A stationary process (or time series) is one whose joint distribution is constant over time. A weakly stationary process or series is one whose mean and covariance function (variance and autocorrelation function) are constant over time.

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P-value of Augmented Dickey-Fuller test and KPSS test

I would like to test if the time series of the US 3-month treasury bills (monthly data from 1934 to 2015) is stationary. I'm using the ADF test in R (from the package ...
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stationary and coefficient of variation [on hold]

I am going to use coefficient of variation to monitor a process, then my problem is that this coefficient is not stationary, so i did log transformation using Sewall Wright (1952) how showed the ...
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Forecasting with no seasonality

I have a set of data, let's say average weight of employees, captured every month over a period of 5 years (2010 - 2014). I cannot find a seasonality trend in the data over these years. Also, I have ...
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Deciding the lag while testing for timeseries data stationarity

I am currently reading up on time series forecasting using ARIMA in SAS. I just began to go through what has been explained here : ...
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EWMA or Moving Average when Estimating Trend in Seasonal Data

What is generally the best practice when estimating trend (non-seasonal component) in seasonal data? Centred Moving Average as suggested by MatLab docs Averaged EWMA (backwards & forwards) as ...
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Making a Time-series Stationary: Order of Operations

Following various sources including this post, which is the correct approach to making a time-series stationary? Remove trend Remove seasonality or Remove seasonality with estimated trend ...
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stationarity using wavelet analysis [closed]

i am going to apply discrete wavelet analysis to several spectra, using matlab [cA,cD] = dwt(X,'wname') all my spectra repsent a step change like the attached figure i want to check the stationarity ...
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21 views

Stationarity of time series data

The following are plots of the original data first order difference values of original data and the first order difference of the log transformed data. Can someone please tell me which of 2 and 3 ...
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24 views

Understanding results from Augmented Dickey Fuller test

I have no background in statistics/econometrics but some theory I'm applying to geophysics data requires the data to be stationary (or at least trend-stationary) and I don't believe they are. I've ...
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31 views

OLS and stationarity

I am using a time series data set and my question is, if my one or two variables are stationary at level I(0) and the other variables are stationary at first difference I(1) then can I use ordinary ...
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17 views

Interpretation of KPSS-Test results

I'm analyzing the monthly german industrial production growth rate which should be a stationary time series. I use different samples and want to compare predictions of different inidcators. I first ...
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6 views

Relation Between Lag length of ADF test and Lag of VAR After that

Suppose I have three variable and they are difference stationary at different lags. How should I decide the no of optimum lags in the VAR of the three variable? I understand the lag length criteria of ...
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32 views

What is a stationary distribution?

Today I was reading about AR(1) processes and I there was something I didn't understand: For the casual solution $X(t-1)$ and $\epsilon(t)$ are independent, and when $\epsilon(t)$-s are standard ...
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32 views

Forecasting a time series with conditional variance (heteroscedasticity) using Arima

I want to forecast a time series and have reason to believe that there are heteroscedastic errors/variance, which could be modelled with GARCH. However, I am not really interested in ...
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71 views

Time Series: Does stationarity imply mean reversion?

I'm trying to see if a time series demonstrates mean reversion. I found two tests: Augmented Dickey Fuller Test and Hurst Exponent. However, the alternative hypothesis is that the series is ...
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33 views

Where is the dominated convergence theorem being used?

I am trying to fully understand the proof of a theorem, I only have a problem with the application of the dominated convergence theorem. For the sake of completeness I will upload the whole statement ...
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60 views

Property of the autocovariance function in time series

In the framework of time series analysis Why does $\lim_{n \rightarrow \infty} n^{-1} \sum_{|h| <n} |\gamma(h)| = \lim_{n \rightarrow \infty} 2|\gamma(n)| $? The LHS (left hand side) sequence of ...
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36 views

When is a Ljung-Box test significant?

I have trouble understanding the output of the Ljung-Box test due to conflicting information: The R documentation doesn't actually say how to interpret the output. This site states that small ...
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341 views

Is it always required to achieve stationarity before performing any time-series analysis?

For example, I know that for ARIMA models stationarity needs to be achieved. What about Exponential Smoothing? Is it also required?
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Explosive processes, non-stationarity and unit roots, how to distinguish?

I understand that if we have a simple model such as: $Y_t$=$\rho$$Y_{t-1}$+$\epsilon_t$ where $\rho$ is less than one in absolute value then we have a stationary process. If $\rho$ equals one then ...
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116 views

Which is the best criterion for DF-GLS lag selection?

When you have an output such as this in Stata for dfgls: ...
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50 views

Is there an optmal lag choice in the KPSS test?

Is there an optimal lag choice in the KPSS test in Stata? For instance, in my example below, for some lags (less than 7) you reject the null for any level of significance. But afterwards, that does ...
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54 views

How do I test the stationarity of data using minitab? [closed]

I am working on a time series and trying to fit ARIMA to predict future values.However, I am facing trouble with finding out whether the data is stationary or not.
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Stationarity after differencing

I have the following two processes: \begin{align} x_t &= x_{t-1} + u_t \tag{1} \\ x_t &= {\beta}_0 + {\beta}_1t + u_t \tag{2} \end{align} Differencing once leads to: \begin{align} \Delta ...
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130 views

Interpreting results of KPSS test in R

I've been trying to create an ARIMA model however, I'm not sure how to determine if the data is stationary or not. I preformed a KPSS test in R using kpss.test from ...
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72 views

Interpretation of VAR and causality

I have two time series(X1 and X2) each having 900 records. I wanted to establish relationship between them and put it in ...
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Does a stationary process necessarily have to be mean-reverting?

