# 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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### Can I utilise time series properties of the data, WITHOUT creating lags?

I am working on a project where the train and test sets are given to me. The data (stock returns) is time series by nature, but the point is that I cannot create lags because that would mean ...
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### Interpret the PACF plot to select the correct lag (AR model order)

I want to select lag (AR model order) for the series Food price inflation. AIC gives 4. SIC gives 3. And also, I print its PACF plot. How can I interpret the PACF plot to select the correct lag?
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### How to determine the optimal lag length in time series?

I am a beginner in time series analysis, and I am always having this problem of selecting the optimal lag length for my time series, especially when using machine learning algorithms for the ...
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### OLS Model with Lags - logged coeff

i am building a OLS model using python, where the dependant and independent variables are lagged. This is a form of econometrics model where i want to figure out how much each independent variable ...
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### In repeated measures, how to distinguish regression to the mean from a negative lagged effect?

I have repeated measures for a quantitative variable "cry" for N = 52 participants (how much you cry at a given time), there are 30 repeated measures. The values range from 0 (not at all) to ...
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### Why does differencing White Noise induce autocorrelation of $-0.5$?

I am curious about the following problem. Let's have a variable given by white noise, $$y_t \sim \operatorname{NID}(0,1).$$ Let's say we difference it, $$\Delta y_t = y_t - y_{t-1}.$$ And now, if we ...
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### Interpreting Lagged Dependent Variable in Binary Logistic Regression

I am running a binary logistic regression to test the purchasing of a gym membership in 2021 against a series of controls (ie. income, gender). Included amongst these control is a lagged dependent ...
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### Can you lag a covariate in a Cox proportional hazards model?

I am using a Cox PH model to study at what point in their lives people decide to move outside of the United States. My sample is 500 people who live in the United States, and the unit of analysis is ...
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### I have a significant change in my outcome with the opposite sign in the lead period. Is this an issue?

Suppose I have a negative significant effect of a variable x on y. Also negative significant effect of the lag ie variable L1.x on y . But I get a positive sign significant effect on y in the future ...
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### Can bootstrap adjustment for $p$-value in AR model be applied to distributed lag model?

In Wang "Multiple testing correction in time series: rolling window analysis with applications of GWAS methods" (2022), the author mentioned that bootstrap minimum $p$-value can be applied ...
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### Use KPSS test with all lags

I have a series with N observation, I want to test the whole series for stationarity with KPSS. However I noticed that when run with all lags, the KPSS test always ...
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### Cross-lagged analysis. Interpretation of Coefficients and Covariates

I am currently, for the first time, conducting cross-lagged panel analyses to test for temporal precendence in the relationship between two variables. I have two questions: How do you interpret, in ...
1 vote
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### How many lags of independent variables to use

I have a panel dataset (26880 observations) of individual decisions ($y_{it}$, a categorical variable) which depends on signals ($x_{it}$). I am trying to find out how many past signals individuals ...
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### Lag operator and stationarity [duplicate]

I just study about time series. I want to ask about in AR(1), why the lag operator, L, need to be bigger than 1 for zt become stationary. And also when |L|>1, it is lie outside of the unit circle ...
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### My "lagged consumption" variable accounts for all the variation in my dependent variable

I chose the topic of consumption for my assignment in econometrics. My explanatory variables are interest rate, consumer credit, oil price, disposable income and lagged consumption by 1 year. Using ...
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### Is it possible to estimate the cumulative effect without using distributed lag model?

I am fitting the temperature and mortality data by using conditional Poisson regression. The following formula and data are used: https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/1471-2288-...
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### What possible effects to include when running a Mixed Model, time variable and or lags for DV's and IV's?

I'm doing analyses in R on 5 repeated observations over a period of 5 years (repeated/random dv: 'amount of professional health care', repeated/random IV's: 'amount of social support' with several ...
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### Evaluate time lag between an event in exogenous variables, and the response of a endogenous variable in regression SARIMAX model

I am currently using autoregressive models to assess the influence of exogenous variables on the dynamics of a shellfish population. These exogenous factors are water temperature, salinity, and food ...
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### Modeling considerations when data spans different events (time) and exhibit a (relatively) low mean and high variance

I have weekday data ($n = 1551$) from the past 5 years (2019-2023) with attendance at a large restaurant. I am just getting started, and for each weekday I calculated the mean and the variance as per (...
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### Regression analysis and time series data

I'm trying to model the effect of flow at entry and flow at exit on the produced energy in a thermal power plant ,The data is collected every 2h for two years,in my internship they want me to model ...
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### How to detect whether Y or X is the lead or lag variable in a time-series using the regression of Y(t) vs X(t-1) and X(t) vs. Y(t-1)?

Coefficient in Black, P-Value in Blue and Standard Error in Red. Using these results, can I deduce whether X or Y is the lead or lag variable in the time-series?
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### Why are lags of the dependent variable a no-no in traditional random effects models?

