The multiplicative model is:
Term | Description |
---|---|
L_{t} | level at time t, α is the weight for the level |
T_{t} | trend at time t, |
γ | weight for the trend |
S_{t} | seasonal component at time t |
δ | weight for the seasonal component |
p | seasonal period |
Y_{t} | data value at time t |
fitted value, or one-period-ahead forecast, at time t |
Term | Description |
---|---|
L_{t} | level at time t, α is the weight for the level |
T_{t} | trend at time t, |
γ | weight for the trend |
S_{t} | seasonal component at time t |
δ | weight for the seasonal component |
p | seasonal period |
Y_{t} | data value at time t |
fitted value, or one-period-ahead forecast, at time t |
Winters' method employs a level component, a trend component, and a seasonal component at each period. It uses three weights, or smoothing parameters, to update the components at each period. Initial values for the level and trend components are obtained from a linear regression on time. Initial values for the seasonal component are obtained from a dummy-variable regression using detrended data.
Winters' Method uses the level, trend, and seasonal components to generate forecasts. Winters' Method also uses data up to the forecast origin time to generate the forecasts.
Term | Description |
---|---|
L_{t} | level |
T_{t} | trend at time t |
Term | Description |
---|---|
S_{t} + m −p | seasonal component for the same period from the previous year |
Mean absolute percentage error (MAPE) measures the accuracy of fitted time series values. MAPE expresses accuracy as a percentage.
Term | Description |
---|---|
y_{t} | actual value at time t |
fitted value | |
n | number of observations |
Mean absolute deviation (MAD) measures the accuracy of fitted time series values. MAD expresses accuracy in the same units as the data, which helps conceptualize the amount of error.
Term | Description |
---|---|
y_{t} | actual value at time t |
fitted value | |
n | number of observations |
Mean squared deviation (MSD) is always computed using the same denominator, n, regardless of the model. MSD is a more sensitive measure of an unusually large forecast error than MAD.
Term | Description |
---|---|
y_{t} | actual value at time t |
fitted value | |
n | number of observations |