Journal of Forecasting. Whittemore School of Business and Economics, The University of New Hampshire, USA, страница 3

Input neurons	Type
Length of the series	Numeric
Time period	M (month) Q (quarter) Y (year)
Industry	MI (micro) MA (macro) IS (industry-speci®c) DE (demographic data)
R-Square	(R) Numeric
Basic trend	(BT) Numeric
Recent trend	(RT) Numeric

Figure 2. System architecture

The criteria for selecting data characteristics include a desire that any input be measurable, in an attempt to avoid discrepancies that may occur if the time series feature is heavily dependent on judgement. The feature should also be readily available and calculated directly from the data, a consideration most important to the practitioner. In addition, the conclusion of the forecasting literature on factors that in¯uence model selection guide the development of the criteria. Lastly, any set of time series characteristics should be manageable with respect to the number of features considered. Based on the above criteria, a set of six distinguishing features of time series data is proposed:

(1)  Length of the time series. This is measured by the number of observations for the data series that is used to estimate the parameters of the model. The length does not include the ex-ante sample size that is used for assessing forecast accuracy.

(2)  Time period between observations. The data is categorized according to three time period speci®cations, monthly, quarterly, or yearly.

(3)  Type of time series data. This classi®cation represents the source of the data and the level of aggregation and is represented by four categories identi®ed as micro level, macro level, industry-speci®c, and demographic data.

(4)  Basic trend. The basic trend for the time series, as measured by the slope of the time series regression model.

(5)  Recent trend. This feature is concerned with the trend of the time series for the most recent observations. A recent trend is indicated by the slope of the time series regression model ®tted to the last one third of the data series.

(6)  Variability of the series. This is an indication of the stability of the series and is measured by the value of R-squared from the ®tted regression model.

The values of the variables that represent the set of time series characteristics are computed for the given data set for which an accurate forecast is desired. The values of these variables for the given data set are the input for Phase 2 of the model selection and forecasting system. Phase 2 contains the neural network engine with the value of the input neurons as speci®ed from Phase 1. A two-stage approach is utilized for the training and testing of the neural network. This two-stage neural network architecture is discussed in the following section.

The ®nal phase of the model selection and forecasting system (Phase 3) is the selection by the neural network of a forecast model, chosen from the models under consideration, that appears to be best suited for the data series. A set of possible forecasting models (the output neurons) are selected according to the following criteria. First, the methods should be well established and extensively studied in the literature. Second, the models are readily available and commonly used

Table II. Forecasting groups and methods

Group 1 (GRP1)	(HOL) Holt 2 Parameter Linear ES (WIN) Winter 3 Parameter ES (BRT) Brown (Triple) ES
Group 2 (GRP2)	(BRD) Brown (Double) ES (LIN) Linear Regression (AES) Adaptive Response ES
Group 3 (GRP3)	(NAI) Naive Deseasonalized (SES) Single ES (SMA) Simple Moving Average

in practice. Third, the models should require a minimal degree of user intervention in the parameter selection and estimation phase. Fourth, the models should represent a robust cross-section of forecasting procedures. Based on these criteria nine forecasting models are selected as possible candidates (Table II). The list of forecasting methodologies is not intended to be exhaustive, but rather a reasonable set of methodologies that re¯ect the selection criteria discussed above and manageable within the training and testing procedures of the neural network.