1
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1answer
29 views

When an ARMAX model is stationary? Why stationarity or invertibility is needed?

Let $y_t$ a stochastic process and $\tau_t$ presents the time duration between the $t$ and $t-1$ event.The ARMA(p,q,r) with exogenous variables is defined as: $$ y_t = \varepsilon_t + ...
1
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0answers
35 views

How to test for wide-sense stationarity with only one sample path of the process?

I have a univariate time series consisting of 70,000 observations (power consumption of a building) over equal time increments (15 minutes). How do I check whether this realization is wide-sense ...
0
votes
0answers
44 views

Time series and stationnarity tests

I perform some time series fitting with the help of the forecast and urca packages. I have a question regarding the correspondance between results coming from statistical test such as KPSS, ADF or ...
1
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1answer
38 views

How to tell stationarity from a sample path?

Given a sample path, we can roughly tell whether the mean changes over the time, and, when it doesn't, whether the deviation from mean changes over the time. (Correct me if I am wrong.) But that is ...
1
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3answers
92 views

Can nonstationarity be told from the autocorrelation function?

Here "stationarity" means the first and second moments don't change over time. From a page of Time Series: Theory and Methods, by Peter J. Brockwell, Richard A. Davis In this chapter we shall ...
0
votes
1answer
98 views

How to simulate only stationary AR(1) with φ = 0.9?

I am interesting in simulating AR(1) processes with 0.9 parameter and n = 10. The itterations should be 10000. When I was trying to run the program it gave me an error in the estimation procedure. ...
3
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0answers
55 views

What are the stationarity requirements of using regression with ARIMA errors for inference?

What are the stationarity requirements of using regression with ARIMA errors (dynamic regression) for inference? Specifically, I have a non-stationary continuous outcome variable $y$, a ...
1
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0answers
31 views

Estimator of autocovariance in a wide-sense stationary process

From Wikipedia http://en.wikipedia.org/wiki/Ergodic_process One can discuss the ergodicity of various properties of a stochastic process. For example, a wide-sense stationary process $x(t)$ has ...
0
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0answers
29 views

A question on transfer modeling for the intervention analysis of time series data

When reading the section of intervention analysis of time series, I have one question regarding the following descriptions. The following graph defines several response patterns for step function ...
2
votes
1answer
101 views

Pros and Cons: Methods for Detrending Time Series Data

My memory is fuzzy on the advantages and disadvantages of various methods for detrending time-series data. I'm looking for a succinct summary of why and when one should or should not use the ...
2
votes
2answers
104 views

Implementing Neural Network for time series

I am currently working on neural networks for time series forecasting, my doubt is do we need to account for issues like trend,non stationarity and seasonality while using neural networks as opposed ...
2
votes
1answer
169 views

How can I check if two numbers are equal (with some allowed error)?

I have a lot (about 10000 or more) measurement results. I measured the performance of different algorithms (it doesnt really matter which algorithms for now on). I want to check if my measurement ...
3
votes
2answers
184 views

Which one of these looks stationary?

Step 1. To answer "Final Question" ( linked: "THE FINAL QUESTION : Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf?") Expecting to find correct order of ...
0
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0answers
129 views

Weak stationarity and ARMA-ARCH/GARCH models?

I am slightly irritated about weak stationarity in connection to ARCH/GARCH models. I do not know the answer and I am not sure about it: The basic question is: Do we have to test weak ...
0
votes
1answer
86 views

What is the real meaning of null hypothesis in unit-root test for a AR(p) process?

