This week, we're gonna talk about exponential smoothing, which is some of the most successful forecasting ways to generate reliable forecasts for a wide range of time-series data. ETS essentially is that we give more weight to the most recent observations, and then the weights will be decaying exponentially. That is, the most recent observations will contain more information.
An example would be the stock price yesterday contains more information as compared to the stock price two days ago
we will look at three types of forecasting models based on
a series with no trend or seasonality → (Simple Exponential Smoothing)
a series with the trend but no seasonality → (Holt's linear trend methods, damped trend methods)
a series with both trend and seasonality → (Holt-Winters’ seasonal method, HoltWinters’ Multiplicative method, HoltWinters’ additive method)
Simple forecasting smoothing
Before introducing Simple forecasting smoothing, you need to know about what Average and Naive methods are :
AVG : All observations are equally weighted
when we were using average method we say that the forecast for the future it is the average of all the values in the time series that is we said that our time series.
that is, we do not distinguish between the previous observation the observation before that or the last observation we give them equal weights
NAIVE : The last observation contains all information; previous observation provides no information, so all weight is given to the last information.
our forecast for the future is whatever observation we observed in the previous period, that is whatever we observed the last time and any information contained in the observation before that observation is zero
that is, only the last observation contains all the information and we can use that information to forecast.
Not being too extreme, Simple forecasting smoothing is lying between the method of AVG and Navie; most recent data should have more weight.
It is suitable for forecasting a series with no trend or seasonality.
Simple Exponential Smoothing (SES)
Used when you don’t know the trend and seasonality.
What is Smoothing params? (??)
Smoothing params controls the rate of change of the components, which are .
Holt's linear trend methods may have a problem of over forecasting in this case, so sometimes it makes more sense if we can dampen this forecast and say that the trend is gonna keep increasing in the same direction, but just gonna keep dampening as we move in time.
That is, it will not be as aggressive as it was, showing recently that is for the long time horizon the trend will be a little bit smaller in slope as compared with the trend that we are observing for our near forecasts
so to do that, we can introduce another parameter phi and now all of our three equations will contain these five parameters.
What will the model be in long run?
In short run, forecasts are trending, but in long run, the forecast remains constant.
WDYM by constant in a trend ?
if the trend is increasing, it will keep on increasing the trend
Holt-Winters’ seasonal method
This method extended Holt’s method to capture seasonality.
Holt-Winters’ seasonal additive method
Holt-Winters’ seasonal multiplicative method
ETS
ETS has 2 meaning 1) ExponenTial Smoothing; 2) Error Trend Seasonality (i.e., state)
fit <- global_economy %>%
mutate(Pop = Population / 1e6) %>%
model(ets = ETS(Pop))
fit %>%
forecast(h = 5)
R interpretation
alpha :
here in this case is optimal value (You need to compare to know).
The smoothing parameter is 0.322, which is pretty big so that means it's moving the intercept pretty quickly to changes in the data. Which is appropriate given the amount of movement that we saw in the data
L_Not : Initial level we talked before
Not the first value nor the mean.
was computed by optimizing for the minimal sum of squared errors.
it's wherever the general location of the data is at that point, which is 100647 here
