In this paper a data analysis tool for analyzing highly correlated time series data is suggested. The main objective is to unify multiple time series into a single series and then apply a univariate method for the purpose of prediction. This method is essentially efficient for analyzing multiple time series with sparse data. Several time series data of relative demand for black and white television receivers in various countries are analyzed and quite accurate predictions are obtained.
KEY WORDS Box-Jenkins Multicollinearity Parallelism Saturation level Trend
Forecasting demand in world markets has become increasingly important due to the vast expansion of international trade. The high costs and risks involved in overseas operations make the accurate forecasting of demand indispensable. Such forecasts, however, are hard to achieve, partly due to the inherent complexities of these markets (Douglas and Craig, 1983; Moyer, 1968; Robock, Simmonds and Zwick, 1977).
One of the major technical problems in forecasting is the lack of sufficient time series data points. Data on the penetration level of a particular product usually entail only the sales levels for several preceding years. Unfortunately, such data are not sufficient for forecasting with methods presently available (e.g. the Box-Jenkins approach for univariate time series or the Tiao and Box (1981) approach for modeling multiple time series).
The utilization of additional related information, however, may help. For instance, several countries may share a similar diffusion pattern.' Similarity in diffusion suggests that consumer adoption behaviour is not different among these countries. Diffusion data taken from several countries may be used to predict demand in other countries. These countries may be located in the same geographical region (e.g. Europe) or there may be a time lag between the introduction of the product between two groups of countries (e.g. the U.S. and Europe, respectively). Similarities in adoption behaviour among several countries, thus, may produce several parallel time series ' Saturation and diffusion levels have the same meaning here, namely the proportions of families in the relevant market adopting the product.