Image gradient - Revision history

en>Philip Trueman: Reverted edits by 195.194.188.5 (talk) to last version by Smitty121981

2014-09-24T14:13:27Z

Reverted edits by 195.194.188.5 (talk) to last version by Smitty121981

← Older revision		Revision as of 16:13, 24 September 2014
Line 1:		Line 1:
	~~In [[statistics]], '''Self-Exciting Threshold AutoRegressive''' ('''SETAR''') '''models''' are typically applied~~ to ~~[[time series]] data as an extension of [[Autoregressive\|autoregressive models]], in order~~ to ~~allow for higher degree of flexibility in model parameters through a '''regime switching behaviour'''.~~		I would like to introduce myself to you, I am Andrew and my spouse doesn't like it at all. It's not a typical factor but what I like doing is to climb but I don't have the time lately. He is an order clerk and it's some thing he truly enjoy. Her family life in Alaska but her spouse desires them to move.<br><br>Also visit my blog post - tarot readings ([http://galab-work.cs.pusan.ac.kr/Sol09B/?document_srl=1489804 More Signup bonuses])

	~~Given a time series of data ''x''<sub>''t''</sub>~~, ~~the SETAR model is a tool for understanding~~ and~~, perhaps, predicting future values in this series, assuming that the behaviour of the series changes once the series enters a different '''regime''~~'. ~~The switch from one regime to another depends on the~~ '~~''past values''' of the ''x'' series (hence the '''Self-Exciting''' portion of the name).~~

	~~The model consists of ''k'' [[autoregressive]] (AR) parts, each for~~ a ~~different regime. The model~~ is ~~usually referred~~ to ~~as the~~ '~~''SETAR'''(''k'', ''p'') model where ''k'' is the number of regimes and ''p'' is the order of the [[autoregressive]] part (since those can differ between regimes,~~ the ~~''p'' portion is sometimes dropped and models are denoted simply as SETAR(''k'').~~

	~~== Definition ==~~

	~~=== Autoregressive Models===~~
	~~Consider a simple AR(''p'') model for a [[~~time ~~series]] ''y''<sub>''t''</sub>~~
	~~:<math>y_{t}=\gamma_{0}+\gamma_{1}y_{t-1}+\gamma_{2}y_{t-2}+...+\gamma_{p}y_{t-p}+\epsilon_{t}.\,</math>~~
	~~where:~~
	~~:<math> \gamma_{i}\,</math> for ''i''=1,2,...,''p'' are [[autoregressive]] coefficients, assumed to be constant over time;~~
	~~:<math> \epsilon_{t}\sim^{iid}WN(0;\sigma^{2})\, </math> stands for [[White_noise#Statistical_properties\|white-noise]] error term with constant [[variance]].~~
	~~written in a following vector form:~~
	~~:<math> y_{t}=\mathbf{X_{t}\gamma}+\sigma\epsilon_{t}~~.~~\,</math>~~
	~~where:~~
	~~:<math>\mathbf{X_{t}}=(1,y_{t-1},y_{t-2},\ldots,y_{t-p})\,</math>~~ is ~~a column vector of variables;~~
	~~:<math>\gamma \,</math> is the vector of parameters :<math>\gamma_{0}, \gamma_{1},\gamma_{2},..., \gamma_{p}\,</math>;~~
	~~:<math>\epsilon_{t}\sim^{iid}WN(0;1)\,</math> stands for [[White_noise#Statistical_properties\|white-noise]] error term with constant [[variance]].~~

	~~===SETAR as~~ an ~~Extension of the Autoregressive Model===~~
	~~SETAR models were introduced by Howell Tong in 1977~~ and more fully developed in the seminal paper (Tong and Lim, 1980). They can be thought of in terms of extension of [[autoregressive]] models, allowing for changes in the model parameters according to the value of weakly [[exogenous]] '~~''threshold variable''' ''z''<sub>''t''</sub>, assumed to be '''past''' values of ''y'', e.g~~. ~~''y''<sub>''t-d''</sub>, where ''d'' is the delay parameter, triggering the changes.~~

	~~Defined~~ in ~~this way, SETAR model can be presented as follows:~~
	~~:<math> y_{t}=\mathbf{X_{t}}\gamma^{(j)}+\sigma^{(j)}\epsilon_{t}\,</math> if<math>r_{j-1}<z_{t}<r_{j}.\,</math>~~
	~~where:~~
	~~:<math> X_{t}=(1,y_{t-1},y_{t-2},...,y_{t-p})\,</math> is a column vector of variables;~~
	~~:<math> -\infty=r_{0}<r_{1}<\ldots<r_{k}=+\infty\,</math> are ''k+1'' non-trivial thresholds dividing the domain of ''z''<sub>''t''</sub> into ''k'' different regimes.~~

	~~The SETAR model is a special case of Tong's general threshold autoregressive models (Tong and Lim, 1980, p. 248). The latter allows the threshold variable~~ to be very flexible, such as an exogenous time series in the open-loop threshold autoregressive system (Tong and Lim, 1980, p. 249), a Markov chain in the Markov-chain driven threshold autoregressive model (Tong and Lim, 1980, p. 285), which is now also known as the Markov switching model.

