Structural blocks for free-form seasonal trends and regressions

Creates the structure for a free-form seasonal (FFS) block with desired periodicity.

Usage

ffs_block(
  ...,
  period,
  sum.zero = FALSE,
  name = "Var.FFS",
  D = 1,
  h = 0,
  H = 0,
  a1 = 0,
  R1 = 4,
  monitoring = FALSE
)

ffs(period, D = 0.95, a1 = 0, R1 = 9, name = "Var.FFS", X = 1)

Arguments

...: Named values for the planning matrix.
period: Positive integer: The size of the seasonal cycle. This block has one latent state for each element of the cycle, such that the number of latent states n is equal to the period.
sum.zero: Bool: If true, all latent states will add to 0 and will have a correlated temporal evolution. If false, the first observation is considered the base line level and the states will represent the deviation from the baseline.
name: String: An optional argument providing the name for this block. Can be useful to identify the models with meaningful labels, also, the name used will be used in some auxiliary functions.
D: Vector or scalar: The values for the discount factors associated with the first latent state (the current effect) at each time. If D is a vector, it should have size t and it is interpreted as the discount factor at each observed time. If D is a scalar, the same discount will be used at all times.
h: Vector or scalar: A drift to be add after the temporal evolution (can be interpreted as the mean of the random noise at each time). If a vector, it should have size t, and each value will be applied to the first latent state (the one which affects the linear predictors) in their respective time. If a scalar, the passed value will be used for the first latent state at each time.
H: Vector or scalar: The values for the covariance matrix for the noise factor at each time. If a vector, it should have size t, and each value will represent the variance of the temporal evolution at each time. If a scalar, the passed value will be used for the first latent state at each time.
a1: Vector or scalar: The prior mean for the latent states associated with this block at time 1. If a1 is a vector, its dimension should be equal to the period of the FFS block. If a1 is a scalar, its value will be used for all latent states.
R1: Matrix, vector or scalar: The prior covariance matrix for the latent states associated with this block at time 1. If R1 is a matrix, its dimensions should be period x period. If R1 is a vector or scalar, a covariance matrix will be created as a diagonal matrix with the values of R1 in the diagonal.
monitoring: Bool: A indicator if the first latent state should be monitored (if automated monitoring is used).
X: Vector or scalar: An argument providing the values of the covariate X_t.

Value

A dlm_block object containing the following values:

FF Array: A 3D-array containing the regression matrix for each time. Its dimension should be n x k x t, where n is the number of latent states, k is the number of linear predictors in the model and t is the time series length.
FF.labs Matrix: A n x k character matrix describing the type of value of each element of FF.
G Matrix: A 3D-array containing the evolution matrix for each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.
G.labs Matrix: A n x n character matrix describing the type of value of each element of G.
G.idx Matrix: A n x n character matrix containing the index each element of G.
D Array: A 3D-array containing the discount factor matrix for each time. Its dimension should be n x n x t, where n is the number of latent states and t is the time series length.
h Matrix: The mean for the random noise of the temporal evolution. Its dimension should be n x t.
H Array: A 3D-array containing the covariance matrix of the noise for each time. Its dimension should be the same as D.
a1 Vector: The prior mean for the latent vector.
R1 Matrix: The prior covariance matrix for the latent vector.
var.names list: A list containing the variables indexes by their name.
period Positive integer: Same as argument.
n Positive integer: The number of latent states associated with this block (2).
t Positive integer: The number of time steps associated with this block. If 1, the block is compatible with blocks of any time length, but if t is greater than 1, this block can only be used with blocks of the same time length.
k Positive integer: The number of outcomes associated with this block. This block can only be used with blocks with the same outcome length.
pred.names Vector: The name of the linear predictors associated with this block.
monitoring Vector: Same as argument.
type Character: The type of block (Harmonic).

Details

For the ..., D, H, a1 and R1 arguments, the user may set one or more of its values as a string. By doing so, the user will leave the block partially undefined. The user must then pass the undefined parameter values as named arguments to the fit_model function. Also, multiple values can be passed, allowing for a sensitivity analysis for the value of this parameter.

For the details about the implementation see ArtigoPacote;textualkDGLM.

For the details about the free-form seasonal trends in the context of DLM's, see WestHarr-DLM;textualkDGLM, chapter 8.

For the details about dynamic regression models in the context of DLM's, see WestHarr-DLM;textualkDGLM, chapters 6 and 9.

References

Examples

# Creating a first order structure for a model with 2 outcomes.
# One block is created for each outcome
# with each block being associated with only one of the outcomes.
season.1 <- ffs_block(alpha1 = 1, period = 12)
season.2 <- ffs_block(alpha2 = 1, period = 12)

# Creating a block with shared effect between the outcomes
season.3 <- ffs_block(alpha1 = 1, alpha2 = 1, period = 12)