7
votes
$I(g)$-terminology
It's hard to tell without more context. But mostly sure it means "$Z_t$ is integrated of order $g$", i.e. $\Delta ^g Z_t=(1-d)^gZ_t$ (where $d$ is the lag operator) is stationary, in other ...
- 821
6
votes
Could you recommend a book or lecture notes about time series that is easy to understand?
The book I currently use for my time series class is "Time Series Analysis and Its Applications With R Examples" by Shumway and Stoffer, 4th edition. It's served me fine, and gives lots of ...
- 6,578
6
votes
Accepted
ARIMA - reason for + MA term
The MA terms are lagged errors (you don’t need to fetch them manually - for example in R you can use Arima function which does this for you and any program/language will have this basic function as ...
- 54.4k
6
votes
Accepted
Stationarity vs weak dependence
Weak stationarity and weak dependence are complementary conditions.
A weakly stationary time series $y_t$ has an underlying statistical process which is time-invariant.
This is characterised by three ...
- 567
5
votes
Accepted
HP Filter Smoothing Parameter
Morten O. Ravn and Harald Uhlig (2002)
This paper complements these insights using two different analytical
approaches. The first approach uses the time domain and focuses on
the ratio of ...
- 16.3k
5
votes
Accepted
What are accepted econometric methods to find out if a time series is I1 or not?
An I(1) series is also known as a series with a unit root. Therefore, the econometric tests to inquire on the order of integration of a time-series are referred to as "unit-root tests".
There are ...
- 250
5
votes
Accepted
Durbin Watson Test for an AR(1) process
Nerlove and Wallis (1966) result
Nerlove and Wallis (1966) have discussed this issue. Their Equation (3) derives the probability limit of the Durbin-Watson statistic as:
$$\mathrm{plim}\, d^* = 2 \...
- 2,104
5
votes
Accepted
How to recognize correlation in spurious regression case
Just regress Y on X:
$$Y=b_0+b_1X+ e$$
and you will likely find some negative significant $b_1$ coefficient even though both series are just unrelated random walks.
You can also see that as one series ...
- 54.4k
5
votes
Does I(1) imply a process is cointegrated with its lag?
You are confusing concept of co-integration with concept of integration. If a series
$y_t−y_{t−1}=u_t$ is stationary
then series is integrated of order 1 not co-integrated. The term co-integration ...
- 2,673
5
votes
Does I(1) imply a process is cointegrated with its lag?
Just to add to the answers already given. I think the easiest way to see that this cannot be the case is using a CVAR formulation. For a reference see Johansen and Juselius (1990) (https://...
- 426
5
votes
Testing for serial correlation with General Regressors
My understanding is that the classical test for serial correlation is actually conditional to the validity of the strict exogeneity assumption: $E[u_t|X]=0,$ or, as the requirement applies to any $t$, ...
- 3,179
4
votes
Why Is Cointegration Important In Practice?
I think it is a very classical economic teaching problem - showing how something is relevant in the real world.
First, it solved a problem where linear regressions could lead to spurious results: ...
- 835
4
votes
Looking for discussion on equilibrium vs dynamic models in econometrics
Economists (most of them) build their models assuming most of the time stochastic dynamic equilibrium. So Economics does not contrast "dynamic" with "equilibrium" - it synthesizes them.
It is ...
- 33.4k
4
votes
Accepted
Difference-in-differences with long time horizon and repeated treatments
This question is related to a post I addressed on CrossValidated. The "generalized" difference-in-differences (DiD) estimator is amenable to settings with multiple groups and multiple ...
- 439
4
votes
Accepted
Recursive Substitution in Time Series
\begin{align}y_t &= \alpha + \theta_1y_{t-1}+u_t \\
&= \alpha+\theta_1(\alpha + \theta_1y_{t-2}+u_{t-1}) + u_{t} \\
&= (1+\theta_1) \alpha + \theta_1^2y_{t-2} + \theta_1u_{t-1}+u_{t} \\
&...
