ARMAEstimateMissing Class |
Namespace: Imsl.Stat
The ARMAEstimateMissing type exposes the following members.
Name | Description | |
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ARMAEstimateMissing |
Constructor for ARMAEstimateMissing.
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Name | Description | |
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetCompleteTimes |
Returns an int array of all time points, including values
for times with missing values in z.
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GetCompleteTimeSeries |
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.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetMissingTimes |
Returns the times at which missing values were estimated.
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GetType | Gets the Type of the current instance. (Inherited from Object.) | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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ConvergenceTolerance |
The covergence tolerance used by the AR_1 and
AR_p missing value estimation methods.
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EstimationMethod |
The method used for estimating the final autoregressive
coefficients for missing value estimation methods AR_1 and
AR_p.
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MaxIterations |
The maximum number of estimation iterations for missing
value estimation methods AR_1 and AR_p.
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Maxlag |
The maximum number of autoregressive lags when method
AR_p is selected as the missing value estimation method.
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Mean |
The mean value used to center the series.
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MissingValueMethod |
The current missing value estimation method.
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NumberMissing |
The number of missing values in the original series
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RelativeError |
The relative error used for the MethodOfMoments and
LeastSquares estimation methods.
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Traditional time series analysis as described by Box, Jenkins and Reinsel (1994) requires the observations be made at equidistant time points where . 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 then this method uses values at to compute the one-step-ahead forecast at origin . This value is used to estimate the missing value at time point . If the value at is also missing then the values at time points are used to recompute the AR(1) model, and then estimate the value at and so on. The coefficient 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 of possible values and to compute the parameters 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 by the one-step-ahead forecast at origin , can be computed by the formula
This value is used as an estimate for the missing value at . 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.