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Time Series Forecasting with ARIMA (p,d,q), Forecasting Accuracy Measure with MAD, MAPE and TS

Chutian Li
Nov 30, 2016
4 min read

Background

Real Sportz has been struggling to meet product demand in recent months. This recommendation report summarizes observations contributing to the challenges involved. Root causes identified include a lack of forecasting accuracy and negligence towards the importance of forecasting. To address the issues at hand, it is recommended that Real Sportz:

Understand the importance of forecasting
Establish a standardized forecasting process
Implement an efficient information transfer system
Assign responsibility to suitable talent

These recommendations target both strategic and operational issues associated with developing a structured forecasting process. Further support is included in the following text, with data provided.

Why is Forecasting important for Real Sportz?

Forecasting has both short-term and long-term impacts on Real Sportz’s business. On a daily basis, company operations rely on projected demand to plan production and control inventory levels, and sourcing groups need to acquire material accordingly in advance. From a long-term perspective, demand projections help Real Sportz adjust capital equipment investments and control inventory. Inaccuracies in these long-term and short-term forecast scopes produce increased costs associated with holding inventory and potential stock-outs. These lead to longer cash conversion cycle times, causing the company portfolio to become less attractive for investors, inhibiting future growth potential. Therefore, improving forecasting accuracy is important to meet short-term demand and optimize long-term growth capabilities.

Current Forecasting Situations in Real Sportz

Currently, forecasting does not seem to be an important consideration for Real Sportz, and is not included in business-level planning. As a result, an appropriate and standardized forecasting process has not been established, causing data collection and analysis to be unreliable. In addition, Real Sportz does not have an information transfer system connected across the company that allows for internal and external communication. Also, there are not specific personnel or functional groups appointed responsibility of the forecasting process. Each relay of forecasting data is assumed to be misappropriated, causing each functional group to, in effect, create their own forecast. These factors compound upon each other with each data exchange, increasing forecast error with each transfer.

Recommendation on Forecasting and Demand Management Process and Approach

Before Working with Data

Collaborative Planning, Forecasting and Replenishment (CPFR) Process Model

As noted previously, it is important for firms to include forecasting in business-level strategy planning; therefore, Real Sportz should integrate cross-functional accountability from Marketing, Sales, Operations, Sourcing, and Finance groups at both regional and corporate levels.

By setting up a CPFR Model, forecasting would not be driven by functional metrics, and a standardized procedure could be introduced with agreement from all departments involved. This will reduce accumulated variance and improve the reliability of the overall result.

To implement CPFR, Real Sportz’ manufacturers use cross-functional customer teams, while their customers (retailers) use cross-functional category teams. Such teams have the benefit of simplifying both inter-firm and intra-firm coordination.

Qualitative Techniques– Based on intuitive or judgmental evaluation

1- Expert Opinion; Market Research, Focus Groups, Historical analogy, Delphi Method, Panel…

2- Demand Characteristics

Intrinsic – based on historical patterns from company data (Product life-cycle, price change, promotion, advertising…)
Extrinsic Methods – based on information outside the company (competition, government policy, economic conditions…)

3- Regression Analysis (RA) to evaluate statement

RA a statistical process for estimating the relationships among variables. The focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors'). It’s a great tool for Real Sportz to re-evaluate prove if the intuitive evaluation match with math evaluation

Quantitative Techniques – Based on mathematical formulas (Time Series Forecasting)

Simple Moving Average

Process: Ft+1 = (Dt + Dt-1 + Dt-2 + . . . + Dt-[N-1]) / N

Where: Dt = demand at time “t”, N = number of periods, and F = forecast

Example: the forecast of the 4th week’s sale for the Northeast region, using a 3-week moving average, is the average of week 1 (135), 2 (114), and 3 (90). Therefore, the projected sales for week 4 is [( 135 + 114 + 90 ) / 3] = 113.

Advantages: A simple technique that is easy to calculate, and can be used to filter out random variation; longer periods provide greater smoothing.

Limitations: If a trend exists, it is hard to detect, and moving averages lag trends

Weighted Moving Average

Process: Ft+1 = SWtAt , where A represents average, and sum of the weights (W) equals 1

Example: the forecast of the 5th week’s sale for the Northeast region, with week 1 weighted 10%, week 2 weighted 20%, week 3 weighted 30%, and week 4 weighted 40%; the projected sales for week 5 is ( 135 x 10% + 114 x 20% + 90 x 30% + 174 x 40%) = 132.

Advantages: Captures trend faster than simpler techniques, and can be used for seasonality analysis by weighting seasonal time frames.

Exponential Smoothing - ARIMA (0,1,1)

Process: Ft+1 = a Dt + (1- a) Ft ; (0 < a < 1); As a approaches zero, exponential smoothing equalizes the weights across all periods (like the average); Projected forecasts for Period 2 is always equal to Period 1.

Example: For the forecast of the 3rd week’s sales for the Northeast region, with a = .0.1, the projected sales for week 3 is week 2’s actual sales (114) times a + week 2’s projected sales (135) times (1-a) = ( 114 x 0.1 + 135 x (1-0.1)) = 132.9

Measuring the accuracy of the forecasting sales

Mean Absolute Deviation (MAD)

MAD it is the average of the absolute value, or the difference between actual values and their average value, and is used for the calculation of demand variability.MAD = Σ|at' −' 'ft| / ; where n is the number of periods, at is the actual value of the quantity being forecast, and ft is the forecast.

Mean Absolute Percent Error (MAPE)

MAPE is a measure of prediction accuracy of a forecasting method in statistics. F = (Σ |(F-A)| /A)/n

Tracking Signal (TS)

TS is a simple indicator that forecast bias is present in the forecast model. It monitors any forecasts that have been made in comparison with actuals, and warns when there are unexpected departures of the outcomes from the forecast. Tracking signal = Σ (at' −' 'ft) / MAD; where at is the actual value of the quantity being forecast, and ft is the forecast.