1 Forecasting Formulas Symbols n Total number of periods, or number of data points. A Actual demand for the period (  Y). F Forecast demand for the period.

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Presentation transcript:

1 Forecasting Formulas Symbols n Total number of periods, or number of data points. A Actual demand for the period (  Y). F Forecast demand for the period (  Y). Y Dependent variable, or actual demand (Y = Actual, Y = Forecast). e Error. T Trend factor.

2 C Cyclical factor. S Seasonal factor. Y Forecast dependent variable. a Y intercept. b Slope of the line.  Alpha. The desired response rate, or smoothing constant.

3 (P) Probability.  P Mean proportion of a large sample.  Sigma standard deviation of the population. x Independent variable. y Dependent variable data point.

4  t Mean of the error for a time interval.  t Error for a single time period. Z Value from normal distribution (i.e. number of standard deviation from the expected distribution). S  Standard deviation of the errors.

5 R 2 Coefficient of determination (The percentage of exploised, eliminated and removed variances). Z  MAD Mean absolute deviation. I Index.  mu  population mead.

6  S x =   ( X -  X ) 2 /(n-1) Sample standard deviation of X.   x =   ( X -  ) 2 /N Population standard deviation of X.  S yx =   ( Y t -  Y t ) 2 /(n-r) Standard deviation of estimate  standard deviation of forecast errors. (n = number of observations, r = smoothing) or regression (2) (a & b) indicators).

7 S yx = S  Standard deviation of estimate  standard deviation of the Errors.  t = A t - F t Forecast error for period t = actual demand for period t less the (should be ~ ND (0,low) forecast demand for period t. F t = F t-1 +  (A t-1 – F t-1 ) The exponentially smoothed forecast for period t = the exponentially smoothed forecast for the prior period + the smoothing constant times (the actual for the prior period less the forecast for the prior period).

8 Y t = a + bt Forecast: Simple Linear Trend. Y t = a + bt + ct 2 Forecast: Quadratic Trend. Y t = T C I S I I Decomposition model: Forecast value = Trend times cyclical indicators times seasonal indicator times irregular indicator. Y t = T S I Simple Decomposition model: Forecast value = Trend times seasonal indicator.

9  2 x+y =  2 x +  2 y Standard deviation squared for x + y = the standard deviation of x + the standard deviation of y.  x+y =  x +  y Population mean for x + y = the mean of x + the mean of y.  e t - 0 TS =  Tracking signal = the total MAD of errors/MAD.

10  t - 0 Z  =  Z – value for S  errors = the mean of the errors for a time interval over the standard deviation of the errors.  APE MAPE =  n

11 MAD = 0.8S e Mean absolute deviation = 0.8 times the standard deviation of the forecast errors. S  = MAD (1.25) Standard deviation of the forecast errors = mean absolute deviation times  t = 0  Z S  Confidence interval for errors = times standard deviation of the forecast errors.

12  A - F  APE =|   A  Absolute value of actual less forecast divided by actual. S yx 2 R 2 = 1 -  s y 2 The coefficient of s e 2 determination = 1 -  s y 2

13 s y 2 - s  2 R 2 =  The coefficient of s y 2 determination.