this rule?

Basic Statistical Formulas

Symbols Used

X (X1, X2, ——) actual value of independent variable(s)

Y actual value of the dependent variable

Ybar average value of Y

Ycap estimated value of Y

Y – Ycap is the error in estimating Y

R^2 coefficient of determination

R coefficient of correlation

Formulas

Unexplainable variation = Σ (Y – Ycap)^2

Total Variation = Σ (Y – Ybar)^2

Variance = Total variation/ Degrees of freedom

Explainable Variation = total – Unexplainable variation

R^2 = Explainable Variation/ Total variation

Analysis of Example 2

Sales for last 7 periods 6,8,10,12,14,16,18: Forecast for period 8. Rule or Regression equation which is Ycap = 4 + 2 X.

Ybar = 84/7 = 12 Residual Variation = 0 Total variation = 112

R^2 = 1 R = +1 Perfect Model Use + sign if Y is going up otherwise use –

Variance of Y =112/6 = 18.67 Standard Deviation of Y =4.32

X | Y | Ycap | Y-Ycap | (Y-Ycap)^2 | Y- Ybar | (Y-Ybar)^2 |

1 | 6 | 6 | 0 | 0 | -6 | 36 |

2 | 8 | 8 | 0 | 0 | -4 | 16 |

3 | 10 | 10 | 0 | 0 | -2 | 4 |

4 | 12 | 12 | 0 | 0 | 0 | 0 |

5 | 14 | 14 | 0 | 0 | 2 | 4 |

6 | 16 | 16 | 0 | 0 | 4 | 16 |

7 | 18 | 18 | 0 | 0 | 6 | 36 |

Total | 84 | 0 | 0 | 112 |

Evaluating Time Series Forecasts

In most real-life situations, you work with a large volume of historical data and a perfect model does not exist. We simply try to reduce the error which is (Y- Ycap) measured in several different ways Mean Absolute Deviation (MAD), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE)

MAD = Average (Absolute value of all the errors)

MSE = Average of All the errors squared

MAPE = Average (Absolute value of Errors as percent of actual values)= Average of all (100 x (Y-Ycap)/Y)

These performance measures are easy to calculate with Excel or POM/QM

Time Series Methods

There are several methods routinely used by the practitioners. In our course we will only work with the following methods which are useful when there is no trend in the data:

Naïve Method #1: Ycap (t+1) = Y(t)

Naïve Method #2: Ycap = Ybar

Simple Moving Average Method: for e.g. Three period MAM : Ycap (4) = {Y(1) +Y(2)+ Y(3))}/3

Exponential Smoothing Method ESM with given alpha: Ycap(t+1) = Y(t) + alpha* (Err in period t) = Y(t) + alpha*(Ycap(t)-Y(t))

Note that One period MAM is same as Naïve Method #1

Also note that if alpha is 1 ESM will be same as Naïve Method # 1

Using software for Time Series

The numerical problems using the time series techniques within the scope of our course could easily be solved with POM/QM or with Excel.

For Trend Analysis we can use POM/QM, or we can use the Regression Module available within the Excel Add-on called Data Analysis.

A separate video tutorial has been posted to illustrate the use of software to solve time series problems.

Forecasting Causal Techniques

Causal Techniques are also known as

Forces at Work

Regression/Correlation

Fundamental Analysis