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IrishStat
IrishStat
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Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as a pulse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ) to emoiricallyt identify local time trends. I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope this helps.

EDIT:

Pulse outliers are often be mis-dagnosed as variance changes. They are 1 period variance changes. THe procedures I refer to are appropriate for single series not parallel series. Pure variance change can be detected by conducting a variance difference F test "before and after" some time point BUT this premises no anomilies .This optimal breakpoint can be found by a simple search procedure. The idea of detecting 4 kinds of Interventions is as follows:

Pulse interventions (PI) temporarily affect the series at 1 point in time 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,…..t

Step/Level interventions permanently (SLI) shift the baseline (implied intercept) of the series. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,…..t

Seasonal Pulse interventions (SPI) permanently affect the series at all subsequent seasonal points in time much like seasonal fixed effects. e.g. 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,…..t

Local Time Trend (LTT) interventions permanently change the slope of the series reflecting steady state change from that point forward. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,…..t

note that LTT = STEP/(1-B) or STEP = (1-B)LTT

As an example of a time series with LTT's consider an example (nob=51). Modelling 10 numbers would be more difficult.

the data enter image description here the plot enter image description here the equation enter image description here ( thus two time trends ) enter image description here

If i took the first 10 values this is waht was resolved enter image description here . Three values were ear-marked as not being represntative.

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as a pulse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ) to emoiricallyt identify local time trends. I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope this helps.

EDIT:

Pulse outliers are often be mis-dagnosed as variance changes. They are 1 period variance changes. THe procedures I refer to are appropriate for single series not parallel series. Pure variance change can be detected by conducting a variance difference F test "before and after" some time point BUT this premises no anomilies .This optimal breakpoint can be found by a simple search procedure. The idea of detecting 4 kinds of Interventions is as follows:

Pulse interventions (PI) temporarily affect the series at 1 point in time 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,…..t

Step/Level interventions permanently (SLI) shift the baseline (implied intercept) of the series. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,…..t

Seasonal Pulse interventions (SPI) permanently affect the series at all subsequent seasonal points in time much like seasonal fixed effects. e.g. 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,…..t

Local Time Trend (LTT) interventions permanently change the slope of the series reflecting steady state change from that point forward. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,…..t

note that LTT = STEP/(1-B) or STEP = (1-B)LTT

As an example of a time series with LTT's consider an example (nob=51). Modelling 10 numbers would be more difficult.

the data enter image description here the plot enter image description here the equation enter image description here ( thus two time trends ) enter image description here

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as a pulse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ) to emoiricallyt identify local time trends. I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope this helps.

EDIT:

Pulse outliers are often be mis-dagnosed as variance changes. They are 1 period variance changes. THe procedures I refer to are appropriate for single series not parallel series. Pure variance change can be detected by conducting a variance difference F test "before and after" some time point BUT this premises no anomilies .This optimal breakpoint can be found by a simple search procedure. The idea of detecting 4 kinds of Interventions is as follows:

Pulse interventions (PI) temporarily affect the series at 1 point in time 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,…..t

Step/Level interventions permanently (SLI) shift the baseline (implied intercept) of the series. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,…..t

Seasonal Pulse interventions (SPI) permanently affect the series at all subsequent seasonal points in time much like seasonal fixed effects. e.g. 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,…..t

Local Time Trend (LTT) interventions permanently change the slope of the series reflecting steady state change from that point forward. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,…..t

note that LTT = STEP/(1-B) or STEP = (1-B)LTT

As an example of a time series with LTT's consider an example (nob=51). Modelling 10 numbers would be more difficult.

the data enter image description here the plot enter image description here the equation enter image description here ( thus two time trends ) enter image description here

If i took the first 10 values this is waht was resolved enter image description here . Three values were ear-marked as not being represntative.

added 1780 characters in body
Source Link
IrishStat
IrishStat
  • 30.1k
  • 5
  • 37
  • 60

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as apulusea pulse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ) to emoiricallyt identify local time trends. I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope tisthis helps.

EDIT:

Pulse outliers are often be mis-dagnosed as variance changes. They are 1 period variance changes. THe procedures I refer to are appropriate for single series not parallel series. Pure variance change can be detected by conducting a variance difference F test "before and after" some time point BUT this premises no anomilies .This optimal breakpoint can be found by a simple search procedure. The idea of detecting 4 kinds of Interventions is as follows:

Pulse interventions (PI) temporarily affect the series at 1 point in time 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,…..t

Step/Level interventions permanently (SLI) shift the baseline (implied intercept) of the series. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,…..t

Seasonal Pulse interventions (SPI) permanently affect the series at all subsequent seasonal points in time much like seasonal fixed effects. e.g. 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,…..t

Local Time Trend (LTT) interventions permanently change the slope of the series reflecting steady state change from that point forward. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,…..t

note that LTT = STEP/(1-B) or STEP = (1-B)LTT

As an example of a time series with LTT's consider an example (nob=51). Modelling 10 numbers would be more difficult.

the data enter image description here the plot enter image description here the equation enter image description here ( thus two time trends ) enter image description here

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as apuluse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ). I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope tis helps.

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as a pulse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ) to emoiricallyt identify local time trends. I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope this helps.

EDIT:

Pulse outliers are often be mis-dagnosed as variance changes. They are 1 period variance changes. THe procedures I refer to are appropriate for single series not parallel series. Pure variance change can be detected by conducting a variance difference F test "before and after" some time point BUT this premises no anomilies .This optimal breakpoint can be found by a simple search procedure. The idea of detecting 4 kinds of Interventions is as follows:

Pulse interventions (PI) temporarily affect the series at 1 point in time 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,…..t

Step/Level interventions permanently (SLI) shift the baseline (implied intercept) of the series. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,…..t

Seasonal Pulse interventions (SPI) permanently affect the series at all subsequent seasonal points in time much like seasonal fixed effects. e.g. 0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,…..t

Local Time Trend (LTT) interventions permanently change the slope of the series reflecting steady state change from that point forward. e.g. 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,…..t

note that LTT = STEP/(1-B) or STEP = (1-B)LTT

As an example of a time series with LTT's consider an example (nob=51). Modelling 10 numbers would be more difficult.

the data enter image description here the plot enter image description here the equation enter image description here ( thus two time trends ) enter image description here

Source Link
IrishStat
IrishStat
  • 30.1k
  • 5
  • 37
  • 60

Detecting trends is similar to detecting step/level shifts insofar as a step is a difference of atrend just as apuluse is the difference of a step/level. Intervention Detection ala Tsay and others has been extended by SAS and AUTOBOX ( a piece of software that I am involved with commercially ). I suggest that you contact both SAS and AUTOBOX and send them your data and have them analyse it (automatically ) and send you back the results. Maybe you can like Yogi said "learn a lot by simply watching !" Hope tis helps.