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16 votes
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When can you apply the bootstrap to time series models?

Before getting to my answer, I think I should point out that there is a mismatch between your question title and the body of the question. Bootstrapping time series is in general a very wide topic ...
Don Walpola's user avatar
  • 1,328
9 votes

Cointegration if both variables are I(0)?

Since calling any linear combination that is I(0) a cointegration relation <...> is not in the spirit of the original definition I will stick to defining a cointegrating combination as one ...
Richard Hardy's user avatar
9 votes
Accepted

OLS - Non stationary variables but stationary residuals - is this OK or not?

...the dependent variable (Y) and the independent variables (X1, X2, X3, ...) are non-stationary. But the residuals are found to be stationary. Does this mean my regression is OK?... This suggests ...
Michael's user avatar
  • 3,328
6 votes
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Cointegration relations - What is the intuition?

I find a constructive example easier than deductive ones, so here it is. Suppose there is a unit-root process $x_t$. It could be the price of a company's share on a stock exchange, for example. ...
Richard Hardy's user avatar
6 votes

Prediction from VECM in R using external forecasts of regressors

You can simply use the newdata argument of the predict method. Note that if you have a VECM with three lags, lags in tsDyn refer ...
Matifou's user avatar
  • 3,083
6 votes

VAR model for first differences (not a good idea?)

Think of it this way, when data is I(1), that is interesting. It tell's us something about the underlying process. Further, if you have two I(1) process and they are co-integrated, then this is ...
Jacob H's user avatar
  • 922
6 votes
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can two AR(1) processes be cointegrated

Cointegration literally means "to be integrated, together" (see the usual "common trend" interpretation). It cannot logically apply to processes which are not integrated. So if you ...
Chris Haug's user avatar
  • 5,850
6 votes
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VECM: alpha is a 0-vector? cointegration rank = $k$ even though $X_t$ is I(1)?

A brief answer: You logic is correct. In theory, this should not happen. In practice, this may be caused by estimation imprecision and/or low power of tests. In theory, the lag does not matter. As ...
Richard Hardy's user avatar
5 votes
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Find cointegrating vectors and loadings from a trivariate VAR(1) equation

Checking out equation by equation $$ \begin{aligned} X_t &= 1 + 0.5 X_{t-1} + 0.5 &Y_{t-1} & &+ \epsilon_{1,t} \\ Y_t &= &Y_{t-1} & ...
Richard Hardy's user avatar
5 votes
Accepted

Estimate time for mean reversion of two time series

The Orstein-Uhlenbeck is a stochastic process which tends to drift, or revert, back to its long term mean (AKA mean-reversion). The 'half life of mean reversion' is the average time it will take a ...
Brian O'Donnell's user avatar
5 votes
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Is it possible to get "spurious cointegration"?

The "spurious regression" phenomenon, has to do not with a contradiction between "theory" and "statistically measured relation", but with the appearance of a statistically significant relation when in ...
Alecos Papadopoulos's user avatar
5 votes

Stationarity test - What is wrong with this timeseries?

From an application domain point of view, what is "wrong" with this series is that this is a bond index with a fixed maturity date ("on or about" December 15th, 2021, see ...
Chris Haug's user avatar
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4 votes
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Testing for cointegration and building a VEC model

You seem to be doing pairwise analysis when you in fact have three variables. This way you may miss cointegrating relationships that are not pairwise but involve more variables. The standard way in ...
Richard Hardy's user avatar
4 votes

Do all variables in a VAR/VEC need to be normally distributed, or only the target variable?

Unless the assumptions of regression modeling have changed, there is no stipulation about the distributions of the variables in the model -- normal or otherwise. There are some technical assumptions ...
user78229's user avatar
  • 10.8k
4 votes
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Granger Causality test pre-conditions

If you have two time series, then the univariate unit-root test results coincide nicely with the cointegration test results. Both indicate that the series are stationary. Moreoever, this is as ...
Richard Hardy's user avatar
4 votes

VAR in levels for cointegrated data

It is not recent but many textbooks, video series, etc in Econometrics still do not acknowledge this. You can have a look into the papers below. The classic reference would be the Sims, Stock and ...
SimonCW's user avatar
  • 181
4 votes

Why do I get a different result for cointegration test when I swap the independent and dependent variables?

