Recreation scientists have used a variety of forecasting techniques during the past decades (Archer, 1994; Uysal & Crompton, 1985). Cummings and Busser (1994) note that the formulation, interpretation, and evaluation of forecasts are critical skills for recreation and park managers.
Quantitative forecasting methods may be classified into two categories: causal methods (e.g., regression and structural models) and time series methods (e.g., basic, intermediate, and advanced extrapolative methods). Causal methods establish methodologies for identifying relationships between dependent and independent variables and attempt to incorporate the interdependencies of various variables in the real world. However, the most common difficulty of applying the causal methods is identifying the independent variables that affect the forecast variables. Thus, the reliability of final forecast outputs depends on the quality of other variables (Uysal & Crompton, 1985).
Time series quantitative methods offer many advantages. Box, Jenkins, and Reinsel (1994) point out that "the use at time t of available observations from a time series to forecast its value at some future time t + 1 can provide a basis for (1) economic and business planning, (2) production planning, (3) inventory and production control, and (4) control and optimization of industrial processes" (p. 2). Time series methods offer concepts and techniques that facilitate specification, estimation, and evaluation; often yielding more accurate forecasting results than causal quantitative approaches (Witt & Witt, 1995). The most important assumption of the time series methods is that the observations made at different time points are statistically dependent. Accurate forecasts made using suitable time series methods and based on appropriate data from the recreation industry may yield benefits in destination marketing and the scheduling of resources (Cummings & Busser, 1994).
The overall purpose of this study is to assess various means of visitation forecasting. We specifically focus on the methodological issues surrounding forecasts of recreation use with seasonal patterns. We begin by providing an overciew of forecasting methods. We follow this with an empirical application to visitation data at the Milwaukee County Zoo. According to Moore (1989), "seasonality refers to movements in a time series during a particular time of year that recur similarly each year" (p. 49).
The research question is, what are the advantages and disadvantages of basic, intermediate, and advanced methods for visitor use forecasting where seasonality and limited data are characteristics of the estimation problem?
Specifications of Forecasting Models: A Review
Basic Extrapolative Methods
Naive 1. The naive 1 forecasting method simply states that the forecast value for this period (t) is equal to the obselazed value for the last period (t-1) (Makridakis, Wheelwright, & Hyndman, 1998) (Appendix A, Equation 1).
Naive 2. The naive 2 forecast for period t is obtained by multiplying the current visitor numbers with the growth rate between the previous visitation in time period, t-1, and the current visitation figures in time period, t (Makridakis et al., 1998; Newbold & Bos, 1994) (Appendix A, Equation 2).
Single moving average (SMA) with decomposition. Based on adding the previous observations together and dividing by the number of observations, the single moving average method uses the resulting average figures to forecast future values. One assumption of the SMA method is that all selected previous data points have the same weight on the forecast value (Kendall, Stuart, & Ord, 1983; Makridakis et al., 1998). The major aim of the decomposition procedure is to distinguish the trend, cyclical, seasonal, and irregular factors (Baxter, 1994; Makridakis et al. …