Questions tagged [stationarity]

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What is a stationary process?

How do you explain what a stationary process is? In the first place, what is meant by process, and then what does the process have to be like so it can be called stationary?
user40's user avatar
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20 votes
8 answers
37k views

How to check if a timeseries is stationary?

I'm using KPSS Method to check if the series is stationary, but I would also like to use another test to confirm if the series is stationary or not, what method coudl I use?
Dam's user avatar
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19 votes
6 answers
23k views

Why non-stationary data cannot be analyzed?

Searching online, i found out that non-stationary cannot be analyzed with traditional econometric techniques as in case of non-stationarity some basic model assupmtions are not met and correct ...
Ice's user avatar
  • 407
12 votes
4 answers
12k views

Is a stationary process necessarily mean-reverting?

Intuitively, a stationary stochastic process needs to be mean-reverting. This should follow immediately from the definition of stationarity: the mean of the process needs to be constant over time, so ...
Abramo's user avatar
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11 votes
2 answers
5k views

How can I compare distributions using only mean and standard deviation?

I only have means and standard deviations of samples of two random variables. What technique can I use to determine how similar the distributions these describe are? Assume that the values are built ...
Mauricio Bustos's user avatar
10 votes
2 answers
2k views

Why does this Co-integrated basket look too good to be true?

You need quantmod & tseries in R to run this: ...
Edwin Jose Palathinkal's user avatar
8 votes
2 answers
3k views

Differencing vs Detrending financial time series

I'm quite newbie to time series analysis and I have to understand what's the difference between differencing time series (i.e considering $Y_t= X_t-X_{t-1}$) and detrending (using linear regression ...
perseo's user avatar
  • 81
8 votes
3 answers
2k views

How is stock data objectively different to this random walk?

I have a random walk that is generated as so using python, numpy, and matplotlib ...
Mark Dunne's user avatar
6 votes
2 answers
8k views

Relationships between white noise and random walk

I would like to ask 5 questions about relations between these processes. 1) Could white noise be also a random walk? 2) Could random walk be also a white noise? 3) Could white noise be stationary? ...
macgivera's user avatar
  • 105
6 votes
2 answers
727 views

Does predictability in a VAR process imply mean reversion or momentum?

There seems to be some disagreement in the literature about this. Define predicability of a stationary series to be $\sigma^2_{t-1} / \sigma^2_t$ Finding mean reverting portfolios using canonical ...
Edward Yu's user avatar
  • 247
6 votes
1 answer
1k views

Ornstein versus AR(1) for modeling stationary data

I've come across several posts regarding parameter estimation for O-U models given some stationary data (say, some sort of mean reverting spread), but I can't seem to find an answer as to why modeling ...
RA334's user avatar
  • 344
5 votes
2 answers
2k views

Why is OU process stationary?

The mean and variance of Ornstein–Uhlenbeck (OU) process have time dependence (exponentially decay in time). So they are not constant in time. How can it to be stationary?
cgao's user avatar
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4 votes
1 answer
4k views

How is the MA (moving average model) useful?

How is the MA model useful in modeling financial data, for example the stock indices? For example, from what i understand in the AR (auto-regressive) model portion, we can use the ADF test to check ...
Ice's user avatar
  • 407
4 votes
0 answers
108 views

Is non-stationarity an issue during copula estimation?

In this paper (1), on page 14 (section 4), the author presents an empirical experiment on the computation of a copula through the use of kernels. To do so, he uses the following stochastic process (...
Pierre's user avatar
  • 143
3 votes
3 answers
10k views

Squared and Absolute Returns

I've always wondered why do one use squared or absolute returns to determine if volatility modeling is required for the return series? We understand that there are various tests for its ...
Dylan Koh's user avatar
  • 121
3 votes
2 answers
537 views

Estimate covariance matrix using prices

We generally estimate the covariance matrix of assets using their returns instead of prices. Why is that the case? I can think of two possible reasons and would appreciate comments/feedback regarding ...
Amrit Prasad's user avatar
3 votes
3 answers
265 views

Is the number of outstanding shares a stationary series?

