Author: Wan, Sai-cheong
Title: The analysis of combined forecast
Degree: M.Sc.
Year: 1998
Subject: Forecasting
Electric power consumption -- China -- Hong Kong -- Forecasting
Tourism -- China -- Hong Kong -- Forecasting
Industries -- China -- Hong Kong -- Forecasting
Hong Kong Polytechnic University -- Dissertations
Department: Multi-disciplinary Studies
Pages: [6], 142 leaves : ill. 30 cm
Language: English
Abstract: In the last few decades, many methods were used for forecasting. Some may be optimal or suboptimal. They may use linear formulation or some other specific functional form. As there are so many choices, decisions have to be made on an appropriate forecasting method for the specific problem being considered. For the same series, different forecasting methods obviously tend to produce different forecasts. As forecasting methods are based on different philosophy and mechanism, their properties and performance differ from each other. As a result, a forecast from any method may provide some useful information that may not convey in forecasts from other methods. In most of the cases, we would like to forecast using all available information. It sounds attractive to aggregate information from different forecasting methods by combining forecasts. The combination of forecasts has been tried before. Different approaches for combining two or more forecasts into a composite forecast have been applied. Two important papers are Bates and Granger (1969) and Newbold and Granger (1974). Doyle and Fenwick (1976), Makridakis and Winkler (1983), Granger and Ramanthan (1984) continued combined forecast studies based on the two previous papers. 'By combining forecasting technique, we retain more insight than is obtainable from the use of any simple technique.'(Doyle and Fenwick 1976 p.63) 'In the case of the absence of one of the assumptions or erroneous data or other violations of the standard assumptions, it is important to consider the possibility of combining technique.' (Krasker 1980 p.1334) 'It is often better to combine sales forecasting methods than to select between them.' (Doyle and Fenwick. 1976 p.60) Doyle and Fenwick (1976) introduced the following three different approaches for combining forecast: 1. Averaging Simply average two or more forecasts for each period. 2. Historical weightings: This refers to weight the forecast based on the accuracy of past forecasting performance that best fits to past data. 3. Subjective weightings: The weight of the forecasts based on the forecaster's personal judgments on which methods more closely reflect the reality. In addition, Makridakis and Winkler (1983) used a weighted average based on the sample covariance matrix of fitting error. The idea behind is that the combined forecast can be improved by considering the accuracy of each method and the covariance between them. Unfortunately, they found that although this method was better than individual method, it was worse than simple average the forecasting methods. Furthermore, they also investigated empirically the impact of the number of forecasting methods to combine forecasting on simple averages. They concluded that the forecasting accuracy improves as the number of methods on the average increases. If there are available two sets of forecasts from two competing theories or information sets, then it has been known that a linear combination of the two forecasts can outperform both of them. In this project we extend previous discussion of the properties of the combined forecasts and show how the results be interpreted to provide a more accurate prediction. In this project, seven combined forecast methods are applied on two groups of preliminary forecasts. One group uses simple methods while the other group uses sophisticated methods. Simple methods do not take trend into account. However, after quadratic or exponential trend using regression is applied on simple methods, they can compete with sophisticated methods. Although it is not necessary that combined forecasts give out of sample forecast that are better than all its preliminaries, in most of cases, combined forecasts would not be worse than the worst of their individual preliminary forecasts. Moreover, it is found that combined forecasts using sophisticated preliminary forecasts need not be better than those using simple preliminary forecasts. Although simple methods do not take trend into account, the trend can be satisfactorily estimated simply using quadratic or exponential regression. This is especially advantageous when long term forecasts are required. The optimal number of preliminary forecasts used for combination is evaluated. It is found also that in most of cases, combinations that use two or three preliminary forecasts out perform combinations that use more than four preliminary forecasts although the latter sometimes give the better results. The best in sample year used is also evaluated and discussed. The conclusion is that the best in sample year used depends on individual time series. In general, the in sample year used should not be less than five years. It is better to use ten in sample year than fifteen as there may be a structural change within the series in the latter one.
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