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Quantlet: |
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annarchtest |
| Description: |
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This quantlet calculates either the Lagrange Multiplier (LM) form
or the T-Rsquare (TR2) form of a test for conditional
heteroskedasticity based on Artificial Neural Networks.
The first argument of the function is the vector of residuals,
the second optional argument is the order of the test, the third
optional argument is the number of hidden units of the Neural
Network. The second optional argument is either a vector or a
scalar. If no second argument is provided, the default orders
are 2, 3, 4, and 5. The third argument may be either a vector,
or a scalar. If both second and third arguments are vectors,
the test will be calculated for all combinations of orders and
hidden units. If no third argument is provided, the number of
hidden units by default is set to 3. The fourth argument is
the form of the test. This argument is a string of characters,
which can be either "LM" or "TR2". The default fourth argument
is "LM", i.e., the Lagrange Multiplier form.
The quantlet returns in the first column the order of the test,
in the second column the number of hidden units, in the third
column the value of the test, in the fourth column the
95% critical value of the null hypothesis for that order,
and in the fifth column the P-value of the test.
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- Example:
;Calculation of the ANN test for ARCH effects. As no optional
;argument is provided, the test is evaluated for the default
;lag orders 2,3,4, and 5, for an Artificial Neural Network with
;3 hidden units. The Lagrange Multiplier form is evaluated.
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
h = annarchtest(y)
;h = annarchtest(y,"LM"); equivalent instruction as "LM" is the default argument
h
- Result:
Contents of h
[1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[2,] units
[3,] _______________________________________________________________
[4,]
[5,] 2 3 14.38089 5.97378 0.00075
[6,] 3 3 8.61509 7.80251 0.03487
[7,] 4 3 13.96671 9.47844 0.00740
[8,] 5 3 18.23967 11.06309 0.00266
- Example:
;In this example, we calculate the TR2 form of the test for ARCH
;effects. As no other optional argument is provided, the test is
;computed for the four lag orders 2,3,4, and 5, with 3 hidden
;units
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
h = annarchtest(y,"TR2")
h
- Result:
Contents of h
[1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[2,] units
[3,] ______________________________________________________________
[4,]
[5,] 2 3 10.94810 5.97378 0.00419
[6,] 3 3 6.50613 7.80251 0.08942
[7,] 4 3 10.54149 9.47844 0.03223
[8,] 5 3 13.79811 11.06309 0.01694
- Example:
;Calculation of the TR2 form of the ANN test for ARCH effects.
;As the first numerical optional argument is equal to 3, the
;lag order is equal to three. The number of hidden units is the
;default one, i.e, 3 units.
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
h = annarchtest(y,3,"TR2")
h
- Result:
Contents of h
[1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[2,] units
[3,] ______________________________________________________________
[4,]
[5,] 3 3 15.71618 7.80251 0.00130
- Example:
; We calculate here the default LM form of the test for ARCH
;effects. The lag orders are given by the vector k, i.e.,
;2,3, and 4, the number of hidden units is given by the second
;optional argument, i.e., the scalar 4.
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
k = #(2,3,4)
h = annarchtest(y,k,4)
h
- Result:
Contents of h
[1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[2,] units
[3,] ______________________________________________________________
[4,]
[5,] 2 4 21.86099 5.97378 0.00002
[6,] 3 4 19.27466 7.80251 0.00024
[7,] 4 4 22.65275 9.47844 0.00015
- Example:
;Calculation of the LM form of the test for ARCH effects.
;We investigate here all the configurations with the number of
;lags being equal to 2, 3, and 4, and the number of hidden units
; being equal to 2,3 and 4 as well.
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
k = #(2,3,4)
h = annarchtest(y,k,k)
h
- Result:
Contents of h
[ 1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[ 2,] units
[ 3,] ______________________________________________________________
[ 4,]
[ 5,] 2 2 14.35325 5.97378 0.00076
[ 6,] 3 2 14.01169 7.80251 0.00289
[ 7,] 4 2 2.78118 9.47844 0.59507
[ 8,] 2 3 23.17970 5.97378 0.00001
[ 9,] 3 3 18.55083 7.80251 0.00034
[10,] 4 3 28.83286 9.47844 0.00001
[11,] 2 4 20.51651 5.97378 0.00004
[12,] 3 4 16.01652 7.80251 0.00113
[13,] 4 4 18.16912 9.47844 0.00114
- Example:
; Calculation of the TR2 form of the ANN test for ARCH effects.
; The lag order is given by the first argument, i.e., 3, the
;number of units are the components of the second argument k,
; i.e., 2,3 and 4.
library("times")
randomize(0)
y = genarch(0.2|0.1,0.5,400)
k = #(2,3,4)
h = annarchtest(y,3,k,"TR2")
h
- Result:
Contents of h
[1,] Lag order Nb of hidden Statistic 95% Critical Value P-Value
[2,] units
[3,] ______________________________________________________________
[4,]
[5,] 3 2 15.11203 7.80251 0.00172
[6,] 3 3 12.17561 7.80251 0.00681
[7,] 3 4 16.90235 7.80251 0.00074