I'm doing a panel data analysis where the log of the freefloat number of outstanding shares is one of the explanatory variables, but it fails the Augmented Dickey Fuller and Person Phillips unit root ...
Cindy88's user avatar
  • 431
3 votes
2 answers
224 views

Transforming a time series

I have a time series that displays time varying volatility how would I take this time series an turn it into a more stationary process this is what the time series looks like , if one can provide r ...
Pelumi's user avatar
  • 329
3 votes
1 answer
282 views

Real time stationarity test

I have a trading system based on Machine Learning which is trading 8 symbols intraday. From the results I found out that some weeks of trading are successful for some symbols, then it usually switches ...
Krzysztof Fajst's user avatar
3 votes
3 answers
342 views

Confusion on stationarity vs deterministic trend

Sorry for the newbie inquiry but I'm having a little trouble making sense of stationarity and how a the presence of a time trend impacts this. I'm working on a model for operating margins and as a ...
user18614's user avatar
3 votes
0 answers
680 views

Test for stationarity and make use of non-stationary points in financial market?

I have two questions to ask: What are the best methods to determine stationarity in a financial market (such as stocks) using MATLAB? What methods would you recommend to use in order to change from ...
Ice's user avatar
  • 407
3 votes
0 answers
1k views

Does the geometric Ornstein-Uhlenbeck process have stationary variance?

I know that the long run variance of the standard OU process is $\lim_{s\rightarrow \infty}\mbox{Var}(P_{t+s}|P_t) = \frac{\sigma^2}{2\theta}$ I'm using the geometric version of the process. I ...
wcampbell's user avatar
  • 253
2 votes
1 answer
125 views

Does Weak stationarity imply ergodicity ?

My intuition of ergodicity is the Law of Large Numbers for time series i.e. Given sufficient, data points, their mean and standard deviation would converge to population mean and standard deviation. ...
whisperer's user avatar
  • 269
2 votes
2 answers
723 views

Does unit root stationary imply mean stationary and variance stationary?

Newbie question. I am reading about stationary series and understand that it has many forms: mean stationary variance stationary covariance stationary My question is does unit root stationary imply ...
pavybez's user avatar
  • 31
2 votes
1 answer
419 views

Testing for stationarity in large sample sizes

I keep struggling with testing 9 samples if they are stationary. Each of these samples is a real valued time series with 714.000 values. If I use the KPSS test with the each compleete sample set, the ...
jcc's user avatar
  • 21
2 votes
3 answers
4k views

Detrending price data for analysis of signal returns

I'm looking to conduct hypothesis tests on some of my trading signals to see if the signal returns are statistically significant enough to falsify my null hypothesis that the signal has no predictive ...
Vazgen's user avatar
  • 311
2 votes
1 answer
562 views

Would you consider yield a stationary or non-stationary process?

Doing some yield curve forecasting and unsure whether should be working with yield or change of yield.
A.L. Verminburger's user avatar
2 votes
2 answers
388 views

Stationary Process with autocorrelation in Variance; square root rule

i am currently analyzing a time series of portfolio log returns and have conducted a ADF test with the result, that the series is stationary, but also found significant autocorrelation in the squared ...
Mh Aztec's user avatar
  • 177
2 votes
0 answers
146 views

Cointegration where first differences are not jointly stationary

Note: This is a crosspost from this post on cross-validated, where it did not receive an answer. I thought I might have better luck here. I am looking for a rigorous and general treatment of ...
Aaron Bergman's user avatar
2 votes
0 answers
175 views

Hurst exponent of stock using R/S analysis

I am attempting to use R/S analysis to estimate the Hurst Exponent on a single stock. At first I directly use the stock price ( instead of stock return) and the Hurst component calculated is > 0.9 ( ...
gary's user avatar
  • 21
2 votes
0 answers
75 views

Is there a different test to check stationarity? [duplicate]

I am using the KPSS test to check stationarity of a financial time series. I would like to know if there is another test to confirm the stationarity. Any advice?
Damiano's user avatar
  • 29
1 vote
3 answers
13k views

What does it mean by autocorrelation coefficient near 1?

It is said that the time series has a stochastic trend if the first autocorrelation coefficient will be near 1. Q1) What does it mean by the above statement? Q2) How do we calculate the first ...
Ice's user avatar
  • 407
1 vote
3 answers
2k views

log return of sp500. Stationary vs strictly stationary

By first glance of this time series; will you say it is stationary? I can easily see some "seasonality" which means that this is not strictly stationary since the distribution will not be the same; ...
KinkyLaura's user avatar
1 vote
2 answers
193 views

Exchange rate trend-stationarity

I am kinda new to time-series analysis, I want model CEE (EUR/HUF, EUR/PLN, EUR/CZK, EUR/CHF) exchange rates with ARIMA. I understand that according to Box-Jenkins modeling, I should first check if my ...
Aron_t's user avatar
  • 11
1 vote
2 answers
165 views

Does forecasting asset returns by default assumes non-stationarity of asset returns?

