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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algebraic derivation-simplification using the lag operator

Hi All: I am asking this with the hope that somebody knows how to simplify an expression which is composed of lag operators. First, the straightforward ones: So, if I have say, $\frac{y_{t}}{\left(1-\...
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Augmented Dickey Fuller test, determining the number of lags used

In a paper by Mark P. Taylor he conducts ADF tests on exchange rates and he describes the determination of lag number with "The number of lagged dependents that we need to include to induce ...
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How to test lagged effect between time series?

I have three time series that should register the number of newly registered users. The source of truth is sould be our database MB and we use Google Analytics and Facebook Ads as confirmations. ...
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Dummy in a VAR-Model with more than one Lag - how to specify?

I am estimating a VAR-model on German data, which has a strcutural break due to the reunification. I want to depict the structural break with a dummy that is 0 before the reunification and 1 ...
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Granger causality in r clarification

Take the example of Chickenegg in lmtest package. We have: ...
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42 views

If B is backshift operator, then how to calculate 1/(1 - B)?

We have known that: when |r|<1, (1−r)^-1 = 1 + r + r^2 + r^3 + r^4 + . . . But for 1/(1-B), since the coefficient of B is 1, the power series 1 + B + B^2 + B^3 + . . . can not converge. In my ...
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How to determine the optimal lag order of asymmetric innovation for a GARCH?

In the python package arch_model, there is an option with which we can give the "lag order of the asymmetric innovation" when we estimate GARCH model. Are there any ways to find the optimal ...
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Investigating lagged effects of an independent variable on a replicated dependent variable

I have data from repeated observations of ~60 independent replicates over 20 consecutive years, along with an environmental index. Let's say these data are the annual quantity of apples produced by 60 ...
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ADF test Which lags to include?

I am doing the ADF test on quarterly data. Lag 1,3,4 are significant at 1%. Lag 2 is significant at 10% (9.7%). What should I do, Should I keep all 4 lags? I am using 5% as a rule of thumb.
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Why ARIMA Ljung-Box p-values tend to decrease for large lag

I am a beginner at ARIMA model fitting. I have observed that after I fit my model, the Ljung-Box statistic tend to discard the null hypothesis for large lag. It could be that it is only random that it ...
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When using longitudinal variables on different time scales in a regression, is it valid backwards fill the dependent variable?

I'm working on a longitudinal project that is assessing an outcome variable through a monthly questionnaire and using daily activity as a predictor. The questionnaire asks about symptoms in the past ...
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Forecast is simply equal to the lag of the original time series

I am currently dealing with the problem of short time series which often involves naive models as they already perform well enough. So I implemented an exponential smoothing that follows $$ F_t = \...
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data for FDI and growth

I am trying to find the absorptive capacity of FDI in affecting economic growth. I have a panel dataset of over 50 countries from 1996 to 2015. I am taking FDI, Human Capital (secondary education) as ...
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Regressing I(1) variable on I(0) variable

I am dealing with time series regression, where I have stationary and nonstationary variables. Can I regress nonstationary I(1) variable on stationary variable when controlling for the lag of the ...
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Including lagged differences - time series

List item Why would the researcher include the additional lagged differences in the second equation? Don't need a full solution, just a tip. Thanks a lot!
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When AIC chooses 2 lags, but 2nd lag is insignificant, do I drop it?

If the AIC criterion chose 2 lags, but the 2nd lag is not significant (see p-value), then am I supposed to drop the 2nd lag or leave it?
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If B is my backshift operator then how do I calculate (1 - B)?

I understand that $(1 - B)x_{t}=x_{t}-x_{t-1}$. I understand that I can do algebra with $B$, treating it like any other variable. But can I do arithmetic operations with $B$? Like, can I subtract $B$ ...
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What does it mean to have only lag significance on certain multiples of 7

I have a dataset named covid and after creating an acf graph of it , it looks something like this Why is it that it is only showing lag significance on lags which are multiples of 7 only , dose it ...
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Lagged dependent variables: Is it safe to ignore bias over a long time horizon?

Suppose I have a Poisson model which investigates the effect of a county level policy on robbery counts. Here is the basic specification: $$ \text{log}(y_{it}) = \theta y_{i,t-1} + \sum_i\text{County}...
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Selecting exogenous factors lag to develop an ARIMA model for daily forecasts

We are trying to assess the possible effect of some meteorological variables on cumulatives reported cases of the actual covid-19 disease for a wide range of countries at the daily timestep. Then, ...
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68 views

Is random walk with drift is random?

I see everywhere in the web that lag-plot or acf are used to see if a time serie is random. If there is no structure in the lag plot then the data are random, and if autocorrelation = 0 then data is ...
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Choosing the right lag order for the LjungBox() test in VAR()

I have several VAR Models with mostly AIC as lag criterion. For the Ljung-Box test I read about the rule of thumb of choosing h=min(10,T/5) with T=number ...
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Does it make sense theoretically to lag my dependent variable?

