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RLS function

arx_rls_core.Rd

This function implements the Recursive Least Squares (RLS) algorithm with exponentially down-weighted past.

Usage

arx_rls_core(
  y,
  X,
  r = matrix(c(0.9, 0.95, 0.975, 0.9875, 0.99375, 0.996875, 0.9984375, 1), ncol = 1),
  n_init = NULL,
  start_of_eval = NULL,
  end_of_train = NULL,
  enhance_conv = TRUE
)

Arguments

y

Vector of doubles. Response variable in regression. There must not be NAs in this vector.

X

Matrix of doubles. Dimension = (length(y) x maximal number of regressors). NAs are not handled separately (i.e. they must be checked before this function is called).

r

Matrix of doubles (a column vector of dimension \(( \text{forgetting\_factors} \times 1)\) containing the forgetting factors.

n_init

Integer. Number of observations used for initial estimate of beta. If no value provided, at least 21 observations (3 weeks) or 3 times the number of regressors is used.

start_of_eval

Integer. Starting value of evaluation period for honest prediction error (if we start too early, there are bad initial estimations involved)

end_of_train

Integer. Index specifying the end of the training set. (Afterwards the forecasting period starts.) Important for calculating the honest prediction error (otherwise it would not be out-of-sample...). comment_bf: If one wants to use arx_rls_core() outside the automated forecasting framework, set end_of_train to length(y).

enhance_conv

Boolean. Indicates whether the convergence enhancing factor as described in Young (2011) page 55.

Value

List containing

  • y_pred: vector of predictions (vector of same length as input y)

  • fev_honest: double. honest prediction error (calculated from end_of_train - start_of_eval + 1 observations)

  • forgetting: double. forgetting factor which produced the minimal honest prediction error

Examples

# Generate simple time series data
set.seed(123)
n <- 100
x1 <- rnorm(n)
x2 <- rnorm(n)
X <- cbind(x1, x2)
y <- 2*x1 + 3*x2 + rnorm(n, sd = 0.5)
y <- matrix(y, ncol = 1)  # Convert to matrix

# Run RLS with default forgetting factors
result <- arx_rls_core(y, X, n_init = 20, start_of_eval = 25, end_of_train = 80)
str(result)
#> List of 3
#>  $ y_pred    : num [1:100] NA NA NA NA NA NA NA NA NA NA ...
#>  $ fev_honest: num 0.187
#>  $ forgetting: num 1