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Test Elliot

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TEST DE ELLIOT - ROTHENBERG Y STOCK
El ERS señala la prueba optima es basado en la regresión cuasi-diferenciando definida en la ecuación dyta=dxtaδa+ ηt.
Al definir los residuos de dyta=dxtaδa+ ηt como ηta=dyta- dxtaδ(a) y permitio SSRa=ηt2 (a) sea la función de los residuos suma de los cuadrados. El ERS (factible) señala el estadístico de la prueba óptima de la hipótesis nula α=1 que contra la alternativa α=a que, se define entonces como:
Pt=(SSRa-aSSR1)f0
H0: La serie tiene una raíz unitaria H1: La serie no tiene una raíz unitaria.
Donde es f0 un estimador del espectro residual al cero de frecuencia y donde es una función residual acumulativa.
Los valores críticos para el ERS prueban la estadística, se computan interpolando los resultados de la simulación proporcionados por ERS para T=50,100,200…∞.
El método busca minimizar la diferencia cuadrática entre los valores de la serie y los valores de la tendencia determinística, para distintos valores de (que dependen del parámetro c) y para =1. Una vez obtenidos los residuos de la estimación eficiente (es decir, aquella que minimiza la diferencia mencionada), se aplica un test de Dickey-Fuller sin constante o deriva y sin tendencia, por cuanto se trabaja con una serie transformada por precisamente la remoción de la tendencia determinística.
EJEMPLO CON DATOS DEL PIB EN EVIEWS
UNIT ROOT EN NIVELES CON 11 REZAGOS

Null Hypothesis: PIB has a unit root | | Exogenous: Constant | | | Lag length: 4 (Spectral OLS AR based on SIC, maxlag=11) | Sample: 1 89 | | | | Included observations: 89 | | | | | | | | | | | | | | | | | P-Statistic | | | | | | | | | | | Elliott-Rothenberg-Stock test statistic | 2305.703 | Test critical values: | 1% level | | | 1.932400 | | 5% level | | | 3.079200 | | 10% level | | | 4.112800 | | | | | | | | | | | *Elliott-Rothenberg-Stock (1996, Table 1) | | | | | | | | | | | | | | | | | HAC corrected variance (Spectral OLS autoregression) | 1.64E+09 | | | | | | | | | | | | | | | |

UNIT ROOT PRIMERA DIFERENCIA CON 11 REZAGOS

Null Hypothesis: D(PIB) has a unit root | | Exogenous: Constant | | | Lag length: 4 (Spectral OLS AR based on SIC, maxlag=11) | Sample (adjusted): 2 89 | | | Included observations: 88 after adjustments | | | | | | | | | | | | | | | | P-Statistic | | | | | | | | | | | Elliott-Rothenberg-Stock test statistic | 461.5597 | Test critical values: | 1% level | | | 1.930800 | | 5% level | | | 3.076400 | | 10% level | | | 4.107600 | | | | | | | | | | | *Elliott-Rothenberg-Stock (1996, Table 1) | | | | | | | | | | | | | | | | | HAC corrected variance (Spectral OLS autoregression) | 6.19E+08 | | | | | | | | | | | | | | | |

UNIT ROOT PRIMERA DIFERENCIA TREND AND INTERCEPT CON 11 REZAGOS

Null Hypothesis: D(PIB) has a unit root | | Exogenous: Constant, Linear Trend | | Lag length: 3 (Spectral OLS AR based on SIC, maxlag=11) | Sample (adjusted): 2 89 | | | Included observations: 88 after adjustments | | | | | | | | | | | | | | | | P-Statistic | | | | | | | | | | | Elliott-Rothenberg-Stock test statistic | 69.87209 | Test critical values: | 1% level | | | 4.250400 | | 5% level | | | 5.659200 | | 10% level | | | 6.785200 | | | | | | | | | | | *Elliott-Rothenberg-Stock (1996, Table 1) | | | | | | | | | | | | | | | | | HAC corrected variance (Spectral OLS autoregression) | 9.76E+09 | | | | | | | | | | | | | | | | | | | | |

