In general, a trend is an observable pattern in the data.

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Selection of additive/multiplicative trend/error/seasonality in ETS

Forecasting: principles and practice. This book tells about 30 different types of ETS models. It describes about additive models and multiplicative model. I would like to know on what basis do we ...
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16 views

Time trend in DF unit root test

I have a couple of questions concerning the time trend (βt) in an augmented Dickey-Fuller test for panel data: 1) From what I understand there is no clear rule/standard or test as to when to include ...
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13 views

Trend or stationary data [closed]

I would to ask about acf data pattern that has shown from minitab output. Can I determine that the data pattern has trend? I'm still confused about how many lag should be a criteria for trend or ...
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21 views

P for trend for quartiles in linear regression in SAS

I am using PROC GLM in SAS to run a linear regression model and have a continuous exposure variable that for a secondary analysis I have categorized into quartiles. I know I can use a contrast ...
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9 views

Data analysis method for seasonality due to independent variable and trend

I have historical average temperature data for each day for about 30 years. I also have historical data for each hour population of certain kind of microbe. The microbe growth rate is about same as ...
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11 views

Trend break in panel data

I have a panel of countries (N= 30) over four decades (T= 40). I would like to test the impact of a policy by analyzing whether it led to a change in the trend in the outcome variable. Note: The ...
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19 views

Removing seasonality when timeseries includes negative or zero values

I am using an x13-arima-seats based solution to remove seasonality and detect data trends. However, many of the series I need to observe trends on contain zero and negative values, which my solution ...
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2answers
32 views

Testing trend in proportions?

Simple question: I have a sequence of 10 proportions $(p_1,\dots,p_{10})$ (indexed by time), $p_j\in(0,1)$, that seems to have an increasing trend. How can I test this trend?
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1answer
58 views

Fitting a nonlinear regression $Y=1 - a^{-bx}$

I have the following dataset: where X:Y 1:0.81 2:0.86 4:0.9 6:0.93 8:0.96 10:0.98 12:0.99 14:0.99 16:1 18:1 20:1 ..:1 Since the limit of the regression ...
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21 views

How we can find trend of time series and turning points?

I want something like this in a time series: Currently I'm using some linear interpolation to find trend and turning points. What other methods can I use to find these turning points in a time ...
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19 views

measure trend in time series / event analysis data

I have a data set of people's buying history for 1 year by day. I am interested in predicting if this person will buy a product in the next coming year. My idea is that if someone has a "upward" ...
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1answer
19 views

Which MA(q) to use for hourly data in Time Series decomposition?

I am trying to do a Time Series decomposition manually (I don't wanna use one of those R packages that give you all already done). I have already removed the mean from my TS by dividing the TS by its ...
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36 views

$c(n)$ is trend, $r(n)$ is fluctuation. Should $\text{cov}[c(n),r(n)]/\text{var}[r(n)]$ be close to zero?

Suppose $y(n)$ is a random time series given as function of the discrete-time variable $n$. Suppose we can decompose it into $y(n) = c(n) + r(n)$, where $r(n)$ is a strict stationary residual ...
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1answer
32 views

Error while decomposing a time series in R

I'm coding to forecast using ARIMA model. The data is one single column in .csv file and it is an annual data. Therefore, the frequency = 1. When I'm trying to decompose my data it gives me an error:...
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41 views

Using repeated measures change/trend as a predictor variable

I have repeated measures of happiness for a sample of participants, and a single measure of satisfaction for each of the ...
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7 views

Weekly Time Series Detrend

I have weekly time series data that has a unit root problem. When i include a trend (in DF), the unit root is gone. This is 10 years worth of data, with gaps, and there are nearly 400 weeks. My idea ...
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12 views

'Level' still seems periodic after Season Decomposition

I've used tbats for this transformation: Exponential smoothing state space model with Box-Cox transformation, ARMA errors, Trend and Seasonal components My (...
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1answer
59 views

Is a trend-stationary variable I(1) or I(0)?

I am trying to do cointegration analysis between two variables. I first used the standard Dickey-Fuller and Phillips-Perron tests; they concluded my variables were I(1). I then did cointegration and ...
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1answer
18 views

Huge discrepancy between analytic Mann-Kendall statistic and its block bootstrap estimate

I am analyzing some environmental time series and I use Mann-Kendall test to check for monotonic trends. However, I am a little bit concerned about autocorrelations in my data, since standard Mann-...
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1answer
45 views

Does stationarity imply absense of upward or downward trend?

I wonder if a time series being stationary implies that there can be no upward or downward trend. It appears to me that such an implication should hold, since in order to be stationary a time series ...
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1answer
79 views

Change point detection test using Pettitt-Mann-Whitney test?

I am getting two change point with same p-value (or 90.27% probability) in an interval of two years i.e., 1955 and 1958. Here the trend is increasing from 1901-1955 and 1958-2015. How it could be ...
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55 views

Interpretation of Mann-Kendall statistics

I am doing a trend analysis for vegetation dynamics using Mann-Kendall test for trend detection and Sen's slope for computing the magnitude of the trend. There are 6 sites inside a conservation area ...
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28 views

Is detrending the same as seasonal adjustment?

I have a time series of Twitter tweet counts against time. Inevitably, Tweet count goes up during the morning and lunch time. I am exploring the topic of seasonal adjustment. This would remove this ...
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2answers
74 views

predict seasonality and trend combined, better approach?

