Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

0
votes
0answers
9 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 ...
1
vote
1answer
19 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 ...
1
vote
0answers
16 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 ...
2
votes
1answer
27 views

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 ...
1
vote
1answer
26 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 ...
1
vote
1answer
32 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 ...
0
votes
0answers
18 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 ...
0
votes
0answers
16 views

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: ...
0
votes
0answers
18 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?
0
votes
1answer
41 views

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 ...
0
votes
0answers
12 views

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 ...
3
votes
2answers
84 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 ...
3
votes
1answer
124 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 ...
1
vote
1answer
20 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, ...
0
votes
1answer
24 views

Questions on making data stationary for ARIMA

When doing a time series analysis I have read these instructions : ...
1
vote
0answers
11 views

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, ...
5
votes
1answer
41 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\}...
0
votes
0answers
13 views

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 ...
8
votes
4answers
402 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 ...
0
votes
1answer
35 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: ...
0
votes
0answers
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 $x_i$ ...
0
votes
0answers
8 views

AR-SIEVE bootstrap for time series

I have a question about the AR-SIEVE Bootstrap proposed by Buhlmann in 1997 and 2002. Here the references: Bühlmann, P. (1997). “Sieve bootstrap for time series”. Bernoulli 3, 123-148. Bühlmann, P. (...
1
vote
2answers
51 views

Should this regression be tested for stationarity?

This is a fairly basic question I am struggling with. I am using the oil prices I have currently to forecast the number of cars bought 8 months from now using the regression below. Would this ...
1
vote
0answers
24 views

Is an AR(p) process with roots inside the unit circle non-stationary? [duplicate]

The title pretty much says it all: is an AR(p) process with roots inside the unit circle non-stationary?
0
votes
0answers
16 views
0
votes
1answer
38 views

A Strict Sense Stationary (SSS) process implies it is a Wide Sense Stationary (WSS) process - proof

Looking for a mathematical proof which shows that a Strict Sense Stationary (SSS) process is necessarily a Wide Sense Stationary (WSS) process.
0
votes
0answers
30 views

Interpret Dickey Fuller and KPSS tests

I have a time-series with the following profile (electricity generation): My series returns the following, when using both Dickey Fuller and KPSS tests: ...
1
vote
0answers
18 views

Understanding Seasonal ARIMA

I'm a bit struggling understanding the concept of Seasonal ARIMA. Because from what I've understood: when we modelize an ARIMA model, we want to transform the time series into a stationary series (...
0
votes
0answers
6 views

Nonstationary ARIMA model fitting by stationary ARIMA

Let me have an ARIMA model like ARIMA(1,1,1): $$\left(1 - \phi L\right)\left(1 - L\right)x_{t} = \left(1 - \theta L\right)a_{t}$$. Look at reduced stationary model: $z_{t} = \Delta x_{t} = \left(1 - ...
0
votes
0answers
34 views

Dickey-Fuller test interpretation (urca package)

I am having trouble with interpreting the Dickey-Fuller test on a time series using the ur.df() function in the urca package. I already read this thread but still need some advise. The command is: ...
1
vote
1answer
39 views

Stationary Process Ergodicity

Can you give me an example of a stationary nonergodic stochastic process that is time continuous?
1
vote
0answers
13 views

First or second difference or log for simulated real GDP data?

For a paper I need to use simulated real GDP data to regress this on average income mobility (how much more the next generation earns). As a hint the assignment indicates that the STATA code for a ...
0
votes
0answers
21 views

How to tell if a process is stationary from a plot of its ACF?

Are there any rules of thumb to quickly tell if a process is stationary by looking at an ACF plot? For example, is the process below stationary or non-stationary? Why?
9
votes
1answer
889 views

If the square of a time series is stationary, is the original time series stationary?

