# Questions tagged [lags]

A lagged value in a time series is a value of a variable corresponding to an earlier time. For example, in a monthly time series, the first lagged value will be the value for the previous month and so on.

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### Lagged variables, data leakage and machine learning

I am reading a paper that fits a random forest (RF) to some data that is grouped by company and quarter. In the data engineering stage, the authors include 'lagged' variables of many of the ...
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### Does $p=0 \implies \sum_{i=1}^{p} \phi_i L^i = 0$?

Let us take this $\operatorname{AR}(p)$ equation $$\left(1 - \sum_{i=1}^{p} \phi_i L^i \right)X_t = \mu + \epsilon_t$$ as an example. When $p=0$ I read this to mean \begin{align*} \mu + \epsilon_t &...
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### Trying to understand lagrange multiplier and lads

I’m trying to do the lagrange multiplier test manually accordig to the below text provided by my supervisor. I do not fully understand what he means. Could anyone maybe describe it in R syntax? He ...
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### Interpret high p and q orders of GARCH models

I am currently working with GARCH models (sGARCH, E-GARCH and GJR-GARCH). My question is very general. I chose my p and q orders with the help of AIC criterion. The best models are sGARCH(2,3), E-...
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### If a time-series achieves max-likelihood at GARCH(1,1), would EGARCH, or other GARCH variations achieve global maximum likelihood at p=1, q=1?

If I find that a time-series fits GARCH(1,1), would EGARCH, or other GARCH variations still be X-GARCH(1,1)?
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### Do Vector Autoregression models have the same p, and q order terms as a ARMA model or same number of ACF/PACF?

Do Vector Autoregression models have the same p, and q order terms as a ARMA model? Do you have n (Partial) autocorrelation function plots (P)ACF, one for each of the n time-series, or do you still ...
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### Time series analysis with non-stationary count data (Poisson/Negative binomial models)

I am trying to model the relationship between real-world events and specific features present in tweets related to these events. Whereas my dependent variable (events) is a count variable and its time ...
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### Temperature Lag calculation

I am working on a data science project on an industrial machine. This machine has two heating infrastructures. (fuel and electricity). It uses these two heatings at the same time, and I am trying ...
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### ACF and PACF Plot

I am a first year stat student. We are tasked to create a SARIMA model from trial and error using ACF and PACF plot. Now here is my generated plot: Now I am trying to understand the plot but I don't ...
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### Is ARIMA the right model to use for the questions I am trying to answer?

I am looking for guidance or suggestions on the best model or method to solve the questions below. My dataset is a time series that contains date, number of orders, and number of Customer Service (CS) ...
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### Best model(s) & suggestion for correlation between two variables , "lag" effect, & forecasting time series

I am looking for guidance or suggestions on the best model or method to solve the questions below. My dataset is a time series that contains date, number of orders, and number of Customer Service (CS) ...
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### Prediction with different lags of independent variables

I am wondering if it is suitable to make 1-step ahead forecast with independent variables of different lags？ Suppose that in practice, one wants to forecast the 1-step head (i.e. 1 month) value of ...
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### What high order lags mean in the VAR/SVAR?

I am new to VAR/SVAR and microeconomics. I learn (from here) that a k-dimension p-order SVAR can be written as $X_{i,t}=f_i(X_t^{-i},X_{t-1},...,X_{t-p},\epsilon_{i,t})$, where $i$ indexes the number ...
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### Lagged predictors in irregular-time / asynchronous / time-unconstrained data

In growth curve modeling or other approaches, when time is constrained/synchronous/regular (i.e. panel/wave data; all observations occur synchronously), lagged prediction is trivial - simply add t-1 ...
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### Include predictor at t when including that same predictor at t-1?

I am very confused about whether I need to include the predictor at t when I also include the predictor at t-1 in a linear mixed effects model. For example, consider this simple model: DV = \beta_0 +...
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### What's the difference between instantaneous and lagged effect?

I am working on causal discovery in time series. I know the difference between instantaneous and lagged causal effect based their graphical definition. Specifically, if we are studying causal ...
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### How to address NA Values when using lead values from the predictor variable in the ARIMAX model in R

Data info- I have a weekly dataset with "Replenishment" being the dependent variable and "ADJUSTEDSALESUNITS" being the Independent variable. I'm trying to use the lead values from ...
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### Lag based numerical features or ID categorical variable?

I have to develop a Machine Learning regression model to predict customer’s delay in paying invoices. In addition to the invoice related variables, of course a very important variable is the customer. ...
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### Calculating AICc for regression with ARMA errors

I am unable to manually calculate the AICc for a regression with ARMA errors. I would appreciate any help, such as: (1) pointing out what I am doing wrong or not doing; (2) advice on a textbook that ...
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### Regression assumption violation: lagged dependent variable as regressor

I am studying regression and a bit lost with conceptually understanding why having an independent variable correlated with the error term is a regression assumption violation. Just to give more ...
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### I have a VAR model, can I use the R-square values to explain how good the model explains the dependent variable and if yes, how will it be done

I have a VAR model, can I use the R-square values to explain how good the model explains the dependent variable (explanatory power of the model) and if yes, how will the values of the R-square be ...
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### Finding lagged time series effects

I have a time series with the number of customers and discounts. I suspect that the percentage of discount has a postponed effect. I tried just lagging the variable and calculating the correlation, ...
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### Understanding Output of ur.df Test: What Do the z.diff.lag# Indicate?

