Difference Class |
Namespace: Imsl.Stat
The Difference type exposes the following members.
Name | Description | |
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Difference |
Constructor for Difference.
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Name | Description | |
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Compute |
Computes a Difference series.
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
ExcludeFirst |
Excludes observations lost due to differencing.
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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.) | |
SetOrders |
Sets the orders for the Difference object.
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ToString | Returns a string that represents the current object. (Inherited from Object.) |
Name | Description | |
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ObservationsLost |
Returns the number of observations lost because of differencing the time
series. Note that the Compute method must be invoked
first before invoking this method. Otherwise, the return value is
0.
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Class Difference performs m = periods.Length successive backward differences of period and order on the n = z.Length observations .
Consider the backward shift operator B given by
for all k. Then, the backward difference operator with period s is defined by the following:
Note that and are defined only for . Repeated differencing with period s is simply
where is the order of differencing. Note that
is defined only for .
The general difference formula used in the class Difference is given by
where represents the number of observations "lost" because of differencing and NaN represents the missing value code. Note that
A homogeneous, stationary time series can be arrived at by appropriately differencing a homogeneous, nonstationary time series (Box and Jenkins 1976, p. 85). Preliminary application of an appropriate transformation followed by differencing of a series can enable model identification and parameter estimation in the class of homogeneous stationary autoregressive moving average models.