I wonder about if a stationary process is by definition mean-reverting too. I know the formal definition of a stationary process, but I'm not sure about the definition of a mean-reverting process. ...
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46 views

How to find if there is a trend in a time series and stationarity

I would like to conclude on a given time series that if it has Trend or not. I have carried out a cox-stuart test in R and have decomposed to inspect the series visually but still a bit confused on if ...
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Intuition for auto-correlation for mean reverting process

How should my auto-correlation plot look like for a mean reverting process? From what I have recently learned, auto-correlation should be low and should decay fast enough. But when I run the following ...
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37 views

Stationary dependent variable

When running a time series, the Dickey-Fuller test of the dependent variable is statistically significant, meaning that it is stationary (which is also confirmed by looking at a plot of the variable). ...
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How can I determine if a time-series is statistically stable?

I have time-series data that tracks the number of sydromics records my organization receives each week. The number of records had been steadily increasing as more organizations started sending us data ...
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Why and when stationarity is achieved by decomposition rather than differencing in ARIMA model

I would like to understand relationships between variables by which cross-correlation function, that means what is the extent one variable influence the other one. ARMA model is used to fit two ...
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24 views

Good TS fit but no stationarity

I have yearly time-series that I want to predict, and for that I fitted an ARX (auto-regressive with a exogenous input) model to previous years (training set) and test it for the last year. My ...
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55 views

Does stationary data need to be normal?

So I already ran some tests to make my data stationary. Differencing and box-cox transformation in particular. According to the augmented-dickey fuller test, after performing the above mentioned ...
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Does the pre-test assignment of values to the pre-sample periods have any negativity on ADF test (that uses common sample)?

Reproducible example added: Tech info: In all of the lag selection procedures in econometrics, same sub-sample must be used to determine the correct optimal minimum lag. The question ...
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79 views

Regression in levels vs. regression in differenced form

I want to compute the following regression using R. lm(EurOis3~EurepOis3+Vstoxx+log(Open.Market.Operations)+CDS). I am using daily data(i.e. I have 5 observations ...
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41 views

Regression with differenced variables

This is my data frame containing some interest rates as well as the amount outstanding of open market operations. Now I want to regress EurOis3 on ...
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64 views

Unit roots and order of differencing

I'm studying the stationarity with unit root tests and the order of integration in time series $\ln(x)$ and $\ln(y)$ found here. I'm using Dickey-Fuller test with constant but no trend. From what I ...
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58 views

The constant term after 1st differencing

My instructor stated that when the dependent variable is 1st differenced, the constant term represents the deterministic change or trend in the dependent variable. When I search for information ...
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71 views

ADF test results confusion

When I ran ADF test with my data set, I got following results. I am confused about why "alternative hypothesis" is always (even for real non-stationary series) showing as "stationary"? ...
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78 views

Difference between random walk and process integrated of order one?

I know that an $I(1)$ process becomes stationary after differencing once. However, I somehow always equated that to its being a random walk because say having a unit root process like \begin{eqnarray} ...
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Stationarity requirements of using regression with ARIMA errors - ROUND 2

Referring to this Post: What are the stationarity requirements of using regression with ARIMA errors for inference? I would like to seek a confirmation of the below practice: The situation is as ...
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63 views

ACF values in identifying non-stationarity

I have used NIST data to calculate ACF in excel which worked fine and coded in our programming language (NOT R). Here is the plot of ACF: Now my questions are: 1) From this ACF series how can I ...
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111 views

How to detect if Ergodicity, Stationarity and Martingale. dif. sequence?

I'm not sure, but I think I've read somewhere that because the Classical Linear Regression model assumes to have a random sample, when researchers they might not be in presence of a sample with that ...
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the decision of being White noise on e-view

And for example, let's take SMA(2) model in this table does there exist white noise ? Which value I observe to decide the existance of white noise? Please explain it. Thank you
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45 views

Stationarity of AR(1) process whose autoregressive parameter could change over time

Imagine an AR(1) has an autoregressive parameter which could change in time. $y_t-\mu=\phi_t (y_{t-1}-\mu)+\varepsilon_t\,$, where $\phi_t$ is not always constant but still lies inside the usual ...
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87 views

Is a Brownian motion non-stationary?

This Wiki-Article quotes "a Brownian motion process, is non-stationary" I dont see why this is the case? A stationary process means that the distribution of ...
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37 views

Stationarity and seasonality of residuals

Why is it necessary to evaluate stationarity and seasonality of model residuals? Or is it? The model in question is an OLS model that represents a relationship between Y and a bunch of economic ...
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Are linear processes stationary?

I am reading Soren Johansen's book on cointegration and I'm wonder about the following definition: Definition 3.1. A linear process is defined by $Y_t=\sum_{i=0}^\infty C_i\epsilon_{t-i}$, $t=0, ...
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48 views

Transforming Series with 2nd Moment Nonstationarity

I am trying to induce stationarity in this series. I have graphed a range-mean plot to detect 1st and 2nd moment nonstationarity. Can anyone suggest a transformation that will remedy the 2nd moment ...