TEST DE KWIATKOWSKI-PHILLIPS-SCHMIDT-SHIN (KPSS)

Las pruebas de Kwiatkowski-Phillips-Schmidt-Shin (KPSS) se utilizan para probar la hipótesis nula de que una serie de tiempo observable es estacionario alrededor de una tendencia determinística, he aquí la principal diferencia con los anteriores contrastes de raíces unitarias. Pruebas KPSS tipo están destinadas a complementar las pruebas de raíz unitaria, tales como las pruebas de Dickey-Fuller. Al poner a prueba tanto la hipótesis de raíz unitaria y la hipótesis de estacionariedad, se pueden distinguir una serie que parece ser una serie estacionaria, que parecen tener una raíz unitaria, y la serie para la que los datos (o las pruebas) no son lo suficientemente informativo para estar seguros de sí que son estacionarios o integrado. También este test permite que los errores pueden estar autocorrelacionados y pueden ser heteroscedasticos y solo tiene dos procesos generadores de datos: modelo con intercepto y modelo con tendencia más intercepto. En la actualidad es muy útil en la investigación, para saber si la serie es fraccionalmente integrada. Contraste de hipótesis
H0 : la serie es estacional en tendencia H1 : La serie no presenta estacionalidad en tendencia
La prueba KPSS en eviews:
Para realizar la prueba se selecciona la serie del pib, abriendo la ventana seleccionar el botón OpenviewUnit Root testen test type seleccionar Kwiatkowski-Phillips-Schmidt-Shin, marcar la opción Level (sin diferenciar la serie) seleccionar también intercepto y tendencia (trend and intercept), en el estimación method (método de estimación) se seleccionara por defecto Barlett Kernel, en Bandwidth (ancho de banda) marcar la selección automática ,para obtener el criterio de rezagos, por el método de Newey – West Bandwidth.

Analizando la serie en niveles e incorporando la constante () y la tendencia ()
Ecuación completa que se recomienda para realizar el test

En la salida de eviews

CONTRASTE HIPOTESIS

H0 : ≠ 0 la serie es estacionaria, no tiene raíz unitaria H1 : =0 La serie es no estacionaria, tiene raíz unitaria
KPSS ͠ V-C 1%,5%,10%
1% level 0.345399> 0.21600 RHo
5% level 0.345399 >0.14600 RHo
10% level 0.345399 >0.11900 RHo

Como se rechaza la hipótesis nula, se concluye que la serie en niveles del PIB no sigue un proceso estacionario en tendencia y por lo tanto tiene raíz unitaria.

APLICANDO LA 1RA DIFERENCIA

CONTRASTE HIPOTESIS
H0 : la serie es estacionaria ,no tiene raíz unitaria
H1 : La serie no presenta estacionariedad, tiene raíz unitaria

KPSS ͠ V-C 1%,5%,10%
1% level 0.099951< 0.21600 NRHo
5% level 0.099951<0.14600 NRHo
10% level 0.099951<0.11900 NRHo

Diferenciando la serie una vez, no se rechaza la hipótesis nula y se concluye que la serie PIB al 1%, 5%, 10% es estacionaria y por lo tanto no tiene raíz unitaria
CONCLUSIONES
Para la prueba de raíz unitaria Kwiatkowski-Phillips-Schmidt-Shin (KPSS), las variables en niveles presentaron raíz unitaria por lo que se tuvo que diferenciar una vez, es decir que la serie del PIB sigue un proceso integrado de orden I (1).

PRUEBA Ng-PERRON (NP)
El test Ng y Perron (2001) es una modificación de la prueba de PP a partir de la remoción de la tendencia de la serie por medio de mínimos cuadrados generalizados (procedimiento que también se utiliza en el test de ERS de la subsección anterior).

