Functional data model

Functional data model of mortality or fertility rates as a function of age. FDM() returns a functional data model applied to the formula's response variable as a function of age.

Usage

FDM(formula, order = 6, ts_model_fn = fable::ARIMA, coherent = FALSE, ...)

Arguments

formula

Model specification.

order

Number of principal components to fit.

ts_model_fn

Univariate time series modelling function for the coefficients. Any model that works with the fable package is ok. Default is fable::ARIMA().

coherent

If TRUE, fitted models are stationary, other than for the case of a key variable taking the value geometric_mean. This is designed to work with vitals produced using make_pr(). Default is FALSE. It only works when ts_model_fn is ARIMA().

...

Not used.

Value

A model specification.

References

Hyndman, R. J., and Ullah, S. (2007) Robust forecasting of mortality and fertility rates: a functional data approach. Computational Statistics & Data Analysis, 5, 4942-4956. https://robjhyndman.com/publications/funcfor/

Hyndman, R. J., Booth, H., & Yasmeen, F. (2013). Coherent mortality forecasting: the product-ratio method with functional time series models. Demography, 50(1), 261-283. https://robjhyndman.com/publications/coherentfdm/

Author

Rob J Hyndman

Examples

hu <- norway_mortality |>
  dplyr::filter(Sex == "Female", Year > 2010) |>
  smooth_mortality(Mortality) |>
  model(hyndman_ullah = FDM(log(.smooth)))
report(hu)
#> Series: .smooth 
#> Model: FDM 
#> Transformation: log(.smooth) 
#> 
#> Basis functions
#> # A tibble: 111 × 8
#>     Age  mean    phi1   phi2    phi3  phi4    phi5    phi6
#>   <dbl> <dbl>   <dbl>  <dbl>   <dbl> <dbl>   <dbl>   <dbl>
#> 1     0 -6.27 -0.0449 0.0255  0.201  0.204 -0.127  -0.201 
#> 2     1 -8.55  0.145  0.138   0.114  0.168 -0.552  -0.0761
#> 3     2 -9.03  0.149  0.0988  0.0483 0.186 -0.425  -0.105 
#> 4     3 -9.25  0.131  0.122  -0.0698 0.187 -0.213   0.0107
#> 5     4 -9.36  0.0949 0.136  -0.174  0.189 -0.0671  0.127 
#> # ℹ 106 more rows
#> 
#> Coefficients
#> # A tsibble: 12 x 8 [1Y]
#>    Year  mean  beta1   beta2  beta3  beta4    beta5   beta6
#>   <int> <dbl>  <dbl>   <dbl>  <dbl>  <dbl>    <dbl>   <dbl>
#> 1  2011     1  2.11  -0.0369 0.245  -0.295  0.252    0.0308
#> 2  2012     1  0.326  0.276  0.0759  1.14  -0.00489 -0.0688
#> 3  2013     1  0.137  0.241  0.668   0.472 -0.0588   0.130 
#> 4  2014     1 -0.855  0.164  0.651  -0.153  0.418   -0.0757
#> 5  2015     1 -0.602 -0.0649 0.798  -0.383 -0.214    0.205 
#> # ℹ 7 more rows
#> 
#> Time series models
#>    beta1 : ARIMA(0,0,0) 
#>    beta2 : ARIMA(0,0,0) 
#>    beta3 : ARIMA(1,0,0) 
#>    beta4 : ARIMA(0,0,0) 
#>    beta5 : ARIMA(0,0,0) 
#>    beta6 : ARIMA(1,0,0) 
#> 
#> Variance explained
#>   32.84 + 27.94 + 19.04 + 14.39 + 2.91 + 1.14 = 98.25%
autoplot(hu)