en>Steve Quinn: add template: {{Calculus}}

2013-08-15T23:17:17Z

add template: {{Calculus}}

← Older revision		Revision as of 01:17, 16 August 2013
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	~~I would like~~ to ~~introduce myself~~ to ~~you~~, ~~I am Jayson Simcox but I don~~'~~t like~~ when ~~individuals use my full title~~. ~~What I love doing~~ is ~~football but I don'~~t ~~have~~ the ~~time recently~~. ~~Mississippi~~ is the ~~only location I've been residing~~ in ~~but I will have to move~~ in a yr or ~~two~~. ~~I am~~ an ~~invoicing officer~~ and I'~~ll be promoted quickly~~.<br><br>~~Feel~~ free to ~~visit my web page~~ :: [http://~~cartoonkorea~~.com/~~ce002~~/~~1093612 real psychics~~]		In [[statistics]] and [[econometrics]], an '''augmented Dickey–Fuller test (ADF)''' is a test for a [[unit root]] in a [[time series]] [[Sample (statistics)\|sample]]. It is an augmented version of the [[Dickey–Fuller test]] for a larger and more complicated set of time series models.
			The augmented Dickey–Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.<ref>[http://econterms.com/glossary.cgi?action=++Search++&query=augmented+dickey-fuller Econterms]</ref>

			== Testing Procedure ==
			The testing procedure for the ADF test is the same as for the [[Dickey–Fuller test]] but it is applied to the model

			:<math>\Delta y_t = \alpha + \beta t + \gamma y_{t-1} + \delta_1 \Delta y_{t-1} + \cdots + \delta_{p-1} \Delta y_{t-p+1} + \varepsilon_t, </math>

			where <math>\alpha</math> is a constant, <math>\beta</math> the coefficient on a time trend and <math>p</math> the lag order of the autoregressive process. Imposing the constraints <math>\alpha = 0</math> and <math>\beta = 0</math> corresponds to modelling a random walk and using the constraint <math>\beta = 0</math> corresponds to modelling a random walk with a drift. Consequently, there are three main versions of the test, analogous to the ones discussed on the Wikipedia page for the [[Dickey-Fuller test]]. See that page for a discussion on dealing with uncertainty about including the intercept and deterministic time trend terms in the test equation.

			By including lags of the order ''p'' the ADF formulation allows for higher-order autoregressive processes. This means that the lag length ''p'' has to be determined when applying the test. One possible approach is to test down from high orders and examine the [[t-value]]s on coefficients. An alternative approach is to examine information criteria such as the [[Akaike information criterion]], [[Bayesian information criterion]] or the [[Hannan-Quinn information criterion]].

			The unit root test is then carried out under the null hypothesis <math>\gamma = 0</math> against the alternative hypothesis of <math>\gamma < 0.</math> Once a value for the test statistic

			:<math>DF_\tau = \frac{\hat{\gamma}}{SE(\hat{\gamma})}</math>

			is computed it can be compared to the relevant critical value for the Dickey–Fuller Test. If the test statistic is less (this test is non symmetrical so we do not consider an absolute value) than the (larger negative) critical value, then the null hypothesis of <math>\gamma = 0</math> is rejected and no unit root is present.

			== Intuition ==

			The intuition behind the test is that if the series is not integrated then the lagged level of the series (<math> y_{t-1}</math>) will provide no relevant information in predicting the change in <math> y_{t} </math> besides the one obtained in the lagged changes (<math> \Delta y_{t-k} </math>). In that case the <math>\gamma = 0</math> null hypothesis is not rejected.

			== Examples ==

			A model that includes a constant and a time trend is estimated using sample of 50 observations and yields the <math>DF_\tau</math> statistic of −4.57. This is more negative than the tabulated critical value of −3.50, so at the 95 per cent level the null hypothesis of a unit root will be rejected.

			{\| class="wikitable" style="text-align: center"
			\|-
			! colspan="5"\|Critical values for Dickey-Fuller t-distribution.
			\|-
			\| \|\| colspan="2"\|Without trend \|\| colspan="2"\|With trend
			\|-
			\| Sample size \|\| 1% \|\| 5% \|\| 1% \|\| 5%
			\|-
			\| T = 25 \|\| -3.75 \|\| -3.00 \|\| -4.38 \|\| -3.60
			\|-
			\| T = 50 \|\| -3.58 \|\| -2.93 \|\| -4.15 \|\| -3.50
			\|-
			\| T = 100 \|\| -3.51 \|\| -2.89 \|\| -4.04 \|\| -3.45
			\|-
			\| T = 250 \|\| -3.46 \|\| -2.88 \|\| -3.99 \|\| -3.43
			\|-
			\| T = 500 \|\| -3.44 \|\| -2.87 \|\| -3.98 \|\| -3.42
			\|-
			\| T = ∞ \|\| -3.43 \|\| -2.86 \|\| -3.96 \|\| -3.41
			\|-
			\|colspan="5"\|Source: Fuller, 1976, p. 373
			\|}

			== Alternatives ==

			There are alternative [[unit root test]]s such as the [[Phillips–Perron test]] or the ADF-GLS procedure developed by Elliot, Rothenberg and Stock (1996).

