# Questions tagged [stationarity]

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36 questions
58 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{\...
234 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 ...
58 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. ...
76 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.
35 views

### Cointegration in Microstructure models

This is from :One Security, Many Markets: Determining the Contributions to Price Discovery Author(s): Joel Hasbrouck Pg 1180-1181 There are assumed to be n price variables closely related to a single ...
354 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; ...
100 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 ...
423 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 ...
181 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 ...
420 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/...
158 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 ...
402 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 ...
215 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 ...
256 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 ...
3k 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? ...
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### Problem - stationarity and relevance

I am doing my Bachelor's thesis at the moment and I ran into a problem I was hoping you could help me out with. While running my data (in Eviews) I had relevant variables. However, when turning to a ...
6k 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 ...
509 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 ...
722 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?
933 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 ...
633 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.
976 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 ...
2k 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 ...
11k 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 ...
246 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 ...
18k 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 ...
658 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 ...
62 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?
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 ...
333 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 ...
7k 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 ...
3k 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 ...
35k 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?
3k 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 ...