	~~For a comprehensive review of developments over the 30 years~~
	~~since the birth of the model, see Tong (2011)~~.

	~~===Basic Structure===~~
	~~In each of the ''k'' regimes, the '''AR'''(''p'') process is governed by a different set of ''p'' variables :~~<~~math~~>~~\gamma^{(j)}\,~~<~~/math~~>. In such setting, a change of the regime (because the past values of the series ''y''<sub>''t-d''</sub> surpassed the threshold) causes a different set of coefficients :<math>\gamma^{(j)}\,</math> to govern the process ''y''.

	~~==See also==~~
	*[[Star_model\|Logistic Smooth-Transmission Model]]

	~~== References ==~~
	*Hansen, B.E. (1997). ''Inference in TAR Models'', Studies in Nonlinear Dynamics and Econometrics, 2, 1-14.
	*Tong, H. & Lim, K. S. (1980) "Threshold Autoregression, Limit Cycles and Cyclical Data (with discussion)", [[Journal of the Royal Statistical Society]], Series B, 42, 245-292.
	*Tong, H. (1983) "Threshold Models in Non-linear Time Series Analysis". Lecture Notes in Statistics, Springer-Verlag.
	*Tong, H. (1990). ''Non-Linear Time Series: A Dynamical System Approach''. Oxford University Press.
	*Tong, H. (2007). "Birth of the time series model". Statistica Sinica, 17, 8-~~14.~~
	*Tong, H. (2011). "Threshold models in time series analysis —30 years on (~~with discussions by P.Whittle, M.Rosenblatt, B.E.Hansen, P.Brockwell, N.I.Samia & F.Battaglia)". Statistics & Its Interface, 4, 107-136.~~
	[http://~~lx2.saas.hku~~.~~hk/research/research-report-471~~.~~pdf]~~
	~~[http://www~~.~~intlpress~~.~~com~~/~~SII~~/~~SII-BrowseJournal.php~~]
	~~http://www.ssc.wisc.edu/~bhansen/papers/saii_11.pdf~~
	*Tsay, R.S. (1989). ''Testing and Modeling Threshold Autoregressive Processes'', Journal of the American Statistical Association, 84 (405)~~, 231-240.~~

	~~[[Category:Nonlinear systems]]~~
	~~[[Category:Time series models]]~~

en>ChrisGualtieri: Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

2013-12-13T17:07:31Z

Remove stub template(s). Page is start class or higher. Also check for and do General Fixes + Checkwiki fixes using AWB

← Older revision		Revision as of 19:07, 13 December 2013
Line 1:		Line 1:
	~~Andrew Simcox~~ is ~~the title his parents gave him~~ and ~~he completely enjoys~~ this ~~title~~. ~~Ohio~~ is where ~~my home~~ is ~~but my husband wants us~~ to ~~transfer~~. ~~Since I was 18 I~~'~~ve been working~~ as a ~~bookkeeper but soon my spouse~~ and ~~I will start our personal business~~. ~~To perform lacross~~ is the ~~factor I love most~~ of ~~all~~.<br><br>~~My site~~: [http://www.~~edmposts~~.com/~~build~~-a-~~beautiful-organic-garden-using-these-ideas/ online reader~~]		In [[statistics]], '''Self-Exciting Threshold AutoRegressive''' ('''SETAR''') '''models''' are typically applied to [[time series]] data as an extension of [[Autoregressive\|autoregressive models]], in order to allow for higher degree of flexibility in model parameters through a '''regime switching behaviour'''.

			Given a time series of data ''x''<sub>''t''</sub>, the SETAR model is a tool for understanding and, perhaps, predicting future values in this series, assuming that the behaviour of the series changes once the series enters a different '''regime'''. The switch from one regime to another depends on the '''past values''' of the ''x'' series (hence the '''Self-Exciting''' portion of the name).

			The model consists of ''k'' [[autoregressive]] (AR) parts, each for a different regime. The model is usually referred to as the '''SETAR'''(''k'', ''p'') model where ''k'' is the number of regimes and ''p'' is the order of the [[autoregressive]] part (since those can differ between regimes, the ''p'' portion is sometimes dropped and models are denoted simply as SETAR(''k'').

