# 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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### Stationarity test for count data time series

can someone give me an overview of stationarity test for time series of count data? For instance, I would like to know if there exists a test similar to the Augmented Dickey Fuller or how this test ...
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### When non stationarity is a problem?

So in the literature one can find many times that ML works on the assumption that data distributions are stationary. Now I can do multiple tests on my dataset to show the violation on the non ...
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### ARIMA Correlogram Classification - Insignificant P-Values (Reposted w/ specific questions) [duplicate]

I am trying to apply ARIMA forecasting to a stock's market close price. It is daily data with 129 observations. I used Augmented Dickey-Fuller Test and a Correlogram to confirm the data is non-...
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### How to handle a structural break of only one variable in a VAR model?

I am estimating a VAR-model with two variables: GDP real and Investments. Investments has a structural break, GDP real not. As I understood it is only possible to add a dummy variable to both ...
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### Find the order of integration of an ARIMA model from a specified equation

Suppose I'm given an equation: $$Y_t = 1.7 Y_{t-1} - 0.7 Y_{t-2} + e_t$$ If I'm given the data, I can use the Box-Jenkins methodology coupled with stationarity tests like the ADF test to find the ...
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### How to select ARIMA model with cyclic ACF?

My annual time series has following ACF/PACF structure. Based on what ARIMA model should be selected here? Exponential decreasing of ACF --> AR(4) probably? Or because of periodical ACF maybe SMA? ...
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### Find the correlation function of stochastic process given differential equations

Assume two systems for which the following differential equations hold between their input and output signals. $$a \dfrac{dv(t)}{dt}+b v(t)=x(t)$$ $$\dfrac{dy(t)}{dt}=v(t)u(t)$$ Also, assume that the ...
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### Stationarity check in ARX

How to formally check stationarity condition in a regression in the form: $$y_{t}=\alpha_{1}y_{t-1}+\alpha_{2}y_{t-2}+\beta_{1}x_{t}+\varepsilon_{t} \ ?$$ In the case of AR(2) there are some ...
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### Strong stationarity and Markov property for an AR(1) process

Suppose I have an AR(1) process of the form $$X_t=\phi X_{t-1}+\epsilon_t,$$ where $\epsilon_t$ is a Gaussian white noise. Suppose that $X_t$ is weakly stationary check if $X_t$ is strongly ...
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### Intuition of Random Walk having a constant mean

I am very new to time series analysis. A random walk is defined as $Y_t=\phi Y_{t-1}+\varepsilon_t$, where $\phi=1$ and $\varepsilon_t$ is white noise. It is said that process is non-stationary for ...
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### AR(1) - Stationarity condition

Consider the well-known AR(1) model: $$x_t = \phi X_{t-1} + \epsilon_t$$ where, as usual, $\epsilon$ is an independent white noise process. I have read many sources. All of them get away saying that ...
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### Regressing I(1) variable on I(0) variable

I am dealing with time series regression, where I have stationary and nonstationary variables. Can I regress nonstationary I(1) variable on stationary variable when controlling for the lag of the ...
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### Create stationary dataset with log, sqrt and cube root layering

I have a time variant dataset with highly non stationary data. The dickey-fuller p value always at the 0.90 to 0.99 area. Even after single transformation, still data generates with p value about 0.80....
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### Does a time series clustering that uses cross-correlation as proximity measure require stationarity?

I have a set of time series which exhibits no autocorrelation but the variance is not constant. I remember that one of the requirements of cross-correlation to be meaningful is weak stationarity (we ...
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### Time series analysis: Why am I getting a reciprocal condition number when trying to estimate VAR-Model? /w reproducible example

I'm currently trying to identify an appropriate VARMA(p, q)-representation for a multivariate time series using the MTS::-package in R. The series comprises n = 126 ...
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### Covariance of a Stationary Process

Let $Y_t$ be a stationary process such that $Y_1 = a_1$ and $Y_2 = \theta a_1 + a_2$, where $\theta$ is a parameter and $a_t$ is the white noise process with mean 2 and variance $\sigma^2_a = 0.5$. ...