Esto permite, comparado con el test PP, por un lado, aumentar el poder estadístico de la prueba cuando el valor de la raíz se halla cerca de la unidad y por el otro reducir las distorsiones que surgen si se aplica el test PP a series con grandes raíces MA o AR negativas. Las hipótesis son: Existe raíz unitaria
No existe raíz unitaria
Construye cuatro estadísticos de prueba que están basadas en los GLS de tendencia en los datos . Estas estadísticas de la prueba se modifican formularios de PHILIPS y PERRON yla estadística de Bhargava (1986) la estadística , y el ERS señala la estadística óptima.

Primero, defina el término:

Las estadísticas modificadas pueden escribirse entonces como;

Dónde:

Las pruebas de Ng Perron requieren una especificación para y una opción de método por estimar .

ESCUELA MILITAR DE INGENIERIA MCAL. ANTONIO JOSE DE SUCRE “BOLIVIA”

PRUEBAS DE RAIZ UNITARIA * KWIATKOWSKI-PHILLIPS-SCHMIDT-SHIN * ELLIOT - ROTHENBERG Y STOCK * Ng-PERRON
INTEGRANTES:
Carla Iveth Soliz Alave 8340378 L.P. Denisse Patrcia G. Sanchez Medina 8328981 L.P. Soraya Ilsen Panamá Coro 5748981 L.P. Ronald Aguilar Apaza 6987084 L.P. Kevin Raúl López Alarcón 9193195 L.P.
CURSO: 6to SEM “A”
ASIGNATURA: Econometría II
CARRERA: Ingeniería Comercial
DOCENTE: Lic. Rubén Aguilar
FECHA: 26/11/2012

LA PAZ – BOLIVIA

ANEXO
BOLIVIA: PRODUCTO INTERNO BRUTO POR TRIMESTRE, SEGÚN TIPO DE GASTO (En miles de bolivianos de 1990)

