Example (US population, millions).
In R
> ## Non-Seasonal Holt-Winters
> x <- uspop
>
> ## Exponential Smoothing
> m2 <- HoltWinters(x, alpha = 0.9999208, gamma = FALSE, beta = FALSE)
> print(m2$fitted)
Time Series:
Start = 1800
End = 1970
Frequency = 0.1
xhat level
1800 3.930000 3.930000
1810 5.309891 5.309891
1820 7.239847 7.239847
1830 9.639810 9.639810
1840 12.899742 12.899742
1850 17.099667 17.099667
1860 23.199517 23.199517
1870 31.399351 31.399351
1880 39.799335 39.799335
1890 50.199176 50.199176
1900 62.898994 62.898994
1910 75.998962 75.998962
1920 91.998733 91.998733
1930 105.698915 105.698915
1940 122.798646 122.798646
1950 131.699295 131.699295
1960 151.298448 151.298448
1970 179.297782 179.297782