The nature of my problem combines seasonality (yearly repeated) and trend (over all data). I have one observation per month. To simplify, let's say I have this: Which can be perceived as this: So ...
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2answers
108 views

Trend and Breakout detection in time series

I am working on several types of system metrics which characterizes several components of an application. The metrics range from system metrics like cpu.utilization to network metrics and database ...
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17 views

A number that shows trend, especially regression

I apologize for the vague title, I am not quite able to form my question except by giving an example. I am trying to quantify the regression in some aspects of software development process. Take ...
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17 views

Statiscal test for ranking time series based on change points and values

I have five time series, each of which consisting of 30 measurements (pressure) from sensors (on three machines located at five different locations). I would like to rank those time series. I run a ...
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1answer
70 views

How can I represent exogenous I(0) variable in VECM / Cointegrating relationship?

So I am doing an econometric study on Bitcoin's USD price. As an exogenous regressor, I have the total number of bitcoins in circulation (nbtc). The graph looks like this: This variable is: ...
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16 views

MATLAB regression showing 'overparametrized' error

So, I'm looking at the time series of earth surface temperatures from 1880 to 2015, a total of 1632 data points (Monthly Data). I was trying to find the trend using a polynomial fit. This is what I've ...
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25 views

How do I detrend this (non-linear) time series before differencing?

I have a variable that looks like this (after taking natural log): I can't run stationarity tests as there are clearly structural changes in the data. How can I get around this – am I supposed to ...
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7 views

Analyzing Average Trend with not matching years

I am working on analyzing census data. Most census data are 5-year average (year 1995 means average of 1991-1995, year 2000 means average of 1996-2000, etc). I am trying to match with other datasets ...
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18 views

autocorrelation interpretation (annual bird surveys)

I am following a method used by others (McCrimmon et al. 1997 Ecological Applications 7(2):581-592) to look for trends in the annual count of nesting pairs of birds at 29 nest sites over a 42 year ...
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20 views

Testing for a Change in Agreement Between Paired Binary Measurements

I would like to know if there is a change in agreement between paired binary measurements from before to after an event occurred. I have two instruments, which are measuring samples from a population ...
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42 views

How do I detrend a GDP time series using country specific deterministic trend?

I am trying to replicate Section 3 of this paper (pdf) which investigates international business cycles. Section 3 is the empirical part whereby they analyze international business cycle transmissions ...
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1answer
30 views

non-parametric trend analysis with data that is both left and right censored

I am assessing the the presence of monotonic temporal trends in E. coli concentration data using a non-parametric approach. These data are both right and left censored (for example the lower detection ...
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26 views

How can I analyze trends in longitudinal NON-panel data?

I want to analyze data from the General Social Survey. The data is longitudinal individual level data but it is not panel data (yes, I know there's a recent implementation of a panel component - I'm ...
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1answer
40 views

Why does differencing once remove not only linear but also nonlinear trends?

Applying first differences to a time series removes linear trends. See e.g. Can I detrend and difference to make a series stationary? I can understand the motivation. And also, why you would need to ...
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19 views

How to interpret lag vs current variable scatter plots

I'm pretty new to stats and time series, and I was following a tutorial for my time series analysis. So, I'm getting stationary time series with my first difference of data, so I'm not taking any log ...
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1answer
65 views

How to extract the common trend in Panel data?

I have a panel dataset that contains many cities' real estate information ( floor sold) . Now I want to study the relationship between the cyclicality of floor sold and some other dependent variable. ...
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1answer
38 views

Nonparametric censored trend analysis: When using cenken (package NADA in R), should I use annual medians or all of data

I am using cenken to perform a nonparametric trend test on concentration data with multiple detection limits (the detection limit changed when a change of labs was made). I have seven years of data ...
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28 views

What's the best strategy for testing 100+ Poisson distributions on seasonality and trend in Excel?

I have pooled data which can be divided into 4 categories, and those can be divided in 6-50 groups each. I tested the pooled data and the categories with time series plots. Now I'd like to test all of ...
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50 views

Seasonality and trend window in the Forecast functions of R

I have time-series power consumption data for one month. The data is sampled at minutes frequency. Thus, for each day I have 1440 observations and for the month (30 days) I have 4320 observations. On ...
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1answer
27 views

Data trending decision criteria

I'm playing a game in which you can buy and sell items (it's an mmorpg). Now, after certain events, there is a huge drop in the price of certain items (there is a seasonal double experience weekend in ...
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1answer
61 views

Calculating R^2: two different results depending on method

So I've fitted a linear trend to my data and calculated R^2 in two different ways (in Matlab), one is using corrcoef and the other is "by hand". These return ...
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1answer
92 views

Fit a trend to Time Series Data

I have got two time series data sets for 63 years. I want to fit a trend line to them. Here is what am doing: I first estimate a linear (y=a+bt+e) and an exponential model (y=at^b) as the graph ...
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1answer
81 views

Aging data in the German tank problem

The German tank problem is about estimating the total size of a set of objects from random samples of serial numbers. It can simply be done by: $$N \approx m+\frac{m}{k}-1$$ Where $m$ is the ...
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18 views

What is the best way to detect anomalous trends in access logs in streaming?

I just began reading some stuff on the state-of-the-art algorithms to do ML in streaming but I'm fairly new to the field. I see there's a lot of literature on anomaly detection and regime change ...
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54 views

Measuring promotion baseline smoothing

I am trying to estimate promo effectiveness for a retail product. To do this I have taken monthly quantity sold data for the product. My question is - Is it logical to model the sales baseline (sales ...
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13 views

Does an approximately long-term cyclical behavior suggest a polynomial trend or a long-term cycle?

Can you tell with certainty if an approximately long-term cyclical behavior suggests a polynomial trend or a long-term cycle? Yes/No and why? I came across this question while looking at some past ...
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32 views

How can I test for seasonality when the trend is not supposed to be monotonic but sinusoidal?

My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have ...