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.

Filter by
Sorted by
Tagged with
0
votes
0answers
6 views

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 ...
0
votes
1answer
21 views

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 ...
0
votes
0answers
17 views

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-...
1
vote
1answer
14 views

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 ...
0
votes
0answers
12 views

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 ...
0
votes
0answers
13 views

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? ...
1
vote
0answers
17 views

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 ...
1
vote
0answers
23 views

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 ...
0
votes
0answers
13 views

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 ...
12
votes
2answers
1k views

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 ...
0
votes
1answer
30 views

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 ...
0
votes
1answer
26 views

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 ...
0
votes
0answers
14 views

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....
0
votes
0answers
6 views

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 ...
0
votes
1answer
42 views

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 ...
0
votes
1answer
18 views

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 $\sigma^2_a = 0.5$. ...
1
vote
1answer
48 views

How to show that $var(\hat{\mu}) < var(\bar{X}) $for a stationary process ${X_t}$, where $X_t = \mu + Z_t + Z_{t-1} $?

If ${X_t}$ is a stationary time series with mean $\mu$ then the usual estimator for $\mu$ is the sample mean $\bar{X} = \frac{X_1+...+X_n}{n}$. Assume we have $X_t = \mu + Z_t + Z_{t-1}$, where ${Z_t}...
0
votes
0answers
5 views

In stationary time series, how much time needed to go back to its mean?

Question I have a time-series data which is stationary as below. If an observation at t time point is far from the mean, how much time do I need, on average, for the timeseries to go back to its ...
0
votes
0answers
10 views

Stationarity of variables for Local Projections

Should we care about the stationarity of the time series when doing Local Projections? In his website Jorda (the author of Local Projections method) provides a code for doing local projections : https:...
1
vote
0answers
8 views

Predicting stationarity of a time series

I have a time series, for example equity prices. This series is weakly stationary (for instance an AR process that does not violate the stability condition). How can I make predictions on how likely ...
0
votes
0answers
20 views

Probability of next item in normal distribution series given a series of values?

Let' say that I have a normal dist data with x as time and y as the dependent variable. For all purposes, the data is normally distributed i.e. stationary. Now it would be clear that all my data ...
0
votes
0answers
3 views

Are there tests for unit root in respondent-driven sampling referal chains?

The assumption of independence in respondent-driven sampling is likely to be violated when there is homophily (individuals are more likely to recruit new study participants who share characteristics ...
0
votes
0answers
28 views

What are the stationarity conditions for an AR(4) process?

The stationarity conditions for an AR(2) process are: $$a_1 + a_2 < 1$$ $$a_2 - a_1 < 1$$ $$a_2 > -1$$ And the stationarity conditions for an AR(3) process are: $$a_1 + a_2 + a_3 < 1$$ $$...
1
vote
1answer
37 views

Is it fine to choose 0 lag for adf test in my data?

The level values weren't stationary so I took percent changes $(P_t-P_{t-1})/P_{t-1}$. Here's the data: These are the PACFs to determine lags. I think the lag can be 0, or 7 or 11 in case of GDP and ...
0
votes
0answers
26 views

Interpreting ACF and PACF plots on trading volume

I'm a fairly new one to time series analysis. I was analyzing the daily trading volume of stock derivatives for the past year and trying to see if there is a seasonality pattern. I tried to make the ...
1
vote
2answers
60 views

Making an AR(3) model weakly stationary

I have a model as:$$r_t=0.05+\frac{7}{6}r_{t-1}+\frac{1}{6}r_{t-2}-\frac{1}{3}r_{t-3}+a_t$$ When checking for stationarity: $$1-\frac{7}{6}x-\frac{1}{6}x^2+\frac{1}{3}x^3=0$$ I get $x\in \{-2,1,1.5\}$....
1
vote
1answer
29 views

Non stationarity and forecasting

Let's assume we have estimated a linear regression model on a dataset from 2000 to 2017. The data were stationary. What happens if the data are no longer stationary in the next years? Do the forecasts ...
0
votes
0answers
18 views

How to interpret regression results when the data have been detrended?

I am planning to build a linear regression model where I explain flight ticket demand with airfares, lagged airfares, GDP etc. based on monthly data from the past 15 years. This is my first time ...
2
votes
1answer
31 views

Do Recurrent Neural Networks assume stationarity or just a general kind of sequential dependence?

Just when I thought I had convinced myself that RNNs make no other assumption about a sequence other than that there are dependencies between the inputs and that (in the case of monodirectional RNNs) ...
1
vote
0answers
9 views

Normality of tau-statistics ($\tau_{\mu}$ and $\tau_{\tau}$) in presence of unit roots

The original Dickey-Fuller (1979) paper, considers three regressions ($(1.1), (2.1)$ and $(2.2)$) but only two DGP ($1.1$ and $2.1$), while deriving the limiting distributions. The paper defines three ...
0
votes
0answers
36 views

Autocorrelation AR(1) process

I am doing a self-study question. I need to find the autocorrelation $\rho(2)$ for the following AR(1) process: $y_t = y_{t-1} + \epsilon_t;\\ \epsilon_t \sim (0,\sigma_\epsilon^2) $ For that I need ...
1
vote
0answers
27 views

