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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45 views

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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63 views

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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Interpretation ARIMA equation

I came across a Wikipedia article ARIMA - Other special forms and I don't understand the interpretation in the small paragraph "Other special forms". I copy it below: "For example, having a factor $...
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21 views

Augmented dickey fuller test

Why augmented dickey fuller test gives me less p-value i.e. less than 0.05 despite of having seasonality my data. My data's plot: Code for adf test : from pandas import Series from statsmodels.tsa....
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How to perform stationarity test on smoothed data?

I have a lot of errors in my data, so I'd like to apply a smoothing process eg ewma. However I am concerned that this will affect the results of e.g an ADF test. Can anyone suggest some relevant ...
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22 views

Integrated time series and continuous time integral

I am new to time series, and have a theoretical (philosphical, if you wish) question on the connection of an integrated time series with the usual concept of integration in calculus. If $x_t$ is an ...
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Proof of Stationarity of dependent variable

I have a linear regression model of time series data where the model developer has found that the dependent variables is not stationary via ADF, KPSS and Phillips Perron tests. The developer claims ...
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32 views

Non-Stationary Data with Lagged Dependent Variable?

I am currently dealing with non-stationary data and I am unsure of how to proceed. My data is stationary in first differences I(1), which I confirmed using a Dickey-Fuller unit root test. However, I ...
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26 views

Example where ACF depends on more than the lag

In a weakly stationary time series, the ACF $\gamma(s, t)$ depends on $s$ and $t$ only through their difference $|s-t|$. I am familiar with cases such as moving average series where there's nonzero ...
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Intuition for MCMC and stationary distribution?

Studying up on Markov-chain Monte Carlo sampling and the theory behind the stationary distribution, I want to validate it. Say we have a stochastic transition matrix $p$ describing events in space $\...
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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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1answer
23 views

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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30 views

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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53 views

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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23 views

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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18 views

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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24 views

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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1answer
41 views

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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1answer
85 views

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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1answer
46 views

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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20 views

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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29 views

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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96 views

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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1answer
131 views

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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1answer
31 views

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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48 views

Is binary mapping of simple stationary series still stationary

Suppose I have a weakly stationary series with a support $\{0, 1, 2, 3\}$. If I were to map all values of this series into a binary series with support $\{0,1\}$ using the rule $\{0,1\}\rightarrow\{0\}...
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Stationarization of 2-dimensional Time-Series

I'm trying to perform a Gaussian Process Regression on time-varying data of the form (t, x, y, z), where t is the time when ...
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414 views

Is the absolute value of a stationary series also stationary?

I know that linear transformations of time series arising from (weakly) stationary processes are also stationary. Is this true, however, for a transformation of a series via taking the absolute value ...
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1answer
125 views

KPSS: Difference between level stationary and trend stationary

Can anyone please clarify for me the differences between level stationary and trend stationary in KPSS test? I run the KPSS test with trend and level on same time series and the results are: H0: ...
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25 views

Is Stationarity Preserved under Binary Mapping [duplicate]

If I have a series arising from a (weakly) stationary process $$\{x_i;i\in\mathbb{Z}\}$$ and create another series by a binary mapping of the form $$f:\mathbb{R}\rightarrow\{0,1\}$$ (i.e. if $x_i$ ...