All the algorithms are based on the Kalman filter which is not proprietary. However, some of the variations we come up with are proprietary. Explanation of the Kalman filter can be found in the outside literature. One of the books I found useful while implementing the predict command is "An Introduction to State Space Time Series Analysis" by Commandeur-Koopman.
Local Level (LL): this a univariate model with no trends and no seasonaility. Seasonal Local Level (LLP): this is a univariate model with seasonality. The periodicity of the time series is automatically computed.
Local Level Trend (LLT): this is a univariate model with trend but no seasonality.
Bivariate Local Level (LLB): this is a bivariate model with no trends and no seasonality.
The lower 95 and upper 95 specifies a confidence interval in which we expect 95% of the predictions to fall.
Most of the time SOME of the predictions will fall outside the confidence interval. That is normal because 1. the confidence interval does not cover 100% of the predictions and 2. the confidence interval is about a probabilistic expectation and things don't match the expectation exactly.
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