If we assume the assets returns are stationary then the best forecast can only be the mean of the distribution. But if we assume non-stationarity we are forecasting the mean parameter (assuming ...
A.L. Verminburger's user avatar
1 vote
1 answer
68 views

Do stationary prices need to be differenced for VaR?

I have a time series of electricity futures prices that I have shown to be stationary via the Augmented Dickey Fuller test (alpha = 0.05). Does that mean that, in calculating their individual values-...
CasusBelli's user avatar
1 vote
2 answers
1k views

Simulate non-stationary time series with cointegration

how can I simulate/generate two non-stationary time series (with unit root) so that they can be also cointegrated (using R or Matlab). Thanks in advance.
Lukas's user avatar
  • 13
1 vote
1 answer
326 views

Price vs log returns - stationarity issues

I am trying to analyze the price of Bitcoin versus the number of Reddit posts about Bitcoin and the sentiment of those posts (daily). The price is I(1) while the sentiment and the number of posts are ...
TheConfax's user avatar
1 vote
1 answer
866 views

Does it make any sense to normalize returns?

I have been going through a course for Time Series Analysis. First we learned to make returns from a time-series of stock index by (Xt - Xt-1)/Xt-1 . This makes the series stationary, which means we ...
Borut Flis's user avatar
1 vote
1 answer
139 views

Persistence and stationarity together in volatility analysis

I am trying to analyse a time series. I want to get only quantitative results (so, I'm excluding things like "looking at this plot we can note..." or "as you can see in the chart ...&...
user96624's user avatar
  • 111
1 vote
1 answer
246 views

Are return time series ergodic?

It seems intuitive to me that return time series would be ergodic. Is there a test statistic that I can use to check this? Would this be affected by sampling rate? One way I can think of checking ...
s5s's user avatar
  • 452
1 vote
2 answers
2k views

How can I approximate Dollar Bars from Minute Data instead of Tick Data?

Having been influenced by de Prado's Advances in Machine learning book, I've set out to build the dollar bars (in which each bar represents a set dollar amount of transactions in the security) that he ...
pmse234's user avatar
  • 15
1 vote
1 answer
2k views

principal component analysis on non stationary data

I read that since stock prices are non-stationary it does not make sense to take their covariance. So I took the log returns of stocks, computed covariance matrix, took the top few eigen vectors that ...
pavybez's user avatar
  • 31
1 vote
1 answer
1k views

ARIMA Forecasting always converges?

I read an article about arima forecasting and i said that before we forecast arima model, its stationarity has to be checked. If the model is stationary, it is clear that forecasting converges to ...
hmmmmm's user avatar
  • 184
1 vote
0 answers
59 views

Johansen Cointegration Test returns non-stationary error even though trace statistics suggest their existence

I'm working with Python and use the statsmodels.tsa.vector_ar.vecm.coint_johansen function to analyze if several stocks have a stationary error term with respect to ...
Marx's user avatar
  • 11
1 vote
0 answers
307 views

Pairs Trading - isn't any spread stationary if your rolling lin-reg window is small enough?

I have a set of 7 assets, and I have run an ADF test on all possible pair-spreads to find possible pair strategies. I am creating the spreads using a rolling window in which I run linear regression to ...
Vladimir Belik's user avatar
1 vote
0 answers
164 views

Pairs trading strategy: Portfolio returns and NAV

Currently trying a pairs trading approach using cointegration. Tried both formations: $$log(P_t^A)=log(P_t^B) \hat{\gamma}+\hat{\mu}+\epsilon_t \hspace{0.5cm} (1)$$ $$P_t^A=P_t^B \hat{\gamma}+\hat{\...
alexbougias's user avatar
  • 1,416
1 vote
0 answers
522 views

Cointegration for forex using ARMA model to forecast the spread

I am working on an automatized quantitative strategy that use cointegration in Forex. I am backtesting this strategy in Python. Please see below the python file: https://drive.google.com/file/d/...
David Hoareau's user avatar
1 vote
0 answers
683 views

How to choose a GARCH model which delivers iid standardized residuals?

For my thesis I first need to examine nine financial time series and fit a conditional volatility model such that the obtained standardized residuals ($z_t = \epsilon_t / \sigma_t$) are approximately ...
Kondo's user avatar
  • 449
0 votes
3 answers
621 views

Are cumulative returns stationary?

Log differenced returns, computed from stock prices, are known to be stationary. What about cumulative returns, are they also stationary? if not why not? Are there other properties, like non-i.i.d., ...
develarist's user avatar
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