Первый слайд презентации
1 Class Forecasting techniques for RM 1. Naïve approach 2. Qualitative methods (EJM) 3. Decision making methods under uncertainty 4. Quantitative methods: - Moving averages (SMA, WMA, EMA) - Linear regression Seasonality (2 techniques) Study materials: Slides
2 Forecasting (Greek: pro + gnosis ) projecting future financial or operational information (e.g., sales, expenses, quantities sold, etc.); - a prediction of future events or conditions; - the process of estimation in unknown situations. (SMA 2A) Forecasting support systems – software with forecasting functions: Statistica, SPSS, ForecastPro, MatLab, StatPad … Based on math methods (regression models, moving averages). They will NOT do the job for you Forecasting
3 “Risk - the chance that an outcome will be different than expected; can be measured as the degree of variability in either an individual’s or an organization’s anticipated investment outcomes.” (SMA 2A) Q: How can we manage risks with effective forecasting? Risk and Forecasting
4 Between Qualitative and Quantitative methods. The next period data will be the same as the previous one’s: F n = X n - 1 Pluses: simplicity, relative precision. Minuses: no seasonality could be applied, looks “doubtful”. 1. Naïve approach (technique)
5 2.a. Expert judgment methods: Aggregated individual method They differ in Delphi method (N. Dalkey, 1963) the degree of Nominal group technique, NGT consensus Consensus group method Expert judgment is typically desirable in the technique when there is little/no data, or when the data is unsuitable, or difficult to understand. In theory, qualitative knowledge built through the experts’ experience can be translated into quantitative data. 2. Qualitative methods
6 2.b. “Grass roots”: Example: Sales units estimate in «Caterpillar CIS» sales estimation based on the concluded and/or prospective sales agreements. The other side of the medal is: “Executive judgment” 2.c. Other methods: - brainstorming, - market research, - historical analogy 2. Qualitative methods
7 Criteria selection methods for Decision making under uncertainty: Inductive probability – P.-S. Laplace (1814) Minimization of maximum possible loss (Minimax) - Abraham Wald (1939) Optimism-pessimism index – Leo Hurwitz Minimax regret criterion – L. Jimmie Savage (1951) Special techniques to work with when for various reasons probability distribution is not available. 3. Decision making under uncertainty (DMUU)
8 (1) Simple Moving Average (SMA) Fn = (Xn- 1 + Xn- 2 + … + Xn-m) / m, where: Fn - forecast for period “n”, m - number of periods to average. Here, m = 3 4. Quantitative methods 4.a. Moving averages
10 (2) Weighted Moving Average (WMA) Fn = (Wa*Xn- 1 + Wb*Xn- 2 + … + Wz*Xn-m), where: Sum of all weights Wa + Wb + … + Wz = 100% Fn - forecast for period “n”, m - number of periods to average. Need to make decisions: “m”, “ww” 4.a. Moving averages
11 (2) Weighted Moving Average (WMA) m = 3 W1=0.1, W2=0.2, W3=0.7 4.a. Moving averages
12 (3) Exponential Moving Average (EMA), 1-parameter Fn = α *An- 1 + (1 – α )*Fn- 1, where: Fn - forecast for period “n”, An- 1 - actual data for period (n-1) α (alpha) - exponential coefficient, α = (0; 1) traditionally, initially set at 0,40 Need to make decision on “ α ”. Includes elements of optimization techniques. 4.a. Moving averages
13 (3) Exponential Moving Average (EMA), 1-parameter Fn = α *An -1 + (1 – α )*Fn- 1 can also be expressed as: Fn = Fn -1 + α*(An -1 - Fn -1 ). We see that if alpha approaches 1, then Fn would tend to the value of An -1. If Fn is equal to An -1, then we face the naïve model. 4.a. Moving averages
14 (3) Exponential Moving Average (EMA), 1-factor 4.a. Moving averages
15 Pluses: simplicity. Minuses: difficult to apply seasonality, only 1 next period can be forecasted. 4.a. Moving averages
16 Evaluation indicators: 1. Mean absolute deviation (error) ( MAD, ABS ε) – to MIN. 2. Mean squared error ( MSE ) - to MIN. 3. Mean absolute percentage error ( MAPE ) – to MIN. 4. Running sum of forecast errors ( RSFE ) – to zero. 5. Tracking signal ( TS, = RSFE/MAD) – to zero Now check: 4.a. Moving averages
17 3-Factor Exponential Moving Average (EMA) Pluses: best precision of the forecast, seasonality could be counted. Minuses: difficult to implement and analyze, only 1 next period is forecasted. 4.a. Moving averages
18 Fn = a + b *n, where: Fn - forecast for period “n”, a, b – constant and variable coefficients, found from the equation. Pluses : seasonality could be applied, forecasting of several periods possible. Minuses : often – low precision as compared to other models. 4.b. Linear regression Y = a + b*X
20 Model Evaluation : the same as for MAs Also: R² must be higher 0. 50. 4.b. Linear regression
21 Linear regressions in Forecasting (pro forma P&L statement) If X = Revenues, then Y = Costs Q: What will our P&L look like if the anticipated sales in the next quarter are $15,000?
23 Vertical analysis vs. Linear regressions in Forecasting (pro forma P&L statement) Q: What will our P&L look like if the anticipated sales in the next quarter are $15,000, based on the vertical analysis?
24 Vertical analysis vs. Linear regressions in Forecasting (pro forma P&L statement)
25 Vertical analysis vs. Linear regressions in Forecasting (pro forma P&L statement) Which one do you think is more realistic?
26 Seasonality – observed periodic and regular changes of input time series data depending on : ► season, quarter, ► month, week, day of the week, ► particular date ( holiday, etc ). Necessary data: at least TWO recurring periods E.g., 8 quarters, 24 months, etc. Seasonality
28 Finding out seasonality factors presence : no less than 75% of periods observed. E.g., in at least 6 quarters out of 8 seasonality is observed, i.e., a seasonality factor is steadily more or less than 1. Seasonality factors
29 Seasonality factors In 3 out of 12 months the seasonality factors do not match. But in 9 months (75% out of 12) we do observe seasonality. Therefore, we start finding the “correct” seasonality factors to apply. Next steps: averaging the factors found in Y1 and Y2; adjusting the results by the average, if the latter is NOT exactly 1,000000.
33 Rule 1: No “ready-made” model would work better that the model you have designed and tested yourself. Rule 2: Apply different criteria to test your model. Rule 3 : Adjustments to your model are necessary to make each time as soon as new actual data are available to include. There will be changes in “a” and “b” coefficients of a linear regression, “alpha” in a 1-parameter EMA, etc. Forecasting techniques / methods Important!
37 Forecasting with 4 models: SMA (m = 3) WMA (m = 3, ww = 0.6, 0.3, 0.1) 1-factor EMA Linear regression. Please find : 10 -th period forecast with the 4 models ( no seasonality ). MSE with the 4 models. Alpha in Model 3. Coefficient of Determination ( R² ) in Model 4. Which model is working better here and why ? Homework
Последний слайд презентации: 1 Class Forecasting techniques for RM 1. Naïve approach 2. Qualitative methods
38 Methods and techniques used: Structural analysis: vertical analysis, etc Ratio analysis Sustainable growth rate model (IGR, SGR, g) Inventory MGT models: EOQ Cash flow MGT models: Baumol – Tobin, Miller - Orr MBO, KPI targets Moving averages Linear regression models Seasonality factors Pro forma Financial Statements