			== Implementations in statistics packages ==
			* In [[R (programming language)\|R]], the ''tseries'' package includes an ''adf.test'' function.<ref>[http://finzi.psych.upenn.edu/R/library/tseries/html/adf.test.html "Augmented Dickey–Fuller Test"] - R documentation</ref>
			* [[Gretl]] includes the Augmented Dickey–Fuller test.<ref>[http://spot.colorado.edu/~mcnownr/gretl_lab/Introduction-to-gretl-presentation.pdf Introduction to gretl and the gretl instructional lab]</ref>
			* In [[Matlab]], the ''adftest'' function <ref>[http://www.mathworks.com/access/helpdesk/help/toolbox/econ/adftest.html adftest function reference]</ref> is part of the Econometrics Toolbox,<ref>[http://www.mathworks.com/products/econometrics Econometrics Toolbox]</ref> and a free version is available as part of the 'Spatial Econometrics' toolbox<ref>http://www.spatial-econometrics.com/</ref>
			* In [[SAS (software)\|SAS]], ''PROC ARIMA'' can perform ADF tests.<ref>http://www2.sas.com/proceedings/sugi30/192-30.pdf</ref>
			* In [[Stata]], the ''dfuller'' command is used for ADF tests.
			* In [[Eviews]], the ''Augmented Dickey-Fuller'' is available under "Unit Root Test."<ref>[https://www.youtube.com/watch?v=lTpUcY3d3qQ at approx 8:30 minutes], [http://forums.eviews.com/viewtopic.php?f=18&t=939#p3291 mentioned in this official forum], [http://faculty.smu.edu/tfomby/eco6375/BJ%20Notes/ADF%20Notes.pdf Just mention of the possibility, not showing how to get there], [http://www.hkbu.edu.hk/~billhung/econ3600/application/app01/app01.html shown for an old version of Eviews]</ref>
			* In [[Python (programming language)\|Python]], the ''adfuller'' function is available in the ''statsmodels package''.<ref>http://statsmodels.sourceforge.net/devel/generated/statsmodels.tsa.stattools.adfuller.html</ref>
			* In [[Java (programming language)\|Java]], the ''AugmentedDickeyFuller'' class is included in ''SuanShu''<ref>[http://www.numericalmethod.com/trac/numericalmethod/wiki/SuanShu SuanShu]</ref><ref>http://www.numericalmethod.com</ref> available under the ''com.numericalmethod.suanshu.stats.test.timeseries.adf'' package.

			==See also==

			* [[KPSS test\|Kwiatkowski–Phillips–Schmidt–Shin test]]

			==References==
			{{reflist}}

			* Elliott, G., Rothenberg, T. J. & J. H. Stock (1996) "Efficient Tests for an Autoregressive Unit Root", '' Econometrica'', 64 (4), 813–836. {{jstor\|2171846}}
			* Fuller, W. A. (1976) "Introduction to Statistical Time Series", "John Wiley and Sons, New York", 373
			* Greene, W. H. (2002) ''Econometric Analysis, Fifth Edition'', Prentice Hall: New Jersey. ISBN 0-13-066189-9 {{page needed\|date=June 2012}}
			* Said E. and David A. Dickey (1984), "Testing for Unit Roots in Autoregressive Moving Average Models of Unknown Order", ''[[Biometrika]]'', 71, 599–607.

			{{DEFAULTSORT:Augmented Dickey-Fuller Test}}
			[[Category:Time series analysis]]
			[[Category:Statistical tests]]

en>Shenme: "viceversa" --> "vice versa"

2012-09-01T21:29:12Z

"viceversa" --> "vice versa"

New page

I would like to introduce myself to you, I am Jayson Simcox but I don't like when individuals use my full title. What I love doing is football but I don't have the time recently. Mississippi is the only location I've been residing in but I will have to move in a yr or two. I am an invoicing officer and I'll be promoted quickly.<br><br>Feel free to visit my web page :: [http://cartoonkorea.com/ce002/1093612 real psychics]

Time dependent vector field - Revision history

en>Steve Quinn: add template: {{Calculus}}

en>Shenme: "viceversa" --> "vice versa"