Average Forecast Error Research Articles

Modeling Daily Milk Yield in Holstein Cows Using Time Series Analysis

Time series analysis of milk yield data collected three times daily was used to create stochastic models for short-term forecasting of milk production. These models can be used in systems for automated registration of daily milk weights. Analyses were carried out on partial or complete lactation yield data from 513 lactations. Time series analysis showed that the exponential smoothing function was most appropriate to model both individual milking and daily yield data. Model parameters were influenced by parity, stage of lactation, occurrence of missed milkings, and treatment for diseases. The model to forecast daily total yield performed equally well as the model to forecast individual-milking yield, since the variance of the residual errors of the forecast daily production was similar to the sum of the variances of the forecast errors of the individual milkings.Average parameter values from heifers and multiparous cows not treated for diseases, and without missing milk weights, were estimated and used to forecast next day milk yield. Average forecast errors preceding disease diagnosis showed a sudden production decline in the case of clinical mastitis and a gradual production decrease in the case of clinical ketosis. Therefore, separate screening tests are needed when screening for these diseases with daily milk weight systems.

Forecasting with combined seasonal indices

Traditional methods of forecasting the demand for products that exhibit a seasonal pattern call for estimation of the seasonal component based on the history of demands for that particular product. It is proposed that the seasonal estimation would be more accurate if the demands for similar products were first combined into a product line. Seasonal indices calculated for the product line would then be used as the estimate of the seasonal component for each of the products. A demonstration of the technique with six product lines shows that combined indices reduce average forecast errors. Reductions of 2–20% are shown for the total mean squared errors for the product lines.

The interpretation and use of economic predictions

Treasury forecasts, both published and unpublished, of GDP and retail prices are analysed with reference to average absolute forecast errors and a benchmark index of variation. Forecasts of both GDP and the RPI looking two years ahead have become more accurate since the early 1970s, but there has been no marked improvement in one year ahead forecasts. The accuracy of annualized forecasts of GDP improves, and that of the RPI forecasts deteriorates, as the forecast time horizon is progressively extended from one to eight quarters ahead. Some evidence of forecast bias is presented ; in the period up to 1979, GDP tended to be over-predicted, and inflation under-predicted. Since 1980 this pattern has been reversed. Analysis of Treasury forecasts and an average of U. S. forecasts shows them to be about equally accurate. The role of forecasts in the implementation of economic policy is discussed. Systematic model-based forecasts provide a consistent framework of analysis, which can improve the operation of economic policy. But prediction errors, and the inertia of the economy, imply that there is only limited scope for discretionary, forecast-based, stabilization policy. Under the medium term financial strategy, MTFS, the policy emphasis has shifted to the medium term. The forecasts have been used to articulate assumptions for output, inflation and money GDP, and to provide the tax and expenditure framework behind the illustrative path of the PSBR. Without the forecasts, the conduct of monetary and fiscal policy would have been considerably more difficult. The paper concludes that, while reductions in the forecast errors of short-term forecasts may be difficult to achieve, there is hope that the accuracy of longer-term forecasts may continue to improve.

Aggregating Subjective Forecasts: Some Empirical Results

The impact on forecast accuracy of aggregating the subjective forecasts of up to 13 individuals was examined for five forecast weighting methods—equal weighting, two ex post methods that took advantage of prior information about the individuals' relative accuracy, and two ex ante methods based on objective and subjective assessments of relative accuracy. The individuals were executives, managers and sales personnel employed by Time. Inc., and the variable forecasted was the number of advertising pages sold annually by Time magazine over a 14-year period. The results show that both the average forecast error and the variance of the error decrease as additional individuals' forecasts are included in the aggregate. Only two to five individuals' forecasts must be included to achieve much of the total improvement available from combining all 13 forecasts. Three of the differential weighting methods produced more accurate forecasts than equal weighting, but the magnitude of the improvement was small. Implications for realistic forecasting situations are discussed, as are conditions under which the use of aggregates seems attractive.

