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Justifying the trend component in a time series?

Examining correlation and long range dependence in time series data with strong diurnal effectsWhich Dickey-Fuller test for a time series modelled with an intercept/drift and a linear trend?First remove seasonal trend or long-term trend in time series?Why is this time-series stationary?deterministic time trend vs stationarityTime series analysis of electricity load questionsTrend and Seasonal component fitting after decomposition of the time seriesTesting trend terms in time series in RIs the Dickey-Fuller tests is a seasonality test as it tests the existence of the unit root?Can we forecast the Trend component of a decomposed time series?

2

$begingroup$

I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.

I decomposed the time series and the trend component does not have any particular pattern.plot-

I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?

time-series statistical-significance

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asked 9 hours ago

A.kumarA.kumar

111

New contributor

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2

$begingroup$

I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.

I decomposed the time series and the trend component does not have any particular pattern.plot-

I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?

time-series statistical-significance

share|cite|improve this question

asked 9 hours ago

A.kumarA.kumar

111

New contributor

A.kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

I am working on a time series forecasting problem ,I used Dickey–Fuller test to check the stationary of the time series and the p value is 0.000835 , hense I rejected the null hypothesis and assumed that it's a stationary time series.

I decomposed the time series and the trend component does not have any particular pattern.plot-

I want to ask how can we justify that a time series has any particular trend, Is this decomposition enough to ensure and guarantee that this time series has no trend ?

time-series statistical-significance

share|cite|improve this question

asked 9 hours ago

A.kumarA.kumar

111

New contributor

A.kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

asked 9 hours ago

A.kumarA.kumar

111

New contributor

A.kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked 9 hours ago

A.kumarA.kumar

111

New contributor

A.kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 9 hours ago

A.kumarA.kumar

111

New contributor

A.kumar is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 9 hours ago

A.kumarA.kumar

111

2 Answers
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The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.

Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):

share|cite|improve this answer

edited 5 hours ago

answered 6 hours ago

StatsStats

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2

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visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.

share|cite|improve this answer

answered 6 hours ago

IrishStatIrishStat

21k42241

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3

$begingroup$

The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.

Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):

share|cite|improve this answer

edited 5 hours ago

answered 6 hours ago

StatsStats

40117

$endgroup$

add a comment | 

3

$begingroup$

The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.

Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):

share|cite|improve this answer

edited 5 hours ago

answered 6 hours ago

StatsStats

40117

$endgroup$

add a comment | 

$begingroup$

The Augmented Dickey–Fuller test is UNIT ROOT test - NOT a stationarity test. The null-hypothesis on this test is that the data have been generated by a restricted AR model containing a unit-root. Rejecting this hypothesis DOES NOT mean the series is stationary. It just means that there is enough evidence to allow you rejecting the hypothesis of a very specific form of NON-stationarity (i.e. unit root). Evidence is assessed contrastively i.e. v.s. an unrestricted AR model. Rejecting the hypothesis that an animal is a chicken with an alternative being a pig doesn't mean the animal might not be a horse! The examined animal might contrastively not look like a chicken (e.g. because it has 4 legs) but that doesn't make it a pig.

Now look at your decomposition. You could see with a bare eye data don't look stationary. Trend as well as variance change with time. The decomposition does not support your conclusion. It supports the opposite view. There both parametric as well as non-parametric ways to check changes in the trend of the series. For example (see following poster about Detecting Changes in the Mean ):

share|cite|improve this answer

edited 5 hours ago

answered 6 hours ago

StatsStats

40117

$endgroup$

share|cite|improve this answer

edited 5 hours ago

answered 6 hours ago

StatsStats

40117

answered 6 hours ago

StatsStats

40117

answered 6 hours ago

StatsStats

40117

2

$begingroup$

visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.

share|cite|improve this answer

answered 6 hours ago

IrishStatIrishStat

21k42241

$endgroup$

add a comment | 

2

$begingroup$

visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.

share|cite|improve this answer

answered 6 hours ago

IrishStatIrishStat

21k42241

$endgroup$

add a comment | 

$begingroup$

visually there is an apparent autoregressive process and a change in model error variance .. thus non-stationarity is the call.

share|cite|improve this answer

answered 6 hours ago

IrishStatIrishStat

21k42241

$endgroup$

share|cite|improve this answer

answered 6 hours ago

IrishStatIrishStat

21k42241

answered 6 hours ago

IrishStatIrishStat

21k42241

answered 6 hours ago

IrishStatIrishStat

21k42241