# Questions tagged [stationarity]

A strictly stationary process (or time series) is one whose joint distribution is constant over time shifts. A weakly stationary (or covariance stationary) process or series is one whose mean and covariance function (variance and autocorrelation function) do not change over time.

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### Multivariate stationarity/cointegration test

Am I right to say that for multivariate time series, we can't use normal stationary test like Dickey–Fuller test and we need to use cointegration Test like Johansen? Or this is not true in general?
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### Identifying Early Indicators Time Series Analysis

I have a time series representing demand for a product which looks as follows: Clearly, this time series shows an upward trend and it's variance does seem non-stationary as well. Further, I have a ...
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### Is applying an ARMA model to a stationary series the same as applying it to a trend and seasonally adjusted series?

Is it true that regular differencing and seasonal differencing of a time-series to achieve stationarity, is the same thing as adjusting a time-series for trend and seasonality? If the above statement ...
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### If $y_t$ is a time series with autocovariance $\gamma$, does $\gamma$ necessarily have to be absolutely-summable?

If $y_t$ is a time series with autocovariance $\gamma$, does $\gamma$ necessarily have to be absolutely-summable; i.e., ${\sum_{i=\infty}^\infty |\gamma (i)}|<\infty$? If not, what could be the ...
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### autocovariance for a strict stationary stochastic process

I'm studying thistleton and sadigov ts analysis course, and the text says that for a strict stationary stochastic process: (A) The joint distribution of $X(t1),X(t2)$ is the same as the joint ...
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### Is my ARIMA Modeling Failing Due to Non-Stationarity or Something Else? [closed]

I'm trying to employ an ARIMA model, and have run into the following conundrum: when I employ differencing or other transforms to successfully achieve stationarity (at least according to the ...
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### Cointegration, Error Correction, and ADF test with lags

I am fitting an error correction model (ECM) of two I(1) variables. I'm following the Engle-Granger approach of first finding the cointegrating relationship. So first, I regress one series against the ...
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### Supervised learning in non-stationary environments?

For real applications, concept drifts often exist, i.e., the relationship between the input and output changes overtime. I'm wondering what are the most common methods to enable neural networks to ...
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### KPSS test with different results for trend and single mean models

I am having some dilemma while interpreting my KPSS stationarity test. As in the image below, null is rejected for single mean model while not for trend model. Does it mean "after considering the ...
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### Is my interpretation of ADF and KPSS correct?

I am new to time series analysis, and I am trying to interpret the ADF and KPSS results. Is my interpretation of stationary correct? ...
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### Help on whole model specification and guide on procedures

Could you guide me what I should do in my research in terms of econometrics. I want to emphasize the causality in energy savings by buildings and various factors (like climate etc.). I don't have a ...
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### Detrending for a large dataset consisting of many group time-series

I have a huge dataset consisting of many individuals (~20000), each with a month of daily data. I am thinking of detrending those individual time series that are non-stationary but visually ...
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### Stationary VAR( 1) process : complex eigenvalues

For a stationary Vector autoregressive process of order 1, eigenvalues of A should be smaller than one. However, I am getting some eigenvalues as a complex number after the estimation. however, the ...
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### How to interpret Dickey-Fuller Results

I want to prove that my data is non-stationary at level, but stationary after first differencing. I am trying to do this with the ur.df() function in R, but I am a ...
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### Conflicting Ljung-Box, ADF & KPSS tests [duplicate]

I'm trying to find the stationarity of my Sales Time Series. Box-Ljung Test says: Non-stationary ADF test says: Stationary KPSS test says: Non-stationary. Or am i interpreting these wrong? Please help....
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### In TSMARS, does the independent variable need to be stationary?

Do time series need to be stationary when fiting a time series multivariate adaptive regression spline (TSMARS) model?
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### Does ADF test in python include F test in trend and constant?

I want to know if the time series without a unit root contains a time or a quadratic form of time. $\Delta y_t=\alpha+\beta t+\gamma y_{t-1}+\sum_{j=1}^{k}\delta_j\Delta y_{t-j}+\epsilon_t$ I would ...
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### Do we have to make cycles and trend covariates/predictors stationary in order to use them as valid predictors in a Dynamic Regression Model?