There are functions in R (e.g., PP.test and adf.test) which have null hypothesis of unit-root in the process ($H_0$: there is a ...
2
votes
2answers
218 views

Unit root tests: how to decide if to include a trend and/or a constant

Applying a test to univariate time series data for checking if the series has a unit root or not, one is faced with a decision if one would like to test if the series is stationary around a constant ...
0
votes
2answers
202 views

Non-Stationary Time Series Forecasting

Suppose I have a non-stationary limited data. Do I have to make it stationary before making forecasts? Can I use exponential smoothing, moving averages or even Holt Winters methods without making my ...
0
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0answers
79 views

Handling stationarity issues in proc ucm/state space time series models

Hope I'm able to find someone who can answer this question. The previous one didn't get answered! Proc ucm is the SAS implementation (using state space concepts) to isolate the unobserved trend, ...
1
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1answer
94 views

$R^2$ from a regression of two trend-stationary processes, $Y_t$ and $X_t$

In Estimation and Inference in Econometrics, by Davidson and MacKinnon, p.671, they claim that $R^2$ from a regression of $Y_t$ on $X_t$, where both time series are trend stationary, tends to 1 as $n$ ...
1
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0answers
38 views

Stationarity of $\nabla x_{t}$

How should I prove that for a given series $x_{t}=\frac{3}{2}x_{t-1}-\frac{1}{2}x_{t-2}+w_{t}$ that is non-stationary, $y_{t}=\nabla x_{t}$ is stationary? I attempted to get an equation based on the ...
0
votes
1answer
199 views

Explaining augmented Dickey-Fuller regression output

I have monthly returns data going back to 1991 and I'm trying to work out if the data has a tendency to mean revert over time. In order to work this out I've used the Augmented Dickey Fuller test on ...
2
votes
1answer
130 views

Downsampling stationary time series data, effect on variance

Suppose I have stationary time series data, like this: The time series has Gaussian noise around a true mean. If I then take windows of N samples across the series and average them to generate a ...
1
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2answers
196 views

How to determine correlation between stationary and non-stationary time series

I have three time series of economic data based on quarterly observations; A, B and C, and I would like to ascertain the correlation (or not) between A and C as well as the correlation between B and ...
2
votes
3answers
206 views

Why is “stationarity” assumed in time series data?

A stochastic process is composed of a sequence of random variables ordered by time, and a time series is just a realization of such a process. The book that I'm reading says: "if we assume ...
1
vote
1answer
711 views

Time series: one I(1) and one I(0) variable, should I use VAR/VEC, test for cointegration?

Like the title says, I've got two time series, one is stationary to begin with and thus has no unit root, the other time serie is stationary after one-time differencing. I want to create a model out ...
0
votes
1answer
526 views

Fitting GEV to non-stationary time series of extremes (general stationarity question?)

I'm fitting the generalized extreme value distribution (GEV) to a series of annual maxima of variable $X$. $X$ exhibits a linear trend. When I fit the GEV to $X$, I think I have the choice to Use ...
0
votes
1answer
1k views

KPSS test - output interpretation in stata

I did KPSS test for some variables in stata to check for stationarity; I want to interpret the the stata outputs, but I don't know how to do that. For instance, in the following case: ...
2
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0answers
1k views

Confusion with Augmented Dickey Fuller test

I am working on the data set electricity available in R package tsa. My aim is to find out if an ...
0
votes
0answers
32 views

dickey-fuller and regressions

I have searched the internet on this, but I could not find any book/lecture/... that relates the ADF test and OLS regressions in practice. Here are my questions: 1) it seems to me unclear what model ...
1
vote
2answers
262 views

'Stationarity requirement' why?

I am working on measuring variability of geotechnical data. I see in the literature it is mentioned that, non-stationary data should be first converted into stationary data (for example by trend ...
2
votes
2answers
204 views

How to model a Time Series which has different nonstationary segments by ARIMA?

I had a monthly river temperature (408 values, separated 360 for modeling). Then I deseasonalized and transformed it to a normal time series by a plotting position technique. Now I need to fit an ARMA ...
2
votes
2answers
126 views

Help with understanding stationarity

I'm new in time series and the concept of stationarity has been bugging me for a while :( I know the definition of stationarity but it is not 100% clear for me why for example we have to difference ...
0
votes
1answer
121 views

Trying to fit a model after detrending

I have data for Hydrogen Sulfide Series, see here http://www.wikiupload.com/Y4WAZJ4Z0IMTK7V I applied a Box-Cox Transformation with $\lambda =1/3$ to try to stabilize the data. I plotted a few sample ...
3
votes
1answer
184 views

What are the assumptions for checking the stationarity of a time series?