DESCRIPCIÓN | PIB A PRECIOS DE MERCADO | I Trimestre 1990 | 3.587.595 | II Trimestre 1990 | 3.926.068 | III Trimestre 1990 | 3.934.132 | IV Trimestre 1990 | 3.995.340 | I Trimestre 1991 | 3.677.805 | II Trimestre 1991 | 4.217.984 | III Trimestre 1991 | 4.149.575 | IV Trimestre 1991 | 4.211.087 | I Trimestre 1992 | 3.795.755 | II Trimestre 1992 | 4.299.703 | III Trimestre 1992 | 4.164.101 | IV Trimestre 1992 | 4.264.554 | I Trimestre 1993 | 3.950.724 | II Trimestre 1993 | 4.553.624 | III Trimestre 1993 | 4.301.545 | IV Trimestre 1993 | 4.423.683 | I Trimestre 1994 | 4.182.022 | II Trimestre 1994 | 4.630.765 | III Trimestre 1994 | 4.648.649 | IV Trimestre 1994 | 4.572.290 | I Trimestre 1995 | 4.401.909 | II Trimestre 1995 | 4.847.210 | III Trimestre 1995 | 4.788.394 | IV Trimestre 1995 | 4.839.881 | I Trimestre 1996 | 4.561.893 | II Trimestre 1996 | 5.122.813 | III Trimestre 1996 | 4.989.894 | IV Trimestre 1996 | 5.026.102 | I Trimestre 1997 | 4.781.223 | II Trimestre 1997 | 5.414.864 | III Trimestre 1997 | 5.185.939 | IV Trimestre 1997 | 5.294.690 | I Trimestre 1998 | 5.104.072 | II Trimestre 1998 | 5.682.209 | II Trimestre. 1998 | 5.428.848 | IV Trimestre 1998 | 5.501.491 | I Trimestre 1999 | 5.141.964 | II Trimestre 1999 | 5.631.525 | III Trimestre 1999 | 5.385.855 | IV Trimestre 1999 | 5.649.982 | I Trimestre 2000 | 5.249.518 | II Trimestre 2000 | 5.904.001 | III Trimestre 2000 | 5.440.791 | IV Trimestre 2000 | 5.761.954 | I Trimestre 2001 | 5.249.128 | II Trimestre 2001 | 5.957.302 | III Trimestre 2001 | 5.581.773 | IV Trimestre 2001 | 5.944.494 | I Trimestre 2002 | 5.321.686 | II Trimestre 2002 | 6.187.345 | III Trimestre 2002 | 5.790.530 | IV Trimestre 2002 | 5.998.172 | I Trimestre 2003 | 5.498.240 | II Trimestre 2003 | 6.387.989 | III Trimestre 2003 | 5.842.775 | IV Trimestre 2003 | 6.200.411 | I Trimestre 2004 | 5.739.403 | II Trimestre 2004 | 6.620.937 | III Trimestre 2004 | 6.202.285 | IV Trimestre 2004 | 6.365.435 | I Trimestre 2005 | 5.994.798 | II Trimestre 2005 | 6.884.146 | III Trimestre 2005 | 6.438.360 | IV Trimestre 2005 | 6.712.936 | I Trimestre 2006 | 6.259.400 | II Trimestre 2006 | 7.150.289 | III Trimestre 2006 | 6.807.897 | IV Trimestre 2006 | 7.061.326 | I Trimestre 2007 | 6.417.302 | II Trimestre 2007 | 7.442.694 | III Trimestre 2007 | 7.171.628 | IV Trimestre 2007 | 7.492.403 | I Trimestre 2008 | 6.837.878 | II Trimestre 2008 | 7.955.173 | III Trimestre 2008 | 7.678.219 | IV Trimestre 2008 | 7.806.556 | I Trimestre 2009 | 7.039.510 | II Trimestre 2009 | 8.130.167 | III Trimestre 2009 | 7.956.762 | IV Trimestre 2009 | 8.167.814 | I Trimestre 2010 | 7.266.227 | II Trimestre 2010 | 8.437.640 | III Trimestre 2010 | 8.251.995 | IV Trimestre 2010 | 8.629.817 | I Trimestre 2011(p) | 7.675.008 | II Trimestre 2011(p) | 8.790.625 | III Trimestre 2011(p) | 8.700.125 | IV Trimestre 2011(p) | 9.105.882 | I Trimestre 2012(p) | 8.070.704 |

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...Billy Elliot Analysis template |Description of scene: Opening scene: Mood, direction of plot and characterisation is established. | |Scene numbers: One, two, three | |Link to Into the World focus: Billy’s natural world is established | |Action |Film techniques used |Meaning conveyed | |Billy puts record onto record player. He |Extreme close up. There is no sound. |There is a sense of anticipation. The | |begins playing the song. |Costume: Billy is dressed simply, |audience is waiting for something to happen| |( to 1 min; 14 secs) |predominately in a bright yellow singlet. |and wondering what it will be. | | |The singlet symbolises both childhood | | | |(children wear singlets) and his working | | | |class background (‘working class’ men | | | |stereotypically wear singlets). It is also | ...

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Interview

...Biosafety, Compliance and You! A seminar by David Cavallaro, Institutional Biosafety Officer at UConn Friday, September 13, 2013 12:20pm – 1pm Storrs Campus, George White 209 Rainbow Cinema: F**k the Disabled Saturday, September 14, 2013, 2pm - 4pm Rainbow Center @ UConn, Student Union 403 Admission Fee: Free and open to all Female Orgasm Dorian Solot and Marshall Miller are renowned sex educators who have put together a hilarious, yet incredibly informative, sex education seminar. Thursday, September 17, 2013 7pm – 8pm Student Union Theater Admission Fee: Free Fall 2013 AACC Annual Welcome Back Soul Food Dinner Friday, September 20, 2013, 7pm - 10pm Student Union , Ballroom Admission: Free Rainbow Cinema: Billy Elliot Saturday, September 21, 2013, 2pm - 4pm Rainbow Center @ UConn, Student Union 403 Admission Fee: Free and open to all Chorus Concert...

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