Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [trend]

An observable pattern in the data.

In general, a trend is an observable pattern in the data. Often this concept is used in time-series analysis but not only. For instance, in a scatter plot the line which most closely fits the data points is also referred to as trend. It may be linear if the trend line is fit with linear regression for example, or non-linear if a polynomial smoother is used.

In the widely used context of time series, a trend is the underlying long term direction of the data. It can be exploited to make predictions about future values of a given series. For instance, moving averages (MA) models make use of this feature of the data. Sometimes it is easy to detect trends via eye-balling, i.e. visual inspection, though in many real-life instances this requires more sophisticated methods. An example is high-frequency price data.

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STL trend of time series using R

I am new to R and to time series analysis. I am trying to find the trend of a long (40 years) daily temperature time series and tried to different approximations. First one is just a simple linear regression and second one is Seasonal Decomposition…
pacomet
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How to add non-linear trend line to a scatter plot in R?

I have a scatter plot. How can I add non-linear trend line?
Karina Khusainova
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Time series and anomaly detection

I would like to setup up an algorithm for detecting an anomaly in time series, and I plan to use clustering for that. Why should I use a distance matrix for clustering and not the raw time series data?, For the detection of the anomaly, I will…
napsterockoeur
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Criteria to set STL s.window width

Using R to perform STL decomposition, s.window con­trols how rapidly the sea­sonal com­po­nent can change. Small val­ues allow more rapid change. Set­ting the sea­sonal win­dow to be infi­nite is equiv­a­lent to forc­ing the sea­sonal com­po­nent to…
Lisa Ann
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Understanding the k lag in R's augmented Dickey Fuller test

I played around with some unit root testing in R and I am not entirely sure what to make of the k lag parameter. I used the augmented Dickey Fuller test and the Philipps Perron test from the tseries package. Obviously the default $k$ parameter (for…
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When is it necessary to include the lag of the dependent variable in a regression model and which lag?

The data we want to use as dependent variable looks like this (it is count data). We fear that since it has a cyclic component and trend structure the regression turns out to be biased somehow. We will use a negative binomial regression in case it…
Mauricio Tec
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How to characterize abrupt change?

This question may be too basic. For a temporal trend of a data, I would like to find out the point where "abrupt" change happens. For example, in the first figure shown below, I would like to find out the change point using some statistic method.…
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Why is it valid to detrend time series with regression?

It may be a weird question at all but as a novice to the subject I am wondering why do we use regression to detrend a time series if one of the regression's assumption is the data should i.i.d. while the data on which regression is being applied is…
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Difference between series with drift and series with trend

A series with drift can be modeled as $y_t = c + \phi y_{t-1} + \varepsilon_t$ where $c$ is the drift (constant), and $\phi=1$. A series with trend can be modeled as $y_t = c + \delta t + \phi y_{t-1} + \varepsilon_t$ where $c$ is the drift…
Michael
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R detect increasing/decreasing trend of time series

I have lots of time series with periods: day, week or month. With stl() function or with loess(x ~ y) I can see how trends of particular time series look. I need to detect if trend of time series is increasing or decreasing. How can I manage that? I…
Jurgita
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Why Time series decomposition is performed

I am new to time series forecasting. In most of the forecasting blogs that I have read so far, the time series is decomposed first. As per my current understanding it is suppose to help us in figuring out whether there is a trend, seasonality etc.…
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Dubious use of signal processing principles to identify a trend

I am proposing to try and find a trend in some very noisy long term data. The data is basically weekly measurements of something which moved about 5mm over a period of about 8 months. The data is to 1mm accuracey and is very noisy regularly changing…
Ian Turner
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Statistical test to verify when two similar time series start to diverge

As from title I would like to know if exist a statistical test that can help me to identify a significant divergence between two similar time series. Specifically, looking the figure below, I would like to detect that the series start to diverge at…
Ugo Giordano
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how can i simulate with arima.sim drift, intercept and trend

I am using arima.sim to simulate data. I want to introduce in the simulation intercept constant drift and trend and i dont know how do it
Carlos Sergio Jara
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Comparison of time series sets

I have three sets of time-series data I am looking to compare. They have been taken on 3 separate periods of about 12 days. They are the average, maximum and minimum of head counts taken in a college library during finals weeks. I have had to do…
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