			== Definition ==

			=== Autoregressive Models===
			Consider a simple AR(''p'') model for a [[time series]] ''y''<sub>''t''</sub>
			:<math>y_{t}=\gamma_{0}+\gamma_{1}y_{t-1}+\gamma_{2}y_{t-2}+...+\gamma_{p}y_{t-p}+\epsilon_{t}.\,</math>
			where:
			:<math> \gamma_{i}\,</math> for ''i''=1,2,...,''p'' are [[autoregressive]] coefficients, assumed to be constant over time;
			:<math> \epsilon_{t}\sim^{iid}WN(0;\sigma^{2})\, </math> stands for [[White_noise#Statistical_properties\|white-noise]] error term with constant [[variance]].
			written in a following vector form:
			:<math> y_{t}=\mathbf{X_{t}\gamma}+\sigma\epsilon_{t}.\,</math>
			where:
			:<math>\mathbf{X_{t}}=(1,y_{t-1},y_{t-2},\ldots,y_{t-p})\,</math> is a column vector of variables;
			:<math>\gamma \,</math> is the vector of parameters :<math>\gamma_{0}, \gamma_{1},\gamma_{2},..., \gamma_{p}\,</math>;
			:<math>\epsilon_{t}\sim^{iid}WN(0;1)\,</math> stands for [[White_noise#Statistical_properties\|white-noise]] error term with constant [[variance]].

			===SETAR as an Extension of the Autoregressive Model===
			SETAR models were introduced by Howell Tong in 1977 and more fully developed in the seminal paper (Tong and Lim, 1980). They can be thought of in terms of extension of [[autoregressive]] models, allowing for changes in the model parameters according to the value of weakly [[exogenous]] '''threshold variable''' ''z''<sub>''t''</sub>, assumed to be '''past''' values of ''y'', e.g. ''y''<sub>''t-d''</sub>, where ''d'' is the delay parameter, triggering the changes.

			Defined in this way, SETAR model can be presented as follows:
			:<math> y_{t}=\mathbf{X_{t}}\gamma^{(j)}+\sigma^{(j)}\epsilon_{t}\,</math> if<math>r_{j-1}<z_{t}<r_{j}.\,</math>
			where:
			:<math> X_{t}=(1,y_{t-1},y_{t-2},...,y_{t-p})\,</math> is a column vector of variables;
			:<math> -\infty=r_{0}<r_{1}<\ldots<r_{k}=+\infty\,</math> are ''k+1'' non-trivial thresholds dividing the domain of ''z''<sub>''t''</sub> into ''k'' different regimes.

			The SETAR model is a special case of Tong's general threshold autoregressive models (Tong and Lim, 1980, p. 248). The latter allows the threshold variable to be very flexible, such as an exogenous time series in the open-loop threshold autoregressive system (Tong and Lim, 1980, p. 249), a Markov chain in the Markov-chain driven threshold autoregressive model (Tong and Lim, 1980, p. 285), which is now also known as the Markov switching model.

			For a comprehensive review of developments over the 30 years
			since the birth of the model, see Tong (2011).

			===Basic Structure===
			In each of the ''k'' regimes, the '''AR'''(''p'') process is governed by a different set of ''p'' variables :<math>\gamma^{(j)}\,</math>. In such setting, a change of the regime (because the past values of the series ''y''<sub>''t-d''</sub> surpassed the threshold) causes a different set of coefficients :<math>\gamma^{(j)}\,</math> to govern the process ''y''.

			==See also==
			*[[Star_model\|Logistic Smooth-Transmission Model]]

			== References ==
			*Hansen, B.E. (1997). ''Inference in TAR Models'', Studies in Nonlinear Dynamics and Econometrics, 2, 1-14.
			*Tong, H. & Lim, K. S. (1980) "Threshold Autoregression, Limit Cycles and Cyclical Data (with discussion)", [[Journal of the Royal Statistical Society]], Series B, 42, 245-292.
			*Tong, H. (1983) "Threshold Models in Non-linear Time Series Analysis". Lecture Notes in Statistics, Springer-Verlag.
			*Tong, H. (1990). ''Non-Linear Time Series: A Dynamical System Approach''. Oxford University Press.
			*Tong, H. (2007). "Birth of the time series model". Statistica Sinica, 17, 8-14.
			*Tong, H. (2011). "Threshold models in time series analysis —30 years on (with discussions by P.Whittle, M.Rosenblatt, B.E.Hansen, P.Brockwell, N.I.Samia & F.Battaglia)". Statistics & Its Interface, 4, 107-136.
			[http://lx2.saas.hku.hk/research/research-report-471.pdf]
			[http://www.intlpress.com/SII/SII-BrowseJournal.php]
			http://www.ssc.wisc.edu/~bhansen/papers/saii_11.pdf
			*Tsay, R.S. (1989). ''Testing and Modeling Threshold Autoregressive Processes'', Journal of the American Statistical Association, 84 (405), 231-240.

			[[Category:Nonlinear systems]]
			[[Category:Time series models]]

186.215.41.223: /* Math */

2012-07-03T22:22:23Z

Math

New page

Andrew Simcox is the title his parents gave him and he completely enjoys this title. Ohio is where my home is but my husband wants us to transfer. Since I was 18 I've been working as a bookkeeper but soon my spouse and I will start our personal business. To perform lacross is the factor I love most of all.<br><br>My site: [http://www.edmposts.com/build-a-beautiful-organic-garden-using-these-ideas/ online reader]