COMBINING FORECASTS WITHIN THE MLTIVARIATE C _ LOGISTIC : A FRESH APPROACH TO FORECASTING

The concept of combining forecasts enables the multivariate C_logistic model to rival all time series and econometric models in computing accurate forecasts from growth data. The “C” notation signifies a multivariate logistic equation that possesses a continuous response variable. The C_logistic model is easy to understand, simple to apply, and derived from both spreadsheets and statistical software. Therefore, this model is attractive to academicians in teaching and practitioners in computing superior out-of-sample forecasts. Indeed, the structural form, innovative seasonal variable (Sj), combined forecasts, and judgmental modifications capabilities make the multivariate C_logistic model ideally suited for forecasting in today’s dynamic environments. INTRODUCTION The multivariate C_logistic equation possesses the needed ingredients of an exceptional forecasting model: an upper asymptote, a point of inflection, event modeling, judgmental modification, and combined forecasts capabilities. There are four stages to this S-shaped growth curve: (a) slow growth, (b) growth at an increasing rate, (c) growth at a decreasing rate, and (d) saturation. A plot of the data and knowledge of the subject matter help identify the current stage of growth. The concept of combining forecasts within the multivariate C_logistic model is unique with these authors. When using growth data, the predictive capabilities of this model enable it to rival all time series (including Box-Jenkins ARIMA) and econometric models in computing accurate forecasts. Since the “C” notation signifies a continuous response variable, this equation should not be confused with the familiar logistic equations that possess a binary or nominal scaled response variable. This article promotes the use of combined forecasts and time series components within the multivariate C_logistic model. The advantages of a single seasonal index variable (Sj) rather than multiple (11 for monthly) indicator variables have only recently been committed to writing (Landram, et al. 2004, 2008). This seasonal variable (Sj) is used as an explanatory variable in describing seasonal variation in the multivariate C_logistic. Since historical conditions of the past may not prevail in the future, structured judgmental modifications are employed thereby increasing the accuracy of future Southwestern Economic Review 244 predictions. Hence, in an effort to produce superior forecasts, an innovative seasonal variable (Sj), combined forecasts, and structured judgmental modifications capabilities are used within the multivariate C_logistic model. In an effort to eliminate any confusion of this model with the logit, probit, or single variable logistic models, the originality of the multivariate C_logistic model is reiterated below: (a) The C_logistic equation conforms to an S-shape growth pattern as does the logistiand Gompertz equations. However, this model possesses a continuous response variable with multiple explanatory variables. (b) Both econometric variables and time series components can be combined in the C_logistic model. (c) In this article, the innovative least squares seasonal index variable is extended to the C_logistic model. Equations with the above characteristics of the C_logistic equation have not appeared in the literature. In reviewing the past 25 years of forecasting, Gooijer and Hyndman (2006) cite the need for additional research into multivariate time series forecasting. They also stress the need for deeper research in forecasting methods based on nonlinear models. These needs are addressed in describing the C_logistic model. Furthermore, many have expressed concern and disappointment over the lack of “new” methods of forecasting (Fildes, 2006). They also prefer the description of an innovative forecasting method be grounded in real data and compared to other proven alternative methods of forecasting. This article addresses all of these concerns. A major goal in forecasting is the integration of judgment and quantitative methods (Armstrong and Collopy, 1998). The judgmental selection of the asymptote enables the C_logistic to easily integrate prior knowledge into a statistical model thereby achieving this goal. COMBINED FORECASTS The multivariate C_logistic equation is defined as