Forecasts produced using exponential smoothing methods are weighted averages of past observations, with the weights decaying exponentially as the observations get older. In other words, the more recent the observation the higher the associated weight.
— Page 171, Forecasting: principles and practice, 2013.
A value close to 1 indicates fast learning (that is, only the most recent values influence the forecasts), whereas a value close to 0 indicates slow learning (past observations have a large influence on forecasts).
超参：
Alpha:smoothing factor for the level.
python实现
from statsmodels.tsa.holtwinters import SimpleExpSmoothing # prepare data data = ... # create class model = SimpleExpSmoothing(data) # fit model model_fit = model.fit(...) # make prediction yhat = model_fit.predict(...)
from statsmodels.tsa.holtwinters import ExponentialSmoothing # prepare data data = ... # create class model = ExponentialSmoothing(data, ...) # fit model model_fit = model.fit(...) # make prediction yhat = model_fit.predict(...)
4 三次指数平滑
三次指数平滑是指数平滑的扩展，它为单变量时间序列增加了对季节性的支持。
这种方法有时被称为 Holt-Winters 指数平滑法，以该方法的两位贡献者 Charles Holt and Peter Winters 的名字命名。
除了alpha和beta平滑因子外，还添加了一个新的参数 gamma，该参数控制对季节成分的影响。
与趋势一样，季节性也有加性（线性）或乘性（指数）过程。
加法季节性(additive seasonality):具有线性季节性的三次指数平滑。
乘法季节性(multiplicative seasonality):具有指数季节性的三次指数平滑。
三次指数平滑是指数平滑最先进的变体，通过参数配置，还可以建立双指数平滑模型和单指数平滑模型。
Being an adaptive method, Holt-Winter’s exponential smoothing allows the level, trend and seasonality patterns to change over time.
a more robust and objective way to obtain values for the unknown parameters included in any exponential smoothing method is to estimate them from the observed data.
the unknown parameters and the initial values for any exponential smoothing method can be estimated by minimizing the SSE [sum of the squared errors].
