Constant Level Forecasting Methods

Under constant level forecasting methods, it is assumed that the random variable X, for period t is given by 

We assume is normally distributed with mean zero and negligible variance. Given the values of X( = D( for f = 1, 2,. .., n, the forecast for period (n + 1) is given by 

There are five commonly used forecasting methods for estimating the value of as follows  

We will discuss them in detail in the following sections. We will then incorporate seasonality and trend into the constant level forecasting methods. 

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Regular exponential smoothing model estimates the constant level (L) to forecast future demands. Holt s model improves it by estimating both the level (L) and trend factor (T). It adjusts both the level and trend factor using exponential smoothing. Holt s method is also known as double exponential smoothing or trend adjusted exponential smoothing method. 

So far in our discussion, we were concerned with forecasting for one period only, namely F +i, given the actual demands Dj, Dj,..D . In prachce, one has to forecast for several periods in the future. Methods for forecasting for multiple periods depend on the type of forecasting method selected—constant level, constant level with seasonality, constant level with trend or constant level with seasonality and trend. 

Jill decides to use Holt s method with seasonality and trend (discussed in Example 2.6, Sechon 2.7) with the inihal estimates of level and trend as 600 and 50 respectively. She also decides to use the first 4 years of data (2007-2010) for determining the smoothing constants (a and P) and use the 2011 data for validating the forecasting method and the chosen smoothing constants. 

Closed type homogenous models determine equilibrium composition of only water and also the content and activity coefficients of its migration forms under the assigned thermodynamical conditions. Object of forecasting is usually any volume of well mixed water (for instance, individual sample or mix of different waters) of assigned analytical composition. The behaviour of nonpolar components, beside O, CO and H S, in these model as a rule is not considered. The content of such models depends on the set of basis components, selected calculation methods of activity coefficients and equations system (2.76)-(2.79) or (2.80)-(2.83). For reactions of complex-formation it is necessary to have constants equilibrium value base. Ozyabkin (1995) treats them as lower level models. Kraynov et al. (2004) call them thermodynamical. 

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