NAG Library Routine Document

g13awf (uni_dickey_fuller_unit)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{type}$ – IntegerInput

On entry: the type of unit test for which the probability is required.

$\mathbf{type}=1$

A unit root test will be performed and $\tau$ returned.

$\mathbf{type}=2$

A unit root test with drift will be performed and ${\tau }_{\mu }$ returned.

$\mathbf{type}=3$

A unit root test with drift and deterministic time trend will be performed and ${\tau }_{\tau }$ returned.

Constraint: $\mathbf{type}=1$, $2$ or $3$.

2:     $\mathbf{p}$ – IntegerInput

On entry: $p$, the degree of the autoregressive (AR) component of the Dickey–Fuller test statistic. When $p>1$ the test is usually referred to as the augmented Dickey–Fuller test.

Constraint: $\mathbf{p}>0$.

3:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the length of the time series.

Constraints:

• if $\mathbf{type}=1$, $\mathbf{n}>2\mathbf{p}$;
• if $\mathbf{type}=2$, $\mathbf{n}>2\mathbf{p}+1$;
• if $\mathbf{type}=3$, $\mathbf{n}>2\mathbf{p}+2$.

4:     $\mathbf{y}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $y$, the time series.

5:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=11$

On entry, $\mathbf{type}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{type}=1$, $2$ or $3$.

$\mathbf{ifail}=21$

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}>0$.

$\mathbf{ifail}=31$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint:

• if $\mathbf{type}=1$, $\mathbf{n}>2\mathbf{p}$;
• if $\mathbf{type}=2$, $\mathbf{n}>2\mathbf{p}+1$;
• if $\mathbf{type}=3$, $\mathbf{n}>2\mathbf{p}+2$.

$\mathbf{ifail}=41$

On entry, the design matrix used in the estimation of ${\beta }_1$ is not of full rank, this is usually due to all elements of the series being virtually identical. The returned statistic is therefore not unique and likely to be meaningless.

$\mathbf{ifail}=42$

${\sigma }_{11}=0$, therefore depending on the sign of ${\hat{\beta }}_1$, a large positive or negative value has been returned.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g13awfe.f90)

10.2

Program Data

Program Data (g13awfe.d)

10.3

Program Results

Program Results (g13awfe.r)