# 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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### What guarantees the existence of a finite representation of the Wold decomposition? Mechanics and Intuition

Every covariance stationary process can be written as a linear, infinite distributed lag of white noise. In other words, every covariance stationary process has a Wold representation. Then we go on to ...
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### Nonstationary solutions for stationary ARMA equations

By "stationary" I mean "weakly stationary". Consider a "stationary" AR(1) equation: $$X_t=\varphi X_{t-1}+\varepsilon_t,$$ where $t\in\mathbb{Z}$ are discrete time moments, $\varepsilon_t$ a zero-...
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### Stationary vs Stability

I am searching for an example of an unstable VAR($p$) process (its reverse characteristic polynomial has no roots inside and on the complex unit circle) which is stationary. I come up with this ...
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### Evaluating if time series need differencing

I am a total beginner with time series analysis. I use R. I understand that time series data need to be stationary for analyses like cross-correlation or modeling. I am, however, struggling with ...
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### Questions regarding geodesics in Adler and Taylor's “Random Fields and Geometry”

I'm working through some calculations in Adler & Taylor's Random Fields and Geometry. $f$ is a real, scalar, zero-mean random field parametrized by $x^i$ (elements of some topological space $T$). ...
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### Stationarity of independent variables in ARIMAX

I am running an ARIMA model with exogenous variables. Do all my exogenous variables have to be stationary or is it okay if one of my exogenous variable is non-stationary?
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### Stationarity tests for time series

I am currently working on time series modeling, especially on stationarity tests. For this purpose, I am extensively using Pfaff's book "Analysis of integrated and cointegrated time series with R" and ...
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### stationarity and fractional differencing

This is a methodology question. I would like to make the data stationary but not transform it "too much" (information loss), before it is fit for statistical/ML purposes such as regression or PCA. ...
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### Identifying lagged effects / Distributed Lag Model

I would like to create a linear distributed lag model in order to do some forecast and also being able to interpret the results. Unfortunately I'm a bit confused with the process I should follow....
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### Regressing nonstationary on stationary variable

I am trying to empirically estimate the coefficient for the Okun's law as a relationship between output growth and unemployment. I am using the simple gap version, where I regress real output growth (...
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### What is a test that I can use to determine if a time series is first-order stationary?

I need to test that one of the time series in my analysis has a constant mean over time. Is there a standard test I can use to help me determine this? I know that I can use a nonparametric procedure ...
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### Averaging time series to improve stationarity - loss of power?

Short version When averaging over a presumed stationary time series and calculating statistics (e. g. normalized mean square error) to compare to a simulation (atmospheric turbulence model) of the ...
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### White noise for level, log and log differences data sets

I am using eviews 7 and I have 3 data sets for DAX stock market index: level (dax), log (ldax), and log differences (dldax). I need to check whether the error terms of these data sets are white noise ...
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### Time series: non-stationary in the short term, but stationary in the long term

I am working two time series y and x, and I try to fit the linear model y ~ x. y is stationary, x is not during the modeling period (most recent 50 quarters). But ADF test on the entire series of x, ...
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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 stationarity a requirement when using neural networks for time series forecasting?

I'm getting conflicting information on whether stationarity is a requirement when using neural networks for time series forecasting: In this lecture, the speaker says it isn't a requirement. In this ...
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### Does stationarity have to be satisfied for a time series regression problem?

I am recently trying to build a time-series regression model to predict for the output flow rate of a reactor given some upstream conditions. The reactor behaves quite cyclically because the ...
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### Not testing for stationarity in a panel data set

Currently, I am analyzing a panel data set (different individuals over time) using panel data models with the lagged dependent variable as an explanatory variable. In this case the stationarity ...
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### Using non-stationary time series in cross-correlation analysis

I have modelled organism dynamics and abiotic factors time series in order to understand their seasonal oscillation and trend over time. Now I want to identify if there are any correlation between ...
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### Removing Variance in Time Series After Applying Log Transformation

I'm trying to look at natural gas prices from 2003-2018. The issue is after applying log transformation and then diffrencing data by 1, I still seem to get an increase in variance from mid 2014-2018. ...
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### How to test for constant mean over time with time series data

I have a data set that looks like it may not be stationary. As a test, I ran a linear regression of the data against an x variable that was an index of time, 1:400 periods. I saw that the slope ...
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### Autocorrelation Functions/Autocorrelograms and the assumption of Weak Stationarity?

Does it make sense to even speak of the autocorrelation function or of the autocorrelogram for a non-weakly stationary series? Anytime we see an autocorrelation function or an autocorrelogram can we ...