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ARMAEstimateMissing Class
Estimates missing values in a time series collected with equal spacing. Missing values can be replaced by these estimates prior to fitting a time series using the ARMA class.
Inheritance Hierarchy
SystemObject
  Imsl.StatARMAEstimateMissing

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
[SerializableAttribute]
public class ARMAEstimateMissing

The ARMAEstimateMissing type exposes the following members.

Constructors
  NameDescription
Public methodARMAEstimateMissing
Constructor for ARMAEstimateMissing.
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Methods
  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetCompleteTimes
Returns an int array of all time points, including values for times with missing values in z.
Public methodGetCompleteTimeSeries
Returns a double precision vector of length tpoints[tpoints.Length-1]-tpoints[0]+1 containing the observed values in the time series z plus estimates for missing values in gaps identified in tpoints.
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetMissingTimes
Returns the times at which missing values were estimated.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyConvergenceTolerance
The covergence tolerance used by the AR_1 and AR_p missing value estimation methods.
Public propertyEstimationMethod
The method used for estimating the final autoregressive coefficients for missing value estimation methods AR_1 and AR_p.
Public propertyMaxIterations
The maximum number of estimation iterations for missing value estimation methods AR_1 and AR_p.
Public propertyMaxlag
The maximum number of autoregressive lags when method AR_p is selected as the missing value estimation method.
Public propertyMean
The mean value used to center the series.
Public propertyMissingValueMethod
The current missing value estimation method.
Public propertyNumberMissing
The number of missing values in the original series
Public propertyRelativeError
The relative error used for the MethodOfMoments and LeastSquares estimation methods.
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Remarks

Traditional time series analysis as described by Box, Jenkins and Reinsel (1994) requires the observations be made at equidistant time points t_0,t_1,\ldots,t_n where t_i = t_0 + i. When observations are missing, ARMA requires that they be replaced with suitable estimates. Class ARMAEstimateMissing offers 4 methods for estimating missing values: Median, CubicSpline, AR_1, and AR_p

The centering method Median estimates the missing observations in a gap by the median of the last four time series values before and the first four values after the gap. If not enough values are available before or after the gap then the number is reduced accordingly. This method is very fast and simple, but its use is limited to stationary ergodic series without outliers and level shifts.

Centering method CubicSpline uses a cubic spline interpolation method to estimate missing values. Here the interpolation is again done over the last four time series values before and the first four values after the gap. The missing values are estimated by the resulting interpolant. This method gives smooth transitions across missing values.

Method AR_1 assumes that the time series before the gap can be approximated using an AR(1) process. If the last observation prior to the gap is made at time point t_m then this method uses values at t_0,t_1,\ldots,t_m to compute the one-step-ahead forecast at origin t_m. This value is used to estimate the missing value at time point t_m + 1. If the value at t_m + 2 is also missing then the values at time points t_0,t_1,\ldots,t_m + 1 are used to recompute the AR(1) model, and then estimate the value at t_m + 2 and so on. The coefficient \phi_1 in the AR(1) model is computed internally by the method of least squares from class ARMA.

Finally, method AR_p uses an AR(p) model to estimate missing values using a one-step-ahead forecast similar to method AR_1. First, class ARAutoUnivariate, is applied to the time series values just prior to the missing values to determine the optimum p from the set \{0,1,\ldots,\rm{maxlag}\} of possible values and to compute the parameters \phi_1,\ldots,\phi_p of the resulting AR(p) model. The parameters are estimated by the least squares method based on Householder transformations as described in Kitagawa and Akaike (1978). Denoting the mean of the series y_{t_0}, y_{t_1},\ldots,y_{t_m} by \mu the one-step-ahead forecast at origin t_m,\,\, \hat{y_{t_m}}(1), can be computed by the formula

\hat{y_{t_m}}(1)=\mu(1 - \sum\nolimits_{j=1}^p\phi_j)+\sum\nolimits_{j=1}^p\phi_j y_{t_m+1-j}\rm{.}

This value is used as an estimate for the missing value at t_{m+1}. The procedure starting with ARAutoUnivariate is then repeated for every further missing value in the gap. All four estimation methods treat gaps of missing values in increasing time order.

See Also

Reference

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