摘要:

AbstractCredibility models in actuarial science deal with multiple short time series where each series represents claim amounts of different insurance groups. Commonly used credibility models imply shrinkage of group‐specific estimates towards their average. In this paper we model the claim sizeyuin groupiand at timetas the sum of three independent components:yit= μr+ δi+ ϵit. The first component, μt= μt−1+mt, represents time‐varying levels that are common to all groups. The second component, δi, represents random group offsets that are the same in all periods, and the third component represents independent measurement errors. In this paper we show how to obtain forecasts from this model and we discuss the nature of the forecasts, with particular emphasis on shrinkage. We also assess the forecast improvements that can be expected from such a model. Finally, we discuss an extension of the above model which also allows the group offsets to change over time. We assume that the offsets for different groups follow independent r

ISSN:0277-6693    

DOI:10.1002/for.3980120102

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractTime‐series data are often contaminated with outliers due to the influence of unusual and non‐repetitive events. Forecast accuracy in such situations is reduced due to (1) a carry‐over effect of the outlier on the point forecast and (2) a bias in the estimates of model parameters. Hillmer (1984) and Ledolter (1989) studied the effect of additive outliers on forecasts. It was found that forecast intervals are quite sensitive to additive outliers, but that point forecasts are largely unaffected unless the outlier occurs near the forecast origin. In such a situation the carry‐over effect of the outlier can be quite substantial. In this study, we investigate the issues of forecasting when outliers occur near or at the forecast origin. We propose a strategy which first estimates the model parameters and outlier effects using the procedure of Chen and Liu (1993) to reduce the bias in the parameter estimates, and then uses a lower critical value to detect outliers near the forecast origin in the forecasting stage. One aspect of this study is on the carry‐over effects of outliers on forecasts. Four types of outliers are considered: innovational outlier, additive outlier, temporary change, and level shift. The effects due to a misidentification of an outlier type are examined. The performance of the outlier detection procedure is studied for cases where outliers are near the end of the series. In such cases, we demonstrate that statistical procedures may not be able to effectively determine the outlier types due to insufficient information. Some strategies are recommended to reduce potential difficulties caused by incorrectly detected outlier types. These findings may serve as a justification for forecasting in conjunction with judgment. Two real examples are employed to illustrate the issues

ISSN:0277-6693    

DOI:10.1002/for.3980120103

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents some procedures aimed at helping an applied time‐series analyst in the use of power transformations. Two methods are proposed for selecting a variance‐stabilizing transformation and another for bias‐reduction of the forecast in the original scale. Since these methods are essentially model‐independent, they can be employed with practically any type of time‐series model. Some comparisons are made with other methods currently available and it is shown that those proposed here are either easier to apply or are more general, with a performance similar to or better than other competing p

ISSN:0277-6693    

DOI:10.1002/for.3980120104

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractA linear regression model with random walk coefficients is extended to allow for linear restrictions between the coefficients to be satisfied at each point in time. Estimation in this model is shown to be no more involved than estimation in the standard model. It is also demonstrated how, after a slight modification to the testing problem, classical test procedures may be applied to the problem of testing for such restrictions. The performance of the Lagrange Multiplier test for a variety of different restrictions is then investigated via simulation. An empirical application involving testing for homogeneity in a random walk coefficient version of the AIDS model is given.

ISSN:0277-6693    

DOI:10.1002/for.3980120105

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractWe examine the implications of allowing lags into forecast combination regressions, thereby extending previous models. The practical conclusion is that lagged dependent variables, but not lagged forecasts, improve forecast combination procedures. Also, improvements are obtained when nonstationarity of the data is recognized.

ISSN:0277-6693    

DOI:10.1002/for.3980120106

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this study the interaction of forecasting method (econometric versus exponential smoothing) and two situational factors are evaluated for their effects upon accuracy. Data from two independent sets ofex antequarterly forecasts for 19 classes of mail were used to test hypotheses. Counter to expectations, the findings revealed that forecasting method did not interact with the forecast time horizon (short versus long term). However, as hypothesized, forecasting method interacted significantly with product/market definition (First Class versus other mail), an indicator of buyer sensitivity to marketing/environmental changes. Results are discussed in the context of future research on forecast accuracy.

ISSN:0277-6693    

DOI:10.1002/for.3980120107

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY

ISSN:0277-6693    

DOI:10.1002/for.3980120101

出版商:John Wiley&Sons, Ltd.    

年代:1993

数据来源: WILEY