impute_AR1_Gaussian {imputeFin}

Impute missing values of time series based on a Gaussian AR(1) model

Description

Impute inner missing values (excluding leading and trailing ones) of time series by drawing samples from the conditional distribution of the missing values given the observed data based on a Gaussian AR(1) model as estimated with the function fit_AR1_Gaussian. Outliers can be detected and removed.

Usage

impute_AR1_Gaussian(
  y,
  n_samples = 1,
  random_walk = FALSE,
  zero_mean = FALSE,
  remove_outliers = FALSE,
  outlier_prob_th = 0.001,
  verbose = TRUE,
  return_estimates = FALSE,
  tol = 1e-10,
  maxiter = 100
)

Arguments

y

Time series object coercible to either a numeric vector or numeric matrix (e.g., zoo or xts) with missing values denoted by NA.

n_samples

Positive integer indicating the number of imputations (default is 1).

random_walk

Logical value indicating if the time series is assumed to be a random walk so that phi1 = 1 (default is FALSE).

zero_mean

Logical value indicating if the time series is assumed zero-mean so that phi0 = 0 (default is FALSE).

remove_outliers

Logical value indicating whether to detect and remove outliers.

outlier_prob_th

Threshold of probability of observation to declare an outlier (default is 1e-3).

verbose

Logical value indicating whether to output messages (default is TRUE).

return_estimates

Logical value indicating if the estimates of the model parameters are to be returned (default is FALSE).

tol

Positive number denoting the relative tolerance used as stopping criterion (default is 1e-8).

maxiter

Positive integer indicating the maximum number of iterations allowed (default is 100).

Value

By default (i.e., for n_samples = 1 and return_estimates = FALSE), the function will return an imputed time series of the same class and dimensions as the argument y with one new attribute recording the locations of missing values (the function plot_imputed will make use of such information to indicate the imputed values), as well as locations of outliers removed.

If n_samples > 1, the function will return a list consisting of n_sample imputed time series with names: y_imputed.1, y_imputed.2, etc.

If return_estimates = TRUE, in addition to the imputed time series y_imputed, the function will return the estimated model parameters:

phi0

The estimate for phi0 (numeric scalar or vector depending on the number of time series).

phi1

The estimate for phi1 (numeric scalar or vector depending on the number of time series).

sigma2

The estimate for sigma2 (numeric scalar or vector depending on the number of time series).

Author(s)

Junyan Liu and Daniel P. Palomar

References

R. J. Little and D. B. Rubin, Statistical Analysis with Missing Data, 2nd ed. Hoboken, N.J.: John Wiley & Sons, 2002.

J. Liu, S. Kumar, and D. P. Palomar, "Parameter estimation of heavy-tailed AR model with missing data via stochastic EM," IEEE Trans. on Signal Processing, vol. 67, no. 8, pp. 2159-2172, 15 April, 2019.

See Also

plot_imputed, fit_AR1_Gaussian, impute_AR1_t

Examples

library(imputeFin)
data(ts_AR1_Gaussian) 
y_missing <- ts_AR1_Gaussian$y_missing
y_imputed <- impute_AR1_Gaussian(y_missing)
plot_imputed(y_imputed)