- 181
4
votes
Accepted
Frequency and time of a time series suddenly changed, are usual methods valid
If you insist on using some standard time series model this will be problematic as standard time series models such as ARIMA require fixed frequency.
There are some possible ways of dealing with this:
...
- 54.4k
4
votes
Accepted
Proof that a Unit Root process is Difference Stationary
It is simple to see once you factorize.
In your set up there is only one unit root so the characteristic polynomial can be factorized as:
\begin{align}
y_t &= a_1 y_{t-1}+a_2 y_{t-2} +...+a_p y_{t-...
- 1,705
3
votes
Conditional variance vs. unconditional variance in ARCH model
I cannot directly answer your question, but I think I can shed some light. What I seem to show is that under some restrictions, the unconditional variance is finite. However, I am not sure how to ...
- 973
3
votes
Replicate Romer and Romer (2004) results
Sorry for any confusion in my previous answer but there are 2 steps to this process 1) tracing out the impact on the $\Delta$y's and the lags of the shocks and then 2) accumulating the shocks to get ...
- 426
3
votes
Accepted
Need Advice Debugging MLE Code to Estimate an ARMA(p,q)
If anyone per chance runs into the same issue,
The reason the MLE is exploding is that a system with explosive roots (eigenvalues outside the unit circle), might make the Kalman-filter predictions ...
3
votes
Data mining in econometric modelling
The critical points here are the phrases "it is recommended that...", and "using four lags is a norm". "Recommended" and "norm" based on what? On a specific prevailing theoretical model, or on past ...
- 33.4k
3
votes
How to linearize the following difference equation?
We have the recurrence relation
$$x_{k+1} = \frac{x_{k+8}}{x_{k+1}}$$
If the denominator is nonzero, this recurrence relation can be rewritten as follows
$$x_{k+7} = x_k^2$$
Assuming positivity ...
3
votes
Accepted
Interpetation of coefficent in AR(1) model
For a second-order stationary series it is the correlation coefficient between the dependent value and its lag.
Specify
$$y_{t+1} = a+ \beta y_t + u_{t+1}\qquad u_{t+1}= \text{white noise}$$
The ...
- 33.4k
3
votes
Accepted
Can PPP adjusted values be compared over time?
There are two questions here:
Whether it is meaningful to compare PPP-adjusted values intertemporaly
Whether the "Big Mac" index is a good index for PPP-adjustment.
I will occupy myself ...
- 33.4k
3
votes
Misspecified autoregressive models
Just think your true model is:
$$y_t = \phi_0 + \phi_1 y_{t-1} + \phi_2 y_{t-2} + u_t \tag{1}$$
So, under your true model, $u_t$ is uncorrelated with all explanatory variables.
So, instead of ...
- 131
3
votes
Misspecified autoregressive models
As Neeraj has explained correctly, omitting a variable will lead to inconsistent estimates of the included variables. They will be biased both in a finite sample and asymptotically because the ...
- 2,270
3
votes
Structural VAR and Granger Causality
Every structural VAR (SVAR) model, e.g.
$$
B_0 y_t = B_1 y_{t-1} + u_t
$$
has an equivalent reduced form (VAR), e.g.
\begin{aligned}
y_t &= B_0^{-1} B_1 y_{t-1} + B_0^{-1} u_t \\
&= A_1 y_{...
- 2,270
3
votes
Limit of random walk auto correlation function
Hi: The expression tends to 1.0. The intuition is that, as $t$ gets larger and larger, the $h$ lags that seperate the two processes become more and more negligible and the processes begin to look the ...
- 486
3
votes
Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables
No in pure time series we generally don't use fixed effects. If you have data on lets say monthly frequency you could include dummies for months in general, e.g. having February, March, April ... ...
- 54.4k
3
votes
How much can we trust macroeconometric analysis?
I do not think that macroeconomic analysis would be 'less trust worthy'. In the same ways as you can solve the issue of omitted variables and reverse causality in microeconomics you can do it ...
- 54.4k
Only top scored, non community-wiki answers of a minimum length are eligible