# Questions tagged [time-series]

statistical techniques for application to data whose observations concern an entity or phenomenon at different points in time.

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• 153
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### Stationarity vs weak dependence

I am doing an undergraduate course in econometrics where we are using the text Introduction to Econometrics by Dougherty. While going through time series, it was mentioned that one of the necessary ...
• 43
310 views

### What does one-sided polynomial on lag operator $L$ mean?

In some time series texts, there are some talks about one-sided polynomial on lag operator $L$. I tried looking up what this means, but I cannot find one. So what does one-sided polynomial on lag ...
• 59
251 views

### Can PPP adjusted values be compared over time?

I'm a little baffled about this: Let's say I want to compare the average income of 2 countries, A and B. Of course I'm interested in the real income so I adjust to PPP using the big mac index of that ...
• 143
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### Why Is Cointegration Important In Practice?

In one of my econometrics classes. I'm nearly finished a problem set and assigned readings on an introduction to cointegration. I've essentially finished the assignment, run dickey fuller tests on ...
• 157
125 views

### VAR inversion - looking for a good resource

I am having trouble with something that should be pretty basic. I need to invert a VAR (vector autoregression). Everything I have read just brushes past the actual inversion process, taking for ...
• 43
69 views

### Proof that a Unit Root process is Difference Stationary

Consider $$y_t =a_1 y_{t-1}+a_2 y_{t-2} +...+a_p y_{t-p} +\varepsilon_t$$ The characteristic polynomial would be: $$(1-a_1L -a_2L^2 -...-a_pL^p)$$ Suppose that there is a unit root, say that $L=1$ ...
• 3,643
174 views

### Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables

I am estimating a dynamic OLS model since I have variables that are non-stationary, but cointegrated. In addition, the data is a standard time-series (i.e. one observation per one time period) so ...
• 41
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### Demand estimation with a lagged dependent variable

Suppose I have the following structural equation for demand estimation in time-series: $$q_t=\beta_0+\beta_1\hat{p_t}+\beta_2incom_t+\beta_3q_{t-1}+\epsilon_t$$ Where $q_t$ stands for the quantity ...
• 423
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### R reproducible example, restrictions on cointegrating equations

The code given below estimates a VEC model with 4 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor). ...
• 1,990
60 views

### Non parametric and parametric tests of martingale?

A martingale is a model in which the expectation for the next value is equal to the presently observed value, even given knowledge of prior values, ie $E(X_{n+1} |X_1, X_2, ..,X_n)=X_n$ What tests ...
• 1,453
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### Stationarity in Time Series

Could you illustrate why a random walk process without a constant term exhibits stationarity in its first moment but not in the second?
• 177
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### ARIMA - reason for + MA term

I have 2 questions regarding ARIMA. 1st: How do we get the MA component - the et's (as we want to regress yt on lagged yt and also et and lagged et's)? If I want to regress yt on lagged yt's, I have ...
• 113
Assume we are given two independent random walks  Y_t = Y_{t-1} + \varepsilon_{1, t}, \quad \varepsilon_{1, t} \sim \mathcal{N}(0, 1) \\ X_t = X_{t-1} + \varepsilon_{2, t}, \quad \varepsilon_{2, t} \...