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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Showing that random process is stationary

Suppose i have $x_t, \bar{x_t}, t\in \mathbb{Z_+}$ independent 2-states $\{0, 1\}$ Markov chains with positive transition probabilities. Initial states are $x_0 = 0; \bar{x}_0 = 1$. For which positive ...
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Converting random non stationary series to stationary series [closed]

Is it possible to convert non stationary random series, for instance the price of BTC, to stationary? While messing around with some code, I subtracted the open from OHLC values of BTC and got a ...
1 vote
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Seasonal and trend adjustment for irregularly spaced time series

I know of different methods that exist to remove seasonality and trend in the data to make it stationary. However, that exists only for regular time series; that is, a series that follows a fixed ...
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Is stationarity of variables neccessary condition for Bayesian VAR?

I am trying to run a BVAR on 5 variables. Four out of five are non-stationary. So shall I do the first difference of the non-stationarity variables or take them in level for running the BVAR? And what ...
1 vote
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Inclusion of year and seasons as variable for regression with non-stationary response?

The common knowledge is that OLS only makes sense if both the response and explanatory variables are stationary (ignoring exceptions like cointegration), as otherwise, there could be effects of ...
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Establish convergence to normal area

I will try and make my question abstract, since I have two problems of the same overall type. I am given a time series $Y_t$, t=1,...,T. I know that this time series has a (slowly) changing ...
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1 vote
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Stationary time series having unusual ACF and PACF plots

I'm analysing a highly stationary time series and while plotting ACF and PACF I noticed a strange bump at a later lag very close to the 0.5 threshold level. Does it affect the AR degree=2 and AM ...
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How do I interpret my autocorrelation and partial autocorrelation of COVID-19 time series data?

Note: I've edited my question based on comments from @whuber. I have a time series of the USA's COVID-19 daily deaths smoothed to mitigate massive, weekly data dumps. My two-plus years of data comes ...
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Can I use non-stationary variables in forecasting problem

I want to build survival analysis model (Cox PH) with time-varying covariates. Time-varying covariates are macroeconomic variables. Therefore, they are same for each individual at the same calendar ...
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Which criteria should I use to evaluate a time series for stationarity?

I have been given two criteria to evaluate the stationarity of a time series: A stationary series will have no sample acf (SAC) or sample pacf (SPAC) values outside of confidence bounds on the chart. ...
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Phillip-Perron test - sample size requirement?

I understand that both Phillips-Perron and Augmented Dickey Fuller tests are for the presence of a unit root in a time series. It is my understanding that these test conduct those tests differently, ...
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How to get around the weaknesses of stationarity tests like ADF test?

I have a large search space of ~600 time series, where I am constantly scanning for stationarity (I have a "rolling window" for all the time series where I run a stationarity test at every ...
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Is this statement of a stationary density function correct?

I'm planning to use a discrete-time stochastic process defined in the following paper: Nicolau, J. (2002). Stationary Processes That Look Like Random Walks—The Bounded Random Walk Process in Discrete ...
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VAR with trend-stationary variables

I'm currently trying to estimate a VAR with 3 variables - consumption, investment and a credit spread. I have inspected the variables and run ADF tests to determine that they are in-fact trend-...
1 vote
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Forward/Backward Iteration and Stationary/Stability

Suppose I have an AR(1) process of the form: $$y_t = \phi y_{t-1} + \epsilon_t$$ where $\epsilon_t$ is a white noise process with mean zero and variance $\sigma^2$. If $|\phi| < 1$ , the model is ...
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1 vote
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How to visually interpret Augmented Dickey-Fuller test results between two time series?

Time-series #1 and #2 are daily reported disease cases in the Central vs. Southern regions, respectively. The p-values from the Augmented Dickey-Fuller test is less than 5% for #1 and more than 5% for ...
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derivation for the standard deviation of autocorrelation

The standard deviation of the estimated autocorrelation coefficient is given as (1/sqrt(sample size). Can someone derive this?
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Cointegrated regression with stationar

For several years, I have been thinking about cointegration regression involving stationary variables as explanatory variables. I am looking for comments on whether the following procedure is ...
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why are there many different ways to achieve stationarity?

In time series analysis, I've read two main ways to achieve stationarity. difference (or log difference) normalize with mean 0 and std 1 What are the main differences between the two and how should ...
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How is this series possibly stationary (by ADF Test)? [duplicate]

Here is an attached image of a time series that I am testing for stationarity using the Augmented Dickey-Fuller test. Here is the command I ran in R: ...
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1 vote
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Autocovariance of Explosive AR(1) model with $|\phi|>1$ expressed as a stationary process

I am working through the book called Time Series Analysis and Its Applications by Shumway and Stoffer. I am stuck deriving an equation given in example 3.4 in the book (page 80 for the fourth edition),...
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Logit with non-stationary predictors

I have a logit with two predictors that are I(1). Can I meaningfully test for cointegration between the predictors. If so, what would I save for the logit? I am assuming that cointegration between the ...
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How to make quarterly population data stationary?

So, I am trying to build the Time Series model for the quarterly population estimate for Ontario provided by Stats Canada (https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=1710000901). As seen ...
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Current best practices for detecting Unit Root in time series data?

I'm trying to get an overview of what are the current best practices for detecting unit roots in time series data. The main approach I came across is the Augmented Dickey Fuller (ADF) test, which ...
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