I am currently doing a research on the correlation between the duration of conflicts and religious organisations. For this, I am doing a multiple linear regression, with my dependent variable being ...
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The Lag in johansen test and VECM

For VEC I used the same lag that I used in johansen test and Instead of use the same lag of johansen, my friend did a lag exclusion wald test. Is that correct? can I change it?
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Two (related) questions about forecasting multivariate models with multi-period lags

I am estimating a bunch of different linear or quasi-linear models on several hundred observations of the same multivariate (economic) time series data set. I hope to use the results both for insight ...
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Autocovariance function depends on lag only - intuitive meaning

On an intuitive level, what does it mean for a weekly stationary time series the autocovariance depends on lag only, that is why dependence on lag is a "nice" property?
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Support Vector Regression applied to time series with lagged predictors

I am relatively new to time series. I am dealing with an energy consumption prediction problem. Data points are sampled on a 15-minutes frequency. I have a set of exogenous variables such as ...
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If $y_t$ and $x_t$ are cointegrated, then are $y_t$ and $x_{t-d}$ also cointegrated?

Assume that $x_t, y_t$ are $I(1)$ series which have a common stochastic trend $u_t = u_{t-1}+e_t$. Particularly, consider the following DGP \begin{align} y_t&=\alpha_y+u_t+a_t \tag{1} \\ \end{...
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arima concept clarification on differencing term d

I have a simple question regarding the d term in the arima(p,d,q). I understand when d = 1, we are essentially differencing the time series by X(t)-X(t-1). however I am confused when d=2 please help ...
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What is the link between the order of the AR process and the order of the Augmented Dickey-Fuller test in case of first differences?

I realize that in general ( for an AR(p) process ), you should include p-1 lagged differences in the ADF specification (when testing for non-stationarity). I was recently told, however, that when ...
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Correlation between lagged residuals and regressors in first difference regression

Why would it be the case that the covariance between the lagged residuals and the (or a) regressor in a first difference regression model be non null, i.e. why $cov(U_{it-1},X_{it}) \neq 0$ where $U$ ...
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21 views

Correlation matrix from VAR(1) model

I have implemented a simple VAR(1) model with gaussian noise and no bias to generate two dimensional data. When computinng the empirical covariance matrice (for lag 0) of of this signal, it is always ...
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Poisson/NB regression with lags on Time Series data

I'm trying to put together a prediction tool for counting time series data. My idea is to go with a lagged Poisson/Negative Binomial regression model. However, I'm uncertain about a many things. Is ...
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Feedback and lagged variables in panel data

In the static linear panel data model we have that: $$y_{it} = \alpha + X_{it}'\beta +n_i + U_{it}$$ where we assume $n_i$ are unobserved individual specific effects. My main question is why strict ...
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Question on lagging environmental variables

I am trying to test environmental variables against fish catch data to see how they impact the species composition. for environmental data, I have river discharge, temperature, rainfall, and salinity. ...
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How to determine the number of lags in autocorrelation

I am working with daily data of a time series and researching its dynamics. I want to know how many days in the past affects the current value of the time series. For this, I am using a simple ...
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175 views

Engineering lag features for the test set in time-series machine learning

I am trying to do time series forecasting through machine learning. I want to engineer lag features, but was wondering what would be the best way to go about generating these features for the test set ...
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23 views

How lag to consider in ADF test to decide that time series is stationary

I'm doing ADF test before doing forecasting of my data in R to check if it's stationary or not So I used following code adf.test(df_foreacast$Utilization) I'm ...
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How the time lag is non-integer in ACF plot? [duplicate]

I'm plotting the ACF of a time series. ...
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44 views

Benefits of using lag operator notation as opposed to subscripts

I have a number of random variables that start at some initial state and then vary along time, I am planning on doing relatively straightforward analysis (nothing that the use of lag operators would ...
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28 views

Random walk and variance [duplicate]

If yt is pure random walk the variance Var(yt-yt-k) will (increase, decrease or remains constant) as lag k increases?
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Lag length for a VAR model

I am working on 2 time series Sentiment and Return(from stock). They are daily data excluded weekend. Both are stationary at I(0). Lag lengths for Sentiment is 22 and Return is 2. What lag length ...
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Lagged features in time series feature engineering

I understand the value of using lagged features in time series analyses, but conceptually I've still quite a bit to learn. When creating lagged features for modeling purposes, should I remove the rows ...
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Expressing the Complete Data Likelihood for Factor Analysis Model with VAR(1) errors

I am working on a model related to that below. For $t=1, 2, \ldots, T$ the vector of $N$ observations, $X_t$, is related to a vector of $K$ latent factors, $F_t$, via the observation equation $$X_t = \...
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122 views

Correcting for auto-correlation when using a lagged DV in the regression

I am conducting a regression where in I have data at the quarterly level for 19 companies (I have data ranging from 2007-2019 so about 30-50 quarters for each company). My regression model in STATA ...
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Interpreting differing results from correlation plots, correlation matrix, GLM, and Lagged linear model

I'm trying to get some advice on the results of the following statistical tests. I'm including the data and the code for said steps for clarity. I'm trying to analyze whether a strong YOY (young of ...
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Can I apply both differentiation on lag 2 and two differentiations on a time-series?

I'm working with time-series and I have seem two approaches from different teachers. One of them used the following code in Python: ...
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Test for lagged time series analysis

I have two time series and there is good reason to believe that one of the has a lagged effect on another one. i.e they move inversely. What are some time series tests I could perform to Validate ...
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Autocorrelation to measure lag effect

Is there something similar to Autocorrelation but instead of measuring "correlation of a signal with a delayed copy of itself", measuring correlation of a signal with a delayed copy of ...
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117 views

Picking optimal lag values and intervals - multivariate time series

I'm working on my first project using time series: I have the weekly stocked amount of a product and I have to predict if it will go up or down (binary), looking for seasonality, I started trying this:...

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