I found a solution that stated that if the square of a time series is stationary, so is the original time series, and vice-versa. However I don't seem able to prove it, anyone has an idea if this is ...
1
vote
1answer
54 views

Make daily business data stationary for ARIMA

For my master thesis I have a dataset with the daily count of orders from a company over ten years. Naturally this data follows strong seasonality with almost no orders on the weekend. To fit an ARIMA ...
0
votes
0answers
24 views

Maximum likelihood and OLS estimation of ARDL model under nonstationarity

Consider the simple ARDL(1,1) model $y_t=\beta_0+\beta_1y_{t-1}+\beta_2x_{t}+\beta_3x_{t-1}+\epsilon_t$ If $y_t$ and $x_t$ are non-stationary can I fit the model with OLS? If not, is assuming that $\...
0
votes
0answers
12 views

does white noise residuals suggest a stationary model?

To fit an ARMA model to a time series, the time series should be stationary to start with. If we obtain a reasonable model fit by looking at mean and variance, ACF ...
0
votes
1answer
43 views

Why my arima model is not stationary?

I want to fit arima model to my data. To do so I run the following code: ...
4
votes
2answers
530 views

How to choose between ARIMA and ARMA model

I am doing time-series analysis in python for the dataset given below- Here's link The plot for the above time series seems to be non-stationary for me because on observing it looks like consisting ...
0
votes
1answer
26 views

Are all non-stationary series random walks?

Are all (non-explosive) time series either stationary around a deterministic trend or random walks? If I run the ADF test and I can't reject the null of non-stationarity does it imply the series is ...
0
votes
0answers
8 views

How Do I Interpret This Table When Testing For A Unit Root?

I'm testing data for unemployment in Poland for the presence of a unit root. I used NumXL (integrated into Excel) to perform an ADF test, which produced the table shown in the picture attached. How ...
1
vote
0answers
27 views

Stationarity in an ADL model

In an ADL model, in order to be consistent do we require both the IV and DV to be stationary? In particular in a process of the form: $$\Phi(L)y_t=\Theta(L)x_t+\epsilon_t$$ where $\Phi(L)$ and $\...
1
vote
2answers
65 views

Fitting an ARIMA Model to Seasonal Data [duplicate]

I am trying to attain an ARIMA model for the following Time Series Data: There is quite obviously a seasonal component - as the plot seems to oscillate between smaller and larger peaks, its seems to ...
2
votes
0answers
26 views

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 ...
2
votes
1answer
40 views

Is the stationarity property invariant by transformation?

In other words, if $X_t$ is $I(0)$, is $f(X_t)$ also $I(0)$? I would say yes: The mean stays constant. The autocovariance still depends only on the lag between the terms.
0
votes
0answers
22 views

Stationarity : drift, trend and zero mean stationary

I have not studied time series but recently had to use R's urca package (ur.df function) to test for stationarity using the ADF test. The function provides 3 options: drift, trend and none ( zero ...
1
vote
0answers
31 views

What is the proper way to standardize non-stationary data?

I have a 19-year time series of satellite imagery (spaced irregularly temporally). The mean and standard deviation of the dataset changes over the 19 years. I get multiple variables from each image; ...
0
votes
0answers
35 views

Sufficient Condition Stationarity AR(2) process

Given the following AR(2) process: $y_{t} = \phi_{1}y_{t-1} + \phi_{2}y_{t-2} + u_{t}$ I need to prove that the sufficient condition for this process to be stationary is $\phi_{1} + \phi_{2} < 1$....
0
votes
0answers
18 views

Interpretation of regression coefficients: second-order differencing

Main Question: How are the coefficients of the second-order differenced explanatory variables to be interpreted? (See the attached screenshot of my result.) Analysis framework: I examine the ...
1
vote
0answers
15 views

Correlation of Aggregate Data on a monthly to quarterly basis

I am working with a data set of 42 countries of monthly migration. I want to extract factors using PCA, and find non stationary errors of my model, so I am working in first difference. However there ...