0
votes
0answers
14 views

“Iterating”? For MA and AR processes

I am not sure what is being done here, but I keep seeing statements like Given $X_t - \phi X_{t-1} = Z_t$ $...(1)$ then $$X_t = -\phi^{-1}Z_{t+1} + \phi^{-1}X_{t+1}$$ $$ = ... $$ $$= ...
0
votes
0answers
25 views

What is the source of nonstationarity in this VAR model?

I am trying to forecast a VAR model, which consists out of 5 variables with a monthly frequency. The problem is that the VAR model produces an unstable forecast and I am not sure what the source of ...
2
votes
3answers
110 views

How do I detrend time series?

How do I detrend time series? Is it ok to just take first difference and run a Dickey Fuller test, and if it is stationary we are good? I also found online that I can detrend the time series by ...
1
vote
1answer
70 views

stationarity in time series

I'm learning a Time series course and I have a few questions. Strictly stationary is a process if the joint distribution of $X_{t1},X_{t2},...,X_{tm}$is the same as the joint distribution of ...
3
votes
3answers
79 views

Does Stationarity for Time Series extend to Independent Variables?

There have been many questions about the importance of stationarity and also its means of calculation here on CV, but one question that I have not seen an answer to is whether or not stationarity (in ...
0
votes
0answers
26 views

Identify the stationary time series

Identify the stationary time series for which $$ \gamma(h) =(-1)^{|h|}+\cos \left(\frac{\pi}{4}h\right)$$ is ACVF. This is a homework problem. Stuck at first level. Please give some hints. Thanks in ...
1
vote
2answers
49 views

How to stationarize profit and loss data with an increasing variance and large negative values for time series analysis?

PnL can take large negative values, and its variance increases over time as the firm grows. If we do differencing, an increasing variance remains. If we take log, negative values cannot be defined. ...
2
votes
1answer
31 views

Can I difference after fitting a time series regression model?

Suppose that I have a time series that exhibits a notable trend, and I want to test a hypothesis that a second variable is related to that trend. I fit a linear regression model with that second ...
1
vote
0answers
146 views

How to compare time series with cyclical data, and describe any changes or trends

I have a bunch of time series where the data has a natural (known) cycle, for example daily or annual (or both). Here is an example (this is 6 years worth of temperature data sampled hourly): ...
0
votes
1answer
125 views

Difference between series with drift and series with trend

A series with drift can be modeled as $y_t = c + \phi y_{t-1} + \epsilon_t$ where $c$ is the drift(constant), and $\phi=1$ A series with trend can be modeled as $y_t = c + \delta t + \phi y_{t-1} + ...
1
vote
0answers
37 views

Transforming time series of different time horizon to stationary

I have a list of monthly time series data with different time periods and different order of integration. I want to transform them all to stationary and a same time period. I noticed that the order ...
1
vote
1answer
45 views

what if I know my time series are cointegrated over a long period but not over a short period?

I am regressing time series on time series. I have tested for cointegration on the entire time sample (3 years) and the series are cointegrated. I need to make a rolling window of regressions (to ...
4
votes
3answers
271 views

How can I show that a random walk is not covariance stationary?

How can I show that a random walk ($y$ follows a random walk) is not covariance stationary? I tried to work on the formula below (with no results) Could you give me just a hint on how to proceed ...
2
votes
0answers
156 views

Time Series: Seasonality and trend

I am interested in financial time series and I have a small question regarding the use of the forecast package. The time series I am interested in is a monthly one and present clear evidences of ...
0
votes
1answer
23 views

What does it mean to build a so-called mean equation?

A series is denoted by Xt. How do we build a time-series model for Xt that is the "mean equation" of Xt? Is this another way of asking to build a stationary time-series?
1
vote
0answers
42 views

condition for a ARMA process to be wide-sense stationary

For a ARMA process, some (e.g. in Tsay's Financial Time Series) said: it is wide-sense stationary, iff all the roots of its AR characteristic polynomial are greater than 1 in magnitude. This is ...
1
vote
1answer
55 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
vote
0answers
81 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 ...
1
vote
0answers
79 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
vote
1answer
44 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
vote
3answers
195 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
322 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. ...
7
votes
1answer
224 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
vote
0answers
70 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 ...
1
vote
0answers
49 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
235 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
193 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
194 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
256 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 ...
1
vote
0answers
340 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
110 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
600 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 ...
1
vote
2answers
438 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
votes
1answer
164 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
vote
1answer
97 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
vote
0answers
42 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
264 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
167 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
vote
2answers
256 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
292 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
1k 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
845 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
2k 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
votes
0answers
2k 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 ...
1
vote
2answers
354 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
274 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
149 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
152 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
239 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
68 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?