Description Usage Arguments Value Author(s) References See Also Examples
View source: R/estimate_impute_AR1_Gaussian.R
Estimate the parameters of a univariate Gaussian AR(1) model to fit the given time series with missing values and/or outliers. For multivariate time series, the function will perform a number of individual univariate fittings without attempting to model the correlations among the time series. If the time series does not contain missing values, the maximum likelihood (ML) estimation is done in one shot. With missing values, the iterative EM algorithm is employed for the estimation until converge is achieved.
1 2 3 4 5 6 7 8 9 10 11 12 
y 
Time series object coercible to either a numeric vector or numeric matrix
(e.g., 
random_walk 
Logical value indicating if the time series is assumed to be a random walk so that 
zero_mean 
Logical value indicating if the time series is assumed zeromean so that 
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 
verbose 
Logical value indicating whether to output messages (default is 
return_iterates 
Logical value indicating if the iterates are to be returned (default is 
return_condMeanCov 
Logical value indicating if the conditional mean and covariance matrix of the
time series (excluding the leading and trailing missing values) given the observed data are to be returned (default is 
tol 
Positive number denoting the relative tolerance used as stopping criterion (default is 
maxiter 
Positive integer indicating the maximum number of iterations allowed (default is 
If the argument y
is a univariate time series (i.e., coercible to a numeric vector), then this
function will return a list with the following elements:

The estimate for 

The estimate for 

The estimate for 

Numeric vector with the estimates for 

Numeric vector with the estimates for 

Numeric vector with the estimates for 

Numeric vector with the objective values at each iteration
(returned only when 

Numeric vector (of same length as argument 

Numeric matrix (with number of columns/rows equal to the length of the argument 

Indices of missing values imputed. 

Indices of outliers detected/corrected. 
If the argument y
is a multivariate time series (i.e., with multiple columns and coercible to a numeric matrix),
then this function will return a list with each element as in the case of univariate y
corresponding to each
of the columns (i.e., one list element per column of y
), with the following additional elements that combine the
estimated values in a convenient vector form:

Numeric vector (with length equal to the number of columns of 

Numeric vector (with length equal to the number of columns of 

Numeric vector (with length equal to the number of columns of 
Junyan Liu and Daniel P. Palomar
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 heavytailed AR model with missing data via stochastic EM," IEEE Trans. on Signal Processing, vol. 67, no. 8, pp. 21592172, 15 April, 2019.
impute_AR1_Gaussian
, fit_AR1_t
1 2 3 4  library(imputeFin)
data(ts_AR1_Gaussian)
y_missing < ts_AR1_Gaussian$y_missing
fitted < fit_AR1_Gaussian(y_missing)

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