By Rob J. Hyndman ... [et al.]
Exponential smoothing equipment were round because the Fifties, and are the most well-liked forecasting equipment utilized in company and undefined. This booklet brings jointly numerous effects at the nation house framework for exponential smoothing. it truly is of curiosity to humans eager to practice the tools of their personal region of interest.
Basic techniques --
Getting began --
Linear concepts kingdom house types --
Nonlinear and heteroscedastic options kingdom house types --
Estimation of concepts nation area versions --
Prediction distributions and durations --
Selection of types --
Normalizing seasonal parts --
Models with regressor variables --
Some homes of linear versions --
Reduced types and relationships with ARIMA versions --
Linear techniques country house types with random seed states --
Conventional country house versions --
Time sequence with a number of seasonal styles --
Nonlinear types for optimistic information --
Models for count number information --
Vector exponential smoothing --
Inventory keep an eye on functions --
Conditional heteroscedasticity and purposes in finance --
Economic functions : the Beveridge-Nelson decomposition --
Author index --
Data index --
Read or Download Forecasting with exponential smoothing : the state space approach PDF
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Extra resources for Forecasting with exponential smoothing : the state space approach
1b) where r (·) and w(·) are scalar functions, f (·) and g (·) are vector functions, and ε t is a white noise process with variance σ2 . , when the series contains only non-negative values). Nevertheless, the Gaussian assumption is often a reasonable approximation when the level of the process is sufﬁciently far from the origin (or, more generally, the region of impossible values) and it will then be convenient to use the Gaussian assumption as a basis for inference. The functions in this model may all be time-indexed, but we shall concentrate on constant functions (the invariant form), albeit with time-varying arguments.
8) j =0 where dt = w F t−1 x0 , k0 = 1 and k j = w F j−1 g for j = 1, 2, . . Thus, the observation is a linear function of the seed state x0 and past and present errors. 8); this is an example of a ﬁnite Wold decomposition (Brockwell and Davis 1991, p. 180). 38 3 Linear Innovations State Space Models The model is described as stationary2 if ∞ ∑ |k j | < ∞ and j =0 lim dt = d. 8) converge rapidly to zero, and the impact of the seed state vector diminishes over time. We may then consider the limiting form of the model, corresponding to the inﬁnite start-up assumption.
Speciﬁcally, a forecastable model has the properties ∞ ∑ |c j | < ∞ j =1 and lim at = a. 3 Model Properties 37 Our deﬁnition of forecastability allows the initial state x0 to have an ongoing effect on forecasts, but it prevents observations in the distant past having any effect. In most cases, a = 0, but not always; an example with a = 0 is given in Sect. 2. 7) to hold is that the eigenvalues of D lie inside the unit circle. In this case, D j converges to a null matrix as j increases. This is known as the “stability condition” and such models are called stable.