Advance forecasting

1. Advance forecasting Forecasting by identifying patterns in the past data • Chapter outline: • Extrapolation from the past • Cause and effect relationships • Trend analysis • - Regression analysis • - Simple linear regression analysis • - Multiple linear regression analysis • - Quadratic regression analysis • 3.Cyclical and seasonal issues • Seasonal decomposition of time series data • Type of seasonal variation • Computing Multiplication seasonal indices • Using seasonal indices to forecast • A caution regarding seasonal indices

2. Extrapolation from the pastCause-and-effect Relationships • Causal forecasting seeks to identify specific cause-effect relationships that will influence the pattern of future data. Causes appear as independent variables, and effects as dependent , response variables in forecasting models. • Independent variable Dependent, response variable • Price demand • Decrease in population decrease in demand • Number of teenager demand for jeans • Causal relationships exist even when there is no specific time series aspect involved. • The most common technique used in causal modeling is least squares regression.

3. Extrapolation from the past Linear Trend analysis Its noticed from this figure that there is a growth trend influencing the demand, which should be extrapolated into the future.

4. Extrapolation from the pastLinear Trend analysis The linear trend model or sloping line rather than horizontal line. The forecasting equation for the linear trend model is Y = +X or Y = a + bX Where X is the time index (independent variable). The parameters alpha and beta ( a and b) (the “intercept” and “slope” of the trend line) are usually estimated via a simple regression in which Y is the dependent variable and the time index X is the independent variable.

5. Extrapolation from the past Linear Trend analysis Although linear trend models have their uses, they are often inappropriate for business and economic data. Most naturally occurring business time series do not behave as though there are straight lines fixed in space that they are trying to follow: real trends change their slopes and/or their intercepts over time. The linear trend model tries to find the slope and intercept that give the best average fit to all the past data, and unfortunately its deviation from the data is often greatest near the end of the time series, where the forecasting action is.

6. Extrapolation from the pastLinear Trend analysis Using a data table (what if analysis ) to determine the best-fitting straight line with the lowest MSE

7. Extrapolation from the past Linear Trend analysis Simple linear Regression Analysis Regression analysis is a statistical method of taking one or more variable called independent or predictor variable- and developing a mathematical equation that show how they relate to the value of a single variable- called the dependent variable. Regression analysis applies least-squares analysis to find the best-fitting line, where best is defined as minimizing the mean square error (MSE) between the historical sample and the calculated forecast. Regression analysis is one of the tools provided by Excel.

8. Simple linear Regression Analysis

10. Extrapolation from the past Linear Trend analysis Multiple linear Regression Analysis Simple linear regression analysis use one variable (quarter number) as the independent variable in order to predict the future value. In many situations, it is advantageous to use more than one independent variable in a forecast.

11. Multiple linear Regression Analysis Two factors that control the frequency of breakdown. So they are the independent variables. Y = a + bX1 + cX2 Intercept Slope 1 Slope2

12. Multiple linear Regression Analysis

14. Extrapolation from the past Linear Trend analysis Quadratic Regression Analysis Quadratic regression analysis fits a second-order curve of the form Y = a + bX + cX2 Quadratic regression is prepared by adding the squared value of the time periods. The coefficients in the quadratic formula are calculated again using regression, where time periods and the squared time periods are the independent variables and the demand remains the dependent variable.

15. Quadratic Regression Analysis

16. Quadratic Regression Analysis

17. Extrapolation from the past Cyclical and Seasonal Issues • The fundamental approach to including cyclical or seasonal factors is to break the forecast into two components: • The underlying growth component • The seasonal variations • To prepare a forecast model: • Use a method to fit a growth curve to the historical record • Determine the pattern of the seasonal variability • In general, two sets of parameters to be estimated: • ( the coefficients in the trend line, and the percents in the seasonal patterns)

18. Extrapolation from the past Cyclical and Seasonal Issues Basically two things must be done: 1- determine the trend line 2- take the trend line out ( calculate deviations from the trend) 3- create a pie, radar, or polar chart of the average period value

19. Cyclical and Seasonal Issues Seasonal Decomposition of Time Series Data • Time series data are usually considered to consist of six component : • Average demand: is simply the long-term mean demand • Trend component : is how rapidly demand is growing or shrinking • Autocorrelation: is simply a statement that demand next period is related to demand this period • Seasonal component: is that portion of demand that follows a short-term pattern • Cyclical component: is much like the seasonal component, only its period is much longer. • Random component is the unpredictable component of demand

20. Cyclical and Seasonal Issues Type of Seasonal Variation There are two types of seasonal variation: Additive seasonal variation : Occurs when the seasonal effects are the same regardless of the trend. Multiplication seasonal variation : Occurs when the seasonal effects vary with the trend effects. It’s the most common type of seasonal variation

21. Cyclical and Seasonal Issues Computing Multiplicative Seasonal Indices • Steps of Multiplicative Time Series Model: • Decide that the data is seasonal in nature. • Then realized that the seasonal variation is quarterly • If the variation of the data is larger to the right, then that seasonal variation is multiplicative. • Seasonal indices is needed to produce the seasonal forecast model.

22. Cyclical and Seasonal Issues Computing Multiplicative Seasonal Indices • Computing seasonal indices requires data that match the seasonal period. If the seasonal period is monthly, then monthly data are required. A quarterly seasonal period requires quarterly data. • Calculate the centered moving averages (CMAs) whose length matches the seasonal cycle. The seasonal cycle is the time required for one cycle to be completed. Quarterly seasonality requires a 4-period moving average, monthly seasonality requires a 12-period moving average and so on. • Determine the Seasonal-Irregular Factors or components. This can be done by dividing the raw data by the corresponding depersonalized value. • Determine the average seasonal factors. In this step the random and cyclical components will be eliminated by averaging them.

23. Cyclical and Seasonal Issues Computing Multiplicative Seasonal Indices Step 1 Step 4 Step 2 = AVERAGE(B2:B5) Step 3 = B3/C3

24. Cyclical and Seasonal Issues Using Seasonal Indices to Forecast To forecast using seasonal indices 1- Compute the forecast using an annual values. Any forecasting techniques can be used. 2- Use the seasonal indices to share out the annual forecast by periods