HAC variance to construct standard errors

I am facing some difficulties understanding this question. It hasn't been long since I started with econometrics, so I'm new to all of this. Suppose we have a function $$E[c_t|y_t,c_{t-1},y_{t-1},c_{t-...
1
vote
1answer
23 views

Recognizing the Seasonal Effects from a Time Plot

From the first plot, I have determined that there is a seasonal pattern of period $L = 12$. However, in my ACF plot (a), it appears that the period is $L = 6$. Am I misinterpreting? The data had a ...
-1
votes
1answer
41 views

Second-order and strictly stationary time series is weakly stationary - proof

I keep reading that second-order and strictly stationary time series has constant mean, variance and its autocovariance is time independent, but I can't find proof of that. My definition of such time ...
0
votes
0answers
9 views

What are the characteristics of a trend and break stationary process?

I have a time series with around 380 data points (day-wise data acquired from instruments). I want to model these in ARIMA. It is my understanding that first I'll have to check for stationarity of the ...
0
votes
0answers
13 views

Is AR timeseries always invertible?

I have just started learning time-series and the foremost thing that I read was that in my book it is explicitly written that an AR process is always invertible. But why is that ? If XT= a X(T-1) + et ...
0
votes
0answers
17 views

Interpretation of several I(1) variables ADL regression

I see a lot of weird interpretation of coefficients, when working with a time-series model with two (or more) variables. Specifically I am thinking of two series that are I(1) and are then log-diffed ...
0
votes
1answer
23 views

Time Series Stationary or Not

Here is my time series plot of some data. There appears to be a constant variance, but I don't believe that the mean is constant (e.g., big dip around time $t=17$ and big increase around time $t = 57$)...
0
votes
0answers
11 views

Trend detection in non consecutive repeated time series

I have daily precipitation data at a single weather station, and I would like to identify the existence of a trend for a specific time period, i.e. between April 25 and June 20 (around 55 consecutive ...
1
vote
1answer
26 views

Writing MA and AR representations

I have to determine if $$(1 - 1.1B + 0.8B^2)Y_t = (1 - 1.7B + 0.72B^2)a_t$$ is stationary, invertible or both. I have shown that $\Phi(B) = 1 - 1.1B + 0.8B^2 = 0$ when $B_{1,2} = 0.6875 \pm 0.8817i$, ...
7
votes
2answers
307 views

Is (covariance) stationarity preserved under log or exponential transformation?

In this lecture note, it (proposition 2) says that strict stationarity is preserved under transformation. However, it doesn't give the proof of this statement. Second, what if the process is ...
1
vote
2answers
32 views

Granger causality in non stationary VAR(1) process

I have VAR(1) process which is not stationary (roots are outside of the unit circle). If I deemed it to be stationary, what can I say about Granger causality?
0
votes
0answers
14 views

Estimating mean and confidence interval for “stairs up, elevator down” time series

I have a time series which exhibits the classic "stairs up, elevator down" pattern of financial time series, i.e. slow rises up and quick drops. Given this series, I wanted to predict the ...
1
vote
0answers
14 views

VAR or VECM for I(0) e I(1)

I have 5 series, four nonstationary series and one stationary series.I tested each pair using Engle-Granger (x1,x2),(x1,x3),(x1,x4); (x2,x3) (x2, x4); (x3,x4) and found cointegration only in x2->x4,...
1
vote
0answers
25 views

test stationarity of multivariate time series

I am using R to make classification on multidimensional time series (MTS). I need to check the stationarity of these time series because I would like to estimate their covariance matrices. So far, I ...
0
votes
1answer
33 views

Finding the variance of a process generated by white noise

Given that $a_t \sim WN(2, 0.5)$, I have generated the process defined by $$Y_1 = a_1$$ $$Y_t = \theta Y_{t - 1} + a_t$$ to be: $$Y_t = \theta^{t - 1}a_1 + \theta^{t - 2}a_2 + \cdots + \theta a_{t - 1}...
1
vote
1answer
24 views

Stationarity of time series with product of white noise time series

Is the time series $\{Yt\}$ given by $Y_{t} = Z_{t} - \frac{1}{2}Z_{t-1}Z_{t-2}$ With $Z_{t} \sim{N}(0\,1)$, weakly stationary? I do not know how to check if the above stated formula is stationary? I ...
0
votes
0answers
30 views

How to test whether a variable is changing over time?

I have a variable called pct_spread(i,t) which is calculated as (ask_price(i,t) - bid_price(i,t))/ask_price(i,t) based on ask ...
1
vote
0answers
35 views

White noise that is not strictly stationary

For an exercise I was asked to provide an example of a white noise sequence that is not strictly stationary. I found in multiple sources that an example of this is $$X_t = \sin(2\pi t U) $$ where $t$ ...
0
votes
1answer
23 views

Checking independence in non-stationary timeseries

I am wanting to apply a changepoint detection method to a timeseries but an assumption is that the data points are independent from each other. I was wondering if there is a way to check this when the ...

1
2 3 4 5
23