This post says: Lagged versions of the dependent variable are a no-no in traditional random effects models. The problem is that they are correlated with the random intercept and produce inconsistent ...
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### Why can't I estimate the target variable when I apply a lag of variable

I applied lag to the exposure variable to adjust for its previous time-point's influence. However, the coefficients of the lagged variables are estimated to be excessively high, leading to the current ...
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1 vote
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### Time series iterated multi-step forecasting autocorrelation issue (propagation of error)

I am trying to model some (quite ugly) time series data with lagged values of the outcome variable using a non-parametric machine learning model as I do not know how to correctly specify the model. ...
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### How many lags to include? (Temperature data set)

I have a time series of daily temperature with autocorrelation that looks like this: Of course, temperature is heavily autocorrelated. When looking at the partial autocorrelation plot, lags are ...
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1 vote
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### Interpreting lagged exogenous variables in ARMAX and regression with ARMA errors

There is an interesting post about the connection of lagged exogenous variables and the autoregressive time series model: Forecasting - Lags vs. AR terms for Exogenous Variables Consequently, by using ...
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### Selecting optimal lag values for Neural Network in univariate time series forecasting - How many lags to use as input variables?

What is the recommended approach for selecting lag values in a univariate time series forecasting problem, specifically for input variables in a feedforward neural network (FFNN)? In my research ...
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### Lagging a quadratic independent variable

In the theoretical framework for my model, there is concern about reverse causality between Y and my main X variable. Additionally, I believe there's an information lag effect where economic agents ...
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### are moving average and lag modeling the same?

I am not clear on the difference between the two concepts but I am interested in air pollution exposure in a given period of time and in the literature, I know that lag models are used. I have also ...
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below is my ADF test for regression residuals. I use alpha=5% My interpretation is : my residuals are non-stationary as my model does not take into account the 4 lags suggested by ADF. In other words, ...
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### Choose optimal lags in months for annual data

I try to forecast annual monthly price changes using annual monthly X changes. To choose the best lag, I run the VAR model and aim for the minimal AIC value. The problem is that the price is ...
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### Time-lagged cross correlation between two measurements across multiple people

I have collected time-series data from a few hundred people. For each person, I have two measurements that I am interested in correlating. Specifically, I want to identify the time point at which ...
1 vote
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### Cross-lagged Pearson correlation in R

I have a dataset where I have two recordings (sessions) of two different variables. ...
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### Lag variables on OLS after PCA (Principal Components Analysis)

I have about 60 macroeconomic and financial indicators; all of them stationary (logs and differencing), with monthly data for the last 25 years. I am trying to predict changes in a financial variable (...
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### How good are inflation expectations as a predictor on inflation?

I want to research inflation expectations and how well they predict inflation. I have found some past articles but none of them explain how to forecast inflation using inflation expectations. I have a ...
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### Should I lag the independent variable or dependent variable to get delayed effects of the IV on DV?

I'm doing research where I am getting the delayed effects of my Xs on my Y using a 2-way fixed effects approach. Since all of my Xs will end up being delayed, should I lag my Y by -1 or should I lag ...
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### Creating a New Predictor Variable From a "Lagged Response Variable"?

Our TA in our stats class told us that when working with regression models, it is generally unadvisable to create a new predictor variable from a "lagged regression variable" (unless you are ...
1 vote
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### Significant Partial Autocorrelations at High Lags

I've been doing some exploratory data analysis on a time series dataset and had some questions about interpreting a PACF plot that I generated. I initially displayed the plot with a maximum lag of 400,...
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### Specify Vector Error Correction Model with different lagged effects?

I'm fitting a Vector Error Correction Model. The general form is like this: $$\Delta y_t = A_0 + \sum_{i=1}^{t-1} A_1 \Delta y_{t-i} + \lambda EC_t + \nu_t$$ In which $EC_t$ is the error correction ...
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### Johansens Cointegration test - VARselect output showing all Lag 1's

I am running a cointegration test on 4 input variables over 1 year and when I run the VARselect it outputs: ...
1 vote
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### Textbook exercise-ARMA model

I have tried hard but cannot solve the below exercise. Any extra hint or solution will be appreciated! Given the below stationary series: \begin{align*} y_t=\frac{L-\phi}{1-\phi L}\varepsilon_t, \end{...
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### Should all variables in a VAR model have the same number of lags?

I'm performing an econometric analysis and all my variables (in daily frequency) are stationary, so I've decided to use a VAR model. After analyzing the data in Stata, it suggests all variables should ...
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### Creating auto-correlated random time series

I want to create random time series that follow a given auto-correlation function. For this I am using an AR(n) model approach: $$X_t = \sum_{i=1}^n\alpha_i X_{t-i} + \epsilon_t$$ where $\epsilon$ is ...
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### Can a Variable Be Both Dependent and Independent?

We can see that the GDP growth, represented by "y" is the dependent variable and independent variable. I would like to perform quantile regression in Eviews, with ...
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### Should a covariate be lagged in a GARCH-X model?

I am modelling Dow Jones returns using a GARCH(1,1) model but I also want to estimate a GARCH(1,1) by inserting a covariate to check if this covariate affects the volatility in some ways. The ...
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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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### 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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