I am checking stationarity or non-stationarity of a time series with R and I am using adf.test and kpss.test in ...
0
votes
1answer
61 views

Stationary time-series and N-order stationarity

Suppose I have a stationary time series, does this imply that the series is also N-order stationary?
1
vote
1answer
390 views

Unit root test confusion

For my time-series regression, I am regressing the difference in variable x on a difference in variable y. Before proceeding, I want to check for stationarity of my variables. Regressing d.x ...
2
votes
2answers
425 views

Treating non-stationarity of time series in seasonal adjusted data with R

I'm currently trying to use a variable x (and others) to explain a dependent variable y in a distributed lag model (with the long term goal of predicting variable y). The plot of variable x shows an ...
5
votes
1answer
403 views

Conceptual distinction between heteroscedasticity and non-stationarity

I'm having trouble distinguishing between the concepts of scedasticity and stationarity. As I understand them, heteroscedasticity is differing variabilities in sub-populations and non-stationarity is ...
1
vote
1answer
192 views

Time-series stationarity

If I difference a time series and take out trend and seasonality ... does it mean we are left with only irregularity on which we plot the acf and pacf to arrive at the MA and AR order? Do 1st ...
1
vote
1answer
130 views

What's a stationary VAR?

What is a stationary VAR (vector autoregression)? Can a VAR with non-stationary variables be stationary? How do you test whether a VAR is stationary or non-stationary? (Example in ...
1
vote
2answers
243 views

Johansen's $\Pi$ is full rank except variables are non-stationary

I have two variables. They're both $I(1)$ even when I fit constant and trend terms into the ADF test. The $p$-values for the stationarity tests are around 0.5 so it's not a marginal case. However, ...
5
votes
0answers
347 views

Stationarity tests for time series

I am currently working on time series modeling, especially on stationarity tests. For this purpose, I am extensively using Pfaff's book "Analysis of integrated and cointegrated time series with R" and ...
2
votes
0answers
99 views

How to test for integrated order 2/non-stationary I(2)?

How do I apply the Augmented Dickey-Fuller (or alternative) test to determine if a variable is $I(2)$ instead of $I(1)$? Is there functionality for this in R ...
1
vote
0answers
175 views

Difference between unrestricted VECM and restricted VECM?

What's the difference between an unrestricted and a restricted VECM? I believe a hint lies within the cajorls()[1] function of R language's ...
1
vote
2answers
184 views

Putting stationary variables through Johansen procedure

Is it okay to feed $I(0)$ variables into the Johansen procedure? I've read three sources that seem to state that this is not what you're supposed to do. However, whenever I've done this, I notice that ...
0
votes
1answer
209 views

Dummy interaction variables are always non-stationary?

I want to know why we can include dummy interaction terms into time series models if they're always non-stationary? For example let $X_t$ be $I(0)$, $X_t \sim N(\mu,\sigma^2)$ and $D_t \in \{0,1\}$. ...
2
votes
2answers
180 views

Identifying periods of non random behavior in time series

Im looking for some pointers on which topics I should be looking into in order to identify periods (of non fixed length) which deviate from randomness. I have a feeling hypothesis testing may be what ...
2
votes
0answers
145 views

Unit root tests and stationarity

Two common methods of testing whether a time series is stationary are the KPSS and ADF tests. If my understanding is correct, these tests essentially work by measuring the residuals of fitting the ...
6
votes
2answers
3k views

Which Dickey-Fuller test should I apply to a time series with an underlying model that includes an intercept/drift term and a linear time trend?

Short version: I have a time series of climate data that I'm testing for stationarity. Based on previous research, I expect the model underlying (or "generating", so to speak) the data to have an ...
9
votes
2answers
1k views

Can I detrend and difference to make a series stationary?

I have a dataset that is clearly increasing as time goes on (exchange rate of a currency, monthly data over 20 years), my question is: Can I detrend the data and then difference it also to make it ...