LackOfFit Class |
Namespace: Imsl.Stat
The LackOfFit type exposes the following members.
Name | Description | |
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Compute(Int32, Double, Int32, Int32) |
Performs lack-of-fit test for a univariate time series or transfer
function given the appropriate correlation function using a minimum
lag of 1.
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Compute(Int32, Double, Int32, Int32, Int32) | Performs lack-of-fit test for a univariate time series or transfer
function given the appropriate correlation function.
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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.) | |
GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
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.) |
LackOfFit may be used to diagnose lack of fit in both ARMA and transfer function models. Typical arguments for these situations are:
Model | lagMin | lagMax | npFree |
---|---|---|---|
ARMA (p, q) | 1 | p + q | |
Transfer function | 0 | r + s |
LackOfFit performs a portmanteau lack of fit test for a time series or transfer function containing nObservations observations given the appropriate sample correlation function for k = L, L+1,...,K where L = lagMin and K = lagMax.
The basic form of the test statistic Q is
with L = 1 if is an autocorrelation function. Given that the model is adequate, Q has a chi-squared distribution with degrees of freedom where m = npFree is the number of parameters estimated in the model. If the mean of the time series is estimated, Woodfield (1990) recommends not including this in the count of the parameters estimated in the model. Thus, for an ARMA(p, q) model set npFree = p + q regardless of whether the mean is estimated or not. The original derivation for time series models is due to Box and Pierce (1970) with the above modified version discussed by Ljung and Box (1978). The extension of the test to transfer function models is discussed by Box and Jenkins (1976, pages 394-395).