When reading the output of summary(ur.df(ts)) in R, what do the z.diff.lag# coefficients indicate? Are they error terms for “at” ...
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### Time series autocorrelation with more than one series [duplicate]

I have several datasets from various dealerships, each with two columns: Time t ranging from 1, 2, 3... n and revenue v in each t. In the case of a single dealership I have calculated a simple Pearson ...
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### Two audio signals in phase at lag = 0,1 but positively and negatively?

Imagine you have two time series of audio signals. You run a time lagged cross correlation analysis and find there is a significant correlation between them at lag = 0 and lag = -1. The correlation at ...
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### Order of integration of a time series process

I am having trouble solving the order of integration of a time series process. Consider the following processes: \begin{align*} \epsilon_t &\sim i.i.d.(0,1) \\ x_t &= \alpha x_{t-1}+\epsilon_t ...
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### Several significant cross correlations at various lags and with different signs? [duplicate]

I have a cross correlation plot here: I’m familiar with interpreting one obvious value at a given lag. For example, consider the positive correlation between x and y at lag -1 in the chart. This ...
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### Finding the $k^{th}$ partial autocorrelation of 100 observations

So, to find $\alpha_{kk}$, do I use the following? And would the order for the ARIMA underlying model be (2,0,0)?
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### Don’t use first differences if you expect lagged effects?

I’m interested in seeing if two first differenced variables are cross correlated with one another (the original data are non stationary, hence I use the first differences which I show with a DF test ...
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### Same coefficient interpretation between first difference and original data?

Assume we have 500 observations, each representing the price in dollars of a rare Tibetan feline (P) measured at the end of each month. Then we take the first differences and arrive at a new set of ...
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### Estimation of lead lag parameter between two simple time series

I was reading the paper "Estimation of the lead-lag parameter from non-synchronous data" (https://arxiv.org/pdf/1303.4871.pdf) and had a question regarding the lead lags estimator for a ...
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### When should we use lag variable in a regression?

In some studies, I saw sometimes people used lag of independent variables, sometimes they use lag of outcome variables as an additional control one. Can I ask what is the mechanic of using lag ...
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### Number of data with lead and lag correlation?

I think it could be a too simple question to someone but I can't find any reliable answer. There are 60 time series monthly data(e.g, 5 years consumer price data and GDP data) and I want to get lead ...
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### Can a time dependent lagged function be used as a rate parameter?

Question: Can the rate parameter in a mm1 queue or a Poisson process be a lagged function of itself? https://en.m.wikipedia.org/wiki/Poisson_point_process https://en.m.wikipedia.org/wiki/M/M/1_queue ...
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### Proof that sum of beta coefficients in lagged multiple linear regression model equals “long run propensity?”

I understand the “long run propensity” or the “long run effect” of a change in an independent variable in a lagged multiple linear regression model is computed by summing all beta coefficients in the ...
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### Lag choice for a VAR model

There is something confusing (for me) about this question. I'm working on a VAR model (7 time series) where i've checked for Granger causality (yes) and stationarity (yes). Now, according to the AIC ...
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### How correctly defined division result for value and their lags (on the R example)?

I design the feature as a ratio for cumulative sum and lags. But how can it be defined in a more "scientific" way, and what can this type of feature mean. ...
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### Treatment of Coefficients from Regression Using Lagged Independent Variables

I'm running a regression on two time series of financial returns, one dependent and one explanatory/independent. For the explanatory time series, I'm creating several lagged versions and using all of ...
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### Testing in a model with lagged variables and control/treatment groups

Say I conduct regression: y ~ x + t + lag(y) Where y is the independent variable, x is some explanatory variable, t is a dummy variable denoting 1 if the observation is from the treatment group and 0 ...
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### Cointegration testing: is there any relation between maximum lag length and the order of integration?

I have some time series and i have to check if they are cointegrated, testing each possible couple. I have understood that the best way to go is, firstly, to verify the order of integration of all the ...
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### Statistical test for time-series lag identified via cross-correlation?

The cross-correlation (https://en.wikipedia.org/wiki/Cross-correlation) is often used to identify the presence of constant time offset between two time-series. In short, two time-series are correlated ...
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### Why does Covid19 confirmed deaths lag behind all causes deaths?

It appears that Covid19 confirmed deaths dates lag about 10 days behind the all causes deaths. This is at least true in European countries (I didn't check this elsewhere) and is particularly obvious ...