SARIMA and Box-Jenkins
1. SARIMA and Box-Jenkins
You've come very far, but there are a few last tricks that will help you when you are dealing with seasonal forecasts.2. Box-Jenkins
We previously covered the Box-Jenkins method for ARIMA models. We go through identification of the model order; estimating or fitting the model; diagnosing the model residuals; and finally production. For SARIMA models the only step in the method which will change is the identification step.3. Box-Jenkins with seasonal data
At the identification step we add the tasks of determining whether a time series is seasonal, and if so, then finding its seasonal period. We also need to consider transforms to make the seasonal time series stationary, such as seasonal and non-seasonal differencing and other transforms.4. Mixed differencing
Sometimes we will have the choice of whether to apply seasonal differencing, non-seasonal differencing or both to make a time series stationary. Some good rules of thumb are that you should never use more than one order of seasonal differencing, and never more than two orders of differencing in total. Sometimes, like in this example, you will be able to make a time series stationary by using either one seasonal difference or one non-seasonal difference. You might build models for each in this case, and see which one makes better predictions.5. Weak vs strong seasonality
This time series only has a weak seasonality, meaning the seasonal oscillations don't always look the same and are harder to identify. When you have a strong seasonal pattern, like the time series on the right, you should always use one order of seasonal differencing. This this will ensure that the seasonal oscillation will remain in your dynamic predictions far into the future without fading out.6. Additive vs multiplicative seasonality
Just like in ARIMA modeling sometimes we need to use other transformations on our time series before fitting. Whenever the seasonality is additive we shouldn't need to apply any transforms except differencing. Additive seasonality is where the seasonal pattern just adds or takes away a little from the trend. When the seasonality is multiplicative, the SARIMA model can't fit this without extra transforms. If the seasonality is multiplicative the amplitude of the seasonal oscillations will get larger as the data trends up or smaller as it trends down. To deal with this we take the log transform of the data before modeling it.7. Multiplicative to additive seasonality
This is the same time series before and after transform. In the figure on the right we have taken the log of the data and so we have transformed the seasonality to make it additive. We can now model this using a normal SARIMA model with seasonal differencing.8. Let's practice!
Now that you know how to make seasonal forecast models, lets go into the last exercises where you can bring all these skills together to make far future predictions.Create Your Free Account
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