# Tag Info

Accepted

### Cross-validation for timeseries data with regression

For the first question, as Richard Hardy points out, there is an excellent blog post on the topic. There is also this post and this post which I have found very helpful. For the second question, ...
• 12.1k

### Can a Variable Be Both Dependent and Independent?

The notation is discussing two different time periods. $y_t$ refers to the GDP at some time $t$. $y_{t+q,b}$ refers to the GDP at some other time. These are measurements of different quantities.
• 65.8k
Accepted

### When should we use lag variable in a regression?

When a lagged explanatory variable is used in a model, this represents a situation where the analyst thinks that the explanatory variable might have a statistical relationship with the response, but ...
• 130k
Accepted

### How many lags should I include in time series prediction?

Looking at individual autocorrelations may help in simple cases, but this way you could miss lags that are important only jointly but not individually. Alternatively, you may try the following: ...
• 68.9k
Accepted

### Why does differencing White Noise induce autocorrelation of $-0.5$?

For notational simplicity, let $$X_t \equiv \Delta Y_t.$$ By definition, $$\text{Corr}(X_t,X_{t-1}) = \frac{\text{Cov}(X_t,X_{t-1})}{\sqrt{\text{Var}(X_t)}\sqrt{\text{Var}(X_{t-1})}}.$$ Here, \begin{...
• 68.9k

### How to determine $p$ and $q$ in my ARIMA model from these ACF and PACF plots?

As you know, you look for patterns of (partial) autocorrelation coefficients that are large. A rough guide to how large is "large" is to pay attention to any coefficient plotted with a spike ...
• 330k
Accepted

• 1,670
Accepted

### How can I reduce the propagation of errors in multi-step time series forecasting?

I do not think there is a way around the issue, fundamentally. There are two ways of $h$-step-ahead forecasting: iterative/recursive (like yours) and direct. The latter goes as follows: for $h$-step-...
• 68.9k

### Lag length selection in ARCH-LM test

The ARCH-LM test is a portmanteau test. It tests a number of lags (lag 1 through lag $q$) at once as a group and tells you whether the average ARCH effect within the group is large. The maximum lag $q$...
• 68.9k

### Inclusion of lagged dependent variable in regression

Some say that the inclusion of LDV will biase downward the coefficient of other IVs. To be more specific, using OLS with the inclusion of a LDV can bias your coefficient downwards. Consider the model ...
• 121

### Why use lag 12 autocorrelation to test January effect?

Let $j_{t}$ be an indicator that month $t$ is January. Imagine the return process is: $$r_t = \mu + b j_t + \epsilon_t$$ Where $\epsilon_t$ is a white noise process. Mean returns are higher in ...
• 22.8k
Accepted

### Showing the covariance and autocorrelation functions of a stationary time series are symmetric around 0

Take a zero mean process for simplicity. Then, $\gamma_j=E(Y_tY_{t-j})$. Under stationarity, the point in time at which we compute the expectation does not matter. Hence, we may add $j$ to each time ...
• 34.3k
Accepted

### How can I use polynomial distributed lag models for longitudinal categorical exposure?

Spline-based distributed lag models are discussed in the book "Longitudinal Data Analysis" by Diggle, Heagerty, Liang, and Zeger. The idea is including one or more lagged covariates in a model to ...
• 64.2k
Accepted

### 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 ...
• 68.9k
Accepted

### What does it mean to have only lag significance on certain multiples of 7

We can be confident that this is a day of the week effect. In many places, and perhaps most, what is reported or done or happens as far as Covid is concerned varies with day of the week. This seems to ...
• 58.8k

### What possible effects to include when running a Mixed Model, time variable and or lags for DV's and IV's?

You ask important questions, which I address below in turn. 1: My main research question is whether or not there is a relation between 'Health Care' and 'Social Support' how should i decide whether i ...
• 5,555

### Lag order selection for Toda-Yamamoto procedure (Granger causality)

The Toda-Yamamoto procedure for testing Granger causality is described very clearly and explicitly as a 13-step sequence in Dave Giles' blog post "Testing for Granger causality". There is no point in ...
• 68.9k
Accepted

### How many lags for ADF test based on ACF, PACF

You can choose not to provide lags, and let AIC or BIC decide the lags for the ADF test. ACF/PACF won't tell you much about the number of lags to put in for the ADF test. PACF being cut off after 1 ...
• 857
Accepted

### Augmented Dickey-Fuller test performed regression in package urca. Problem with lags

Perhaps when setting the maximum lag to $k$, all models are estimated on a sample where $k$ initial observations are not considered (but they are used when lags of the original time series are formed),...
• 68.9k

### "Zero-lag" for ARMA model

This is the representation as a lag polynomial and not as regression coefficients, i.e. standard ARMA(p, q) can be represented as A(L) $y_t$ = B(L) $u_t$ where L is the lag operator and A(L) is the ...
• 3,272

### Lag length selection in a VAR model: information criteria favour zero lag

Based on the criteria (lowest AIC, lowest BIC, etc.), zero lag is preferred, which means a model with just an intercept but no lags. From such a model you will not be able to obtain impulse response ...
• 68.9k
Accepted

### Autocorrelation of concatenated independent AR(1) processes

Executive summary: It seems that you are mistaking noise for true autocorrelation due to a small sample size. You can simply confirm this by increasing the k ...
• 1,030

### Inclusion of lagged dependent variable in regression

Yes, you should be wary of Nickell bias in a small T large N situation (Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica: Journal of the Econometric Society, 1417-1426.) ...
• 245
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 \$...
• 68.9k