I want to extract patterns from macroeconomic indicators for use in predictor a target variable. In particular, I plan to decompose the macroeconomic variables into trend, cycle, maybe seasonality and ...
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### Diagnostics for first and second order (weak) stationarity

I am currently running a time series analysis which is mostly exploratory in nature. The data consist of a single sample of a univariate time series (equally spaced) and contains about 200 data points....
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### trend stationary with external regressors

Suppose I have two trend - stationary time series with strong correlation. In the case where there are no regressors, if a time series is trend-stationary, it becomes stationary by subtracting a ...
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### Relationship between weak and covariance stationary

I have read that the definition of weak stationary is : $Mean(t) = mean(t + \tau)\\ Cov(t_1,t_2) = cov(t_1-t_2,0)\\ E[|x(t)|^2] < \infty$ In this definition of weakly stationary, can the ...
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### Detecting significant trend / non-stationarity in small sample time series

I am trying to detect whether there is a significant change in plankton size over time. As I understand, this is referred to as stationarity testing in time series analysis. Unfortunately, my time ...
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### What is the largest n root transformation I should consider for making a time series stationary?

Currently, I am working with multiple time series and not all of them are stationary. In order to make them stationary I am considering different transformations and checking the augmented dickey ...
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### Do we need to stationarize a time series signal when using Kalman filter?

I am working on forecasting the number of logins. I know that before using ARIMA, it is important to remove trend and seasonality. But in the case of Kalman filter, I am not sure. After all it is a ...
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### How do the forecast intervals from an AR model behave when the time series is inherently stationary?

I'm trying to wrap my head around two contradictory intuitions behind how forecast intervals should behave when we use an AR process to model a stationary time series: (a) On one hand, since the time ...
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### ARIMA vs SARIMA

I am a self learner, and I am studying time series analysis. I came through the fact that ARIMA can be used to model a time series which is not stationary (Integrated ARMA model). The non ...
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### Is this method to make data approximatly stationary valid?

I thought up this method to make data stationary for time series modeling with Arima. Does this method make any sense or is it completely flawed? For stationary data we need a constant mean and ...
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### Automatic process to determine stationarity of AR(p) model

I have read that an AR(p) process is stationary if all of the roots of it's characteristic equation are greater than one in absolute value. Does this mean that I can find out if my data set is ...
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### What to do in the case when you have trend stationary data?

I am having difficulties to find out what to do in the case when your data is not stationary but trend stationary. I have tested the data using Augmented-Dickey-Fuller Unit Root Test using the code: ...
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### Stationarity in logistic regression

For a time series dataset, is it required for the independent variables to be stationary for logistic regression? If yes, how can we check for stationarity?
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### Why is spectral density only defined for stationary processes?

I read Brockwell and Davis(2016), Shumway and Stoffer(2016), and Stoica and Moses(2004). However, none of them laid out clearly the reasoning behind the presumption of stationarity when conducting ...
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### In r, can I put non stationary regressors into auto.arima?

In R, can I put non stationary regressors into auto.arima? The dependent variable is also non stationary. I believe auto.arima attempts to make the dependent variable stationary, but does it also do ...
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### Seasonality after 1st differencing

I am working with a financial time series (monthly frequency) and the raw data is not stationary according to ADF, KPSS. I then apply deflation (accounting for inflation), log transformation (to make ...
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### Decomposing U.S. Imports of Goods by Customs Basis from China

I'm working on a project which aims at analyzing the dataset U.S. Imports of Goods by Customs Basis from China (IMPCH). The main point is to make some prediction but we also want to do a little ...
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### Difference between differencing data and removing trend line for stationarity

In reference to making data stationary for Arima: Is there a difference between subtracting a best fit line from data, and a first order difference? Or, subtracting an exponential fit from data, ...
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### Questions on making data stationary for ARIMA

When doing a time series analysis I have read these instructions : ...
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### Must a binary time series with a constant mean be stationary?

Suppose I have a binary time series $Y$ with support $\{0,1\}$ and a constant mean (i.e. $E[Y_t]=\mu,\forall t$). I know that this means the variance of the series is constant in time as well since, ...
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