# 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 ...
1 vote
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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)?
1 vote
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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 ...
1 vote
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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 ...
1 vote
9 views

### 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 ...
60 views

### 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 ...
31 views

### 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 ...
136 views

### 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 ...
42 views

### 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 ...
311 views

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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 ...
14 views

### 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 ...
15 views

### 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 ...
35 views

### 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 ...
22 views

### 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 ...
12 views

### 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. ...
1 vote
31 views

### 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 ...
10 views

### 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 ...
43 views

### 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 ...