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- The Lee–Carter model is a numerical algorithm used in mortality forecasting and life expectancy forecasting. The input to the model is a matrix of age specific mortality rates ordered monotonically by time, usually with ages in columns and years in rows. The output is a forecasted matrix of mortality rates in the same format as the input. The model uses singular value decomposition (SVD) to find:
* A univariate time series vector that captures 80–90% of the mortality trend (here the subscript refers to time),
* A vector that describes the relative mortality at each age (here the subscript refers to age), and
* A scaling constant (referred to here as but unnamed in the literature). Surprisingly, is usually linear, implying that gains to life expectancy are fairly constant year after year in most populations. Prior to computing SVD, age specific mortality rates are first transformed into , by taking their logarithms, and then centering them by subtracting their age-specific means over time. The age-specific mean over time is denoted by . The subscript refers to the fact that spans both age and time. Many researchers adjust the vector by fitting it to empirical life expectancies for each year, using the and generated with SVD. When adjusted using this approach, changes to are usually small. To forecast mortality, (either adjusted or not) is projected into future years using an ARIMA model. The corresponding forecasted is recovered by multiplying by and the first diagonal element of S (when ). The actual mortality rates are recovered by taking exponentials of this vector. Because of the linearity of , it is generally modeled as a random walk with trend. Life expectancy and other life table measures can be calculated from this forecasted matrix after adding back the means and taking exponentials to yield regular mortality rates. In most implementations, confidence intervals for the forecasts are generated by simulating multiple mortality forecasts using Monte Carlo Methods. A band of mortality between 5% and 95% percentiles of the simulated results is considered to be a valid forecast. These simulations are done by extending into the future using randomization based on the standard error of derived from the input data. (en)
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- The Lee–Carter model is a numerical algorithm used in mortality forecasting and life expectancy forecasting. The input to the model is a matrix of age specific mortality rates ordered monotonically by time, usually with ages in columns and years in rows. The output is a forecasted matrix of mortality rates in the same format as the input. The model uses singular value decomposition (SVD) to find: Many researchers adjust the vector by fitting it to empirical life expectancies for each year, using the and generated with SVD. When adjusted using this approach, changes to are usually small. (en)
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