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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