Cointegration is not "directional" because its defining property is intrinsically "nondirectional": a linear combination of the original, integrated series must be a stationary series (here I ...
Richard Hardy's user avatar
4 votes
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Eviews : How to test for cointegration in the right way

I'll answer your questions pertaining to cointegration. 1) If the context of your exercise is the forecasting of a particular dependent variable by using a set of independent variables as opposed to ...
ColorStatistics's user avatar
4 votes
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If $y_t$ and $x_t$ are cointegrated, then are $y_t$ and $x_{t-d}$ also cointegrated?

To answer your title question: Yes, if $y_t$ and $x_t$ are cointegrated, then $y_t$ and $x_{t-d}$ are also cointegrated. I think you got the intuition right: $y_t$ and $x_t$ are cointegrated and thus ...
Richard Hardy's user avatar
3 votes

Purpose of the first step in Engle-Granger cointegration test

These are two different hypotheses: $y$ and $x$ are cointegrated for any vector (hence estimate vector $(1, -\beta)$ $y$ and $x$ are cointegrated for the vector $(1,-1)$ Usually, you would start ...
Matifou's user avatar
  • 3,083
3 votes
Accepted

VAR lag length vs Johansen cointegration test outcome?

This is a usual problem with the two steps procedure, where one selects first the lag, then the cointegration rank depending on the lag chose in the first step. Puzzle 1: The claim that the lag ...
Matifou's user avatar
  • 3,083
3 votes

VAR or VECM for a mix of stationary and nonstationary variables?

Should I use VAR or VECM to find relation between them? In practice, it depends on the power of cointegration tests: If your variables are cointegrated and you used a VAR model: you could have done ...
rmojab63's user avatar
  • 216
3 votes

Example of 2 series correlated but not cointegrated and vice versa

Correlation is a statistical measure of how two variables, $X$ and $Y$, move in relation to each other. If the two variables are correlated, they move either in tandem, when they are positively ...
rsl's user avatar
  • 1,085
3 votes
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Interpretation of the Error Correction Term as time to correct

I'm afraid your exploration so far of the intuition behind $b$ is incorrect. By definition, the correction mechanism is asymptotic. This means that it always takes infinite time to adjust. As such, $b$...
luchonacho's user avatar
  • 2,750
3 votes

VAR in levels for cointegrated data

I want to expand on derFuchs post. Further, I feel that too often when a unit root is present, people automatically just first difference their data. It's not always necessary! Prediction We've always ...
Jacob H's user avatar
  • 922
3 votes
Accepted

Is a High R squared a Sufficient condition for a spurious regression?

No. For example, suppose $Y$ is a random variable caused by $x$ such that $Y = 0$ when $x = 0$ and $Y = 1$ when $x = 1$. If you choose $x$ to equal independent draws from a standard normal ...
Kodiologist's user avatar
  • 20.3k
3 votes

Johansen Cointegration Test with I(0)?

Consider the definition of cointegration: There exists a linear combination of several time series that is stationary despite the fact that each of the individual series is nonstationary. Hence, per ...
Christoph Hanck's user avatar
3 votes
Accepted

Cointegration with lagged variables

Suppose you have two $I(1)$ series, $y_{1,t}$ and $y_{2,t}$. They can be decomposed into \begin{aligned} y_{1,t} &= x_{1,t} + s_{1,t}, \\ y_{2,t} &= x_{2,t} + s_{2,t}; \\ \end{aligned} where $...
Richard Hardy's user avatar
3 votes

Cointegration if both variables are I(0)?

There is no point in searching for a cointegration relationship between two stationary variables, I(0). When the time series are integrated of order one (or higher), standard linear regression ...
javlacalle's user avatar
  • 11.7k
3 votes
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What is an overall procedure for cointegration test?

You don't specify what software you are using to run these tests, but the examples I provide are carried out using R. Stationarity To start with, stationarity is a condition where the mean, variance,...
Michael Grogan's user avatar

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