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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12 views

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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32 views

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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30 views

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)[12] and it would show me what ACF and PACF should look like for a 12-seasonal ...
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36 views

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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Advantages of using PACF

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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20 views

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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17 views

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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34 views

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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102 views

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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32 views

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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28 views

sign symbol above or below the sigma operator

the below two expressions are the same according some references, so, my question is, why does it change the sign in $Y_{i+k}$ or $Y_{i-k},$ when there is a plus or a minus sign above or below the $\...
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19 views

What does my ACF and PACF plots indicate for ARIMA order?

I am looking at forecasting first-order differences oil prices using the ARIMA models. However, I struggle to see what p and q orders my ACF and PACF plots would indicate. I have added the act and ...
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Where did I go wrong when using ARMAacf function in R? [closed]

I recently had an exam in forecasting where I was one point short of an A. The biggest mistake I made which cost me 3 points was that I incorrectly used the ARMAacf() function to calculate the implied ...
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18 views

How to interpret these acf and pacf graphs? [closed]

I am trying to analyze these pltos but having a hard time since I don't know if they are even right... So i follow your advice and these new plots is what i got:
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Residual Acf plot---autocorrelations always significant

I have a time series and I feel confident it is a stationery process after detrending it and deseasonalize it. It looks to have constant mean and variance and also satisfies the ADF test. I fitted ...
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30 views

Time series forecasting without significance in autocorrelation

My data which has no significance in ACF and PACF plot fits very poorly to my observed data. There are similar cases like my case too which when there's no significance in PACF and ACF their ...
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Determining order of ARMA model in R

I am working with a time series dataset and wish to do some ARMA modeling in R. I believe that I have detrended and deseasonalized the data correctly and now have a stationary time series. Now the ...
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44 views

How would a select an ARIMA model based on the ACF and PACF?

I am trying to estimate a model based on the ACF and PACF. I understand the ACF applies to MA and PACF applies to AR. Do I just count the significant lines and order it that way? I have used a Box Cox ...
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18 views

How should you determine the order of an AR(p) model using PACF with fluctuating significance?

While plotting the PACF of the sample, the PACF values become insignificant post the second lag, then significant again post the 8th lag and so on. Basically, there's cyclicality in the partial ...
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30 views

Determining Value of p or q if both ACF and PACF plots are dies down

Is there any straight way to know the value of p and q if ACF and PACF plots are both dies down?(d=0) I have tried ARIMA(3,0,3) because of the third lag that significant on both. I also tried ARIMA(2,...
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Can ARIMA Models be used to models stock prices?

I'm learning about ARIMA models and other variants (SARIMAX, ARIMAX...etc) The problem is that whenever I try fitting the closing prices for a given stock (Google, Amazon or Netflix for example), the ...
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45 views

Interpretation of pacf and acf plots with no lag value exceeding significance bounds

I am trying to estimate a model for my time series data. The data contains Quality Of Life Index values from 1975-2006. auto.arima() suