# Questions tagged [acf-pacf]

The AutoCorrelation Function and Partial AutoCorrelation Function pertain to the correlation of a time series with itself at different lags. They are used to detect non-independence & suggest p, d, q terms in the Box-Jenkins approach to ARIMA modeling.

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### Why ACF is used in MA and PACF is used AR models?

I'm reading Analysis of Financial Time Series(Third Edition) RUEY S. TSAY. The author summarizes the model selection of AR(p) and MA(q) as follows: For MA models, ACF is useful in specifying the ...
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### Autocorrelation in linear mixed models (lme)

To study the diving behaviour of whales, I have a dataframe where each row corresponds to a dive (id) carried out by a tagged individual (whale). For each dive I calculate a series of parameters (...
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### Pacf plots show unusual spike at high lag

The time series data has 108 points altogether with a few outliers. So after removing the outliers, I plotted pacf and acf of the original as well as differenced series. Acfs: Pacfs: ...
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### Tool to print/plot ACF and PACF of a thoeretical model

Is there a tool to plot the "ideal" ACF/PACF for a theoretical model? For example, I could input (0,0,0),(2,0,0) and it would show me what ACF and PACF should look like for a 12-seasonal ...
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### Help understanding Autocorrelation and Partial Autorcorrelation (PACF)

I understand the layman concept of PACF - it is the correlation with the linear dependence of the earlier lags removed. However, I am confused as to how this relates to Autocorrelation. Consider ACF(2)...
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Box-Jenkins approach to time series analyses uses a series of diagnostics, one of which calculating Partial autocorrelation function (PACF). The goal is to determine the order ...
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### ACF of differenced MA(p) process

I have an MA(4) process applied to the first order seasonal difference of $Y_t$ as follows: $(1-B^s) Y_t = (1+\theta_1B+\theta_2B^2+\theta_3B^3+\theta_4B^4) Z_t$ where $Z_t \sim N(0,\sigma^2)$ This ...
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### Doubts with interpretation of ACF & PACF plots

I am new to Time Series and I have some doubts interpreting ACF & PACF plots. I have found the following cheat sheet (link to source: https://www.linkedin.com/pulse/reading-acf-pacf-plots-missing-...
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### Why doesn't PACF cut off for MA processes?

While studying for a time series paper I came across the terms 'partial autocorrelation function' (PACF) and 'autocorrelation function' (ACF) in conjugation to $AR$ and $MA$ processes, why is it such ...
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### Why I Iose correlation when diff has been done?

Good Morning I’m trying to study a set of samples. In the original set there are several samples along the day. Samples time is not regular. But I can get average of that sample and fill the gaps. So ...
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### How to interpret Autocorrelation plots?

I have sales data per day. To create an ARIMA model, they suggest to first look at an autocorrelation plot. How I interpret this is that they look how my sales are correlated to eachother for ...
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### Determining the numerical value of the parameters of a Moving Average process

Is it possible to determine the numerical value of the parameters of a moving average process just by looking at the correlogram (Autocorrelation function and Partial Autocorrelation function) of the ...
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### How does statsmodel.tsa.model.AR.fit find the correct lag 'p' when it is not specified?

In the documentation, all I find is the following: ...
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### Choosing ARIMA lag orders based on ACF and PACF: a case

Trying to figure out arima parameters. Performed dicky fuller test to make sure no unit root exists at the first difference. When plotting the pacf and acf, how do I chose AR and MA parameters for the ...
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### ACF and PACF functions for AR(2) model

I am trying to practice calculating the autocovariance function and the partial autocorrelation functions of a time series $X_t$. I am familiar with how to calculate the autocovariance functions of an ...
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### ACF and CCF interpretion

I plotted ACF and CCF for two time series. But, I do not know how to exactly interpret them. I want to know how and which information can be found from these plots. Can I get any coefficient from CCF ...
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### Determining order of ARIMA(p,d,q) from ACF and PACF

I know that when trying to determine if you have an AR(p) or MA(q) process, you look at the PACF and if it drops off significantly at a lag p, then you can say it's an AR(p), but if it's geometrically ...
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### What is the take away from such ACF and PACF plot?

I plotted the ACF and PACF after taking the first difference of my time-series. What is the take away from such plots? What should be the AR and MA order in such case? The data is as follows, <...
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### Autocorrelation (acf) and Partial Autocorrelation (pacf) to identify Box-Jenkins models

Can you help me to identify which Box-Jenkins models in these pictures? I have read behavior ACF and PACF to identify whether this is AR, MA, ARMA or ARIMA but I'm so confused because none of the ...
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### R: understanding the acf() function

Studying autocorrelation using R I ran into a brief exposure by Ryan Sheehy named Autocorrelation in R. In this exposure, the topic and the use of the function acf()...
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### Estimating autocovariance from repeated time series

Consider a parent process $Z_t$ whose characteristics I wish to estimate. Consider two time series (or any stochastic process) realizations of this parent process $$X_1, X_2, \dots, X_T\,,$$ and ...
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### Checking for autocorrelation

I would like to check my GLM model for autocorrelation - I am wondering for Poisson, Negative Binomial and Binomial GLMs whether to use the deviance residuals or the Pearson residuals? This is how I ...
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### ACF and PACF with daily data

I am modeling with daily time series and some forecasting models from forecast package.But at the beginning I have some problem with time series.Namely I want to try to explain ACF and PACF but I can'...
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### What should be the (p,d,q) and (P,D,Q) for SARIMAX

I'm working on time series data using SARIMA. So far I made the data stationary, I plotted ACF, PACF of the stationary data. But i'm unable to guage the parameters from the ACF, PACF plots. Could ...
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### GEEs and GLMs: what can I do about the auto-correlation?

I want to run a model that somehow incorporates temporal autocorrelation. I have a dataset which consists of the minutes of Species A vocalizing at a single site. This is data recorded continuously ...
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### IS that possible to write a code to detect the AR (p) through PACF chart?

In the past, I learn how to decide the AR (p) in a visual way. For example, in the following figure, I realize that after the bar at leg 3, all the bars are roughly inside the blue envelope. In ...
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### How to decide p P q Q of ARIMA through ACF and PACF?

(Preface) My problem is that when I do the time series forecast with auto.arima(), it gives me a ARIMA(1,1,1) model which generate a flat forecast line as the below ...