Ts Final Exam Practice Problems Forecast Variance
Terms: Forecast vs Forecast Error We clarify the terms used in the practice problems and the final exam problems. Some statisticians speak of the standard deviation or variance of the forecast. The forecast here is the distribution of future values. It is a random variable, which has a standard error (standard deviation and variance). Other statisticians use the term forecast for the mean of the distribution of future values. The forecast error (the error term in the forecast) is the distribution of future values minus its mean. Using these terms: ! The forecast is a scalar with a non-zero value (unless the forecasted value is zero). ! The forecast error is a random variable with a mean of zero and a non-zero standard error. The final exam problems may use either view. The meaning is clear from the context.
Objectives Actuaries forecast loss costs, mortality rates, reserves, and other values. We want a measure of the quality of the forecast. Illustration: An actuary uses a time series to estimate the average claim severity next year as $10,000. We use this forecast to set rates for auto insurance policies. The procedure used to estimate the future average claim severity may be unbiased, bu the actual claim severity next year will not be exactly $10,000. If the actuary’s estimate is a normal distribution with a mean of $10,000 and a standard deviation of $500, we are 95% confident that the true average claim severity will lie between $9,000 and $11,000. We rely on the actuary’s estimate to set rates for next year. If the actuary’s estimate is a normal distribution with a mean of $10,000 and a standard deviation of $5,000, we are 95% confident that the true average claim severity will lie between zero and $20,000. The actuary’s estimate is less persuasive. To set rates for next year, we may rely on industry averages or the rates of a major competitor. The standard error of the forecast also indicates whether a high or low future value reflects random fluctuation
Objectives Actuaries forecast loss costs, mortality rates, reserves, and other values. We want a measure of the quality of the forecast. Illustration: An actuary uses a time series to estimate the average claim severity next year as $10,000. We use this forecast to set rates for auto insurance policies. The procedure used to estimate the future average claim severity may be unbiased, bu the actual claim severity next year will not be exactly $10,000. If the actuary’s estimate is a normal distribution with a mean of $10,000 and a standard deviation of $500, we are 95% confident that the true average claim severity will lie between $9,000 and $11,000. We rely on the actuary’s estimate to set rates for next year. If the actuary’s estimate is a normal distribution with a mean of $10,000 and a standard deviation of $5,000, we are 95% confident that the true average claim severity will lie between zero and $20,000. The actuary’s estimate is less persuasive. To set rates for next year, we may rely on industry averages or the rates of a major competitor. The standard error of the forecast also indicates whether a high or low future value reflects random fluctuation