Econometric and Computational Issues in Estimating Demand for Energy by Time-of-Day

A two-step time-series and cross-section model is used to estimate time-of-day (TOD) demand for electricity or natural gas and to demonstrate an efficient computational method. Post-sample validation of the model results in several regions found average forecast errors in the aceptable range of 4.5% to 15%. Future hourly electricity-demand forecasts made for 32 regions using an historical trend scenario and a Data Resources Inc. macro model scenario indicate a good potential for the model. 12 references. (DCK)

A Robust Sequential Projection Algorithm for Traffic Load Forecasting

Forecasts of busy season trunk group traffic loads are required for planning the Bell System's message network. Forecasting algorithms currently in use obtain estimates of future loads by multiplying the most recent measurement of busy season load by an aggregate growth factor. Because of statistical errors in measured loads and differences between individual trunk group and aggregate growth factors, the resulting forecasts can have large statistical errors. In this paper we extend earlier work to develop a new algorithm, called the sequential protection algorithm (SPA), based on a linear two-state Kalman filter, together with logic for detecting and responding to unusually large measurement errors or changes in trend. In typical applications of Kalman filtering, the statistics of system noises, measurement errors, and initial conditions are known and the filter parameters (Kalman gains) are selected accordingly. For our application, however, these statistics cannot be determined without error. Consequently, we develop a method for selecting robust filter parameters which provide improved performance, independent of system noises, measurement errors, and initial conditions. In particular, under the assumption of linear growth for 5-year intervals, the average rms 1-year forecast error of SPA is about 10 percent less than that of the existing algorithms. Field test results confirm the theoretical results presented here. Accordingly, specifications have been written for inclusion of SPA in the Bell System's standard trunk forecasting systems.

An experiment on the modification procedures of seasonal factors in exponential smoothing models

Abstract Adapting to changes over time is a primary point in any forecasting system. The quicker the adaptation the better the resulting forecasts. This is very important in computerized forecast-inventory control systems that manage thousands of parts. In such environments, it is difficult, if not impossible, to have all forecasts reviewed for possible changes in behaviour. This paper proposes two modifications to Winters' exponentially weighted moving-average model that provides improved forecasts for time series exhibiting seasonal behaviour. A set of tests is conducted to evaluate the performance of the original and modified Winters s models using 25 time series. The results indicate that average forecast errors have been reduced for the test series. The paper concludes with a discussion of the suitability of the proposed modifications under certain conditions.

THE APPLICATION OF A DYNAMIC FORECASTING MODEL WITH INVENTORY CONTROL PROPERTIES

This article summarizes the application of a forecasting model. Forecasts are made of monthly sales of products which do not change in style on an annual basis. The model is an exponential smoothing model. Adjustments of the parameters of the model are made whenever the average forecast error over the previous four periods is too large to be explained solely by unassignable causes. The efficiency gained in using the model is measured by the ratio of the standard deviation of the forecast errors to the standard deviation of sales. If this ratio is less than one, then the safety stock level that is carried for a given product can be reduced if sales are forecasted with the model and the standard deviation of the forecast errors is used to determine the safety stock level. The net effect is the reduction in the cost of carrying safety stocks. The results of the proposed model are also compared to a similar set of results generated from a basic, exponential model.

Application of Economic Analyses to Hurricane Warnings to Residential and Retail Activities In the U.S. Gulf of Mexico Coastal Region

Abstract Hurricane warnings cause people and businesses in the predicted path of the cyclone to take actions that will reduce damage and/or loss of life. Sometimes these actions and their attendant costs are avoidable, since a larger section of the coast is alerted than that which the hurricane actually affects. Using general population densities and the average damage costs due to storms, the authors present a combined game- and decision-theory approach to estimating the economic benefits of more accurate prediction. The potential savings to this economic sector for a substantial improvement in 24-hr forecasting accuracies (that is, the reduction of the average forecast error to one-half its present value) is shown to be at least $15.2 million in the first year. A general equation is presented for various combinations of improvement levels, population densities, percentage of those who protect, and number of warnings per season.

Sales Forecasting Errors and Inventory Fluctutions: Random Errors and Random Sales

The purpose of this paper is to study the effects of errors in the sales forecast on inventory changes and production rates. This is done by computing the ratio of the standard deviation of inventory change or production rate to the standard deviation of sales rate. By use of this ratio the effects of the average forecast error, the variance of the forecast error, and the serial correlation of sales can be studied. Both analytical method and simulation procedures are used.