# 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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### Can I model a trend and seasonal component for a stationary time series?

I modelled quarterly german inflationdata in a state space model with a stochastic level and stochastic seasonal. But now I recognized that I need a stationary time series because I have to compare it ...
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### Addition or subtraction of lag terms in the autocorrelation expectation formula?

I have some confusion about autocorrelation. In my notes I have defined, $$r[k] = E[y[n]y^*[n-k]]$$ Is this the standard way of writing autocorrelation? What are conditions such that $r[k] = r[-k]$?...
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### co-variance of strictly stationary process

How to prove mathematically that co-variance is dependent on time-lag(k) for strictly stationary process? Given that distribution function is time invariant.
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### Can a ratio variable be trend stationary?

Can a ratio variable, e.g. the wage share of factor incomes, really be trend stationary? It is bounded between 0 and 1 and moves in between during long periods, acting like a non-stationary variable. ...
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### Interpretation of time series residual and stationarity

Does it mean that time series model is well generalized (or is a better model) if residual from time series data and model prediction is stationary? Or it means something else?
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### Modelling transient effects together with permanent effects [closed]

I have the time series with transitory non-seasonal shocks (possibly, with exponential decay, but I need to obtain the shape explicitly). In particular, I have trading data and need to predict price ...
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### constant variance for strictly stationary process

How to prove mathematically that variance is constant for strictly stationary process? Given that distribution function is time invariant. It is intuitive but not sure where to start to prove it.
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I have a time series data for 18 months. To check for stationary I conducted adf test, to which my p value is 0.8. And kpss test has a p value of 0.1 , so at 95% confidence level I fail to reject null ...
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### How to confirm if the series is stationary?

Visually, the below plot doesn't seem to be stationary. However, on differencing, I am not very sure if the time series is stationary. Visually, it's not. Please suggest any statistical techniques ...
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### How to check whether a given ARIMA (p, d, q) process is stationary or not?

I know that a finite MA process $X_t = \Theta(B)Z_t$ is always stationary. Also, whether an AR(p) process is stationary or not can be verified by checking the roots of $\Phi(B)=0$ where the process ...
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### Stationarity for an AR(2) process

How can I show that the following AR(2) process is stationary $X_t = X_{t-1} + cX_{t-2}+Z_t$, provided -1 < c < 0 ? I represented the series as $\Phi(B)X_t = Z_t$ and then tried to find out ...
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### ML preprocess to achieve stationarity

I would like to use Machine learning models on top of multivariate time series data to forecast long horizons (for example 400 items and their historical sales in the last year & content features)...
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### What's the intuition behind re-parameterization in the Dickey-Fuller test?

In text books and lecture slides, people often explain that the normal t-test of, say, the AR(1) parameter in the Dickey-Fuller test does not follow the usual distribution. It also explain that after ...
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### logic of stationary property?

I am extremely puzzled... In textbooks I read that the "stationary property" is having the same statistical properties, in two chunks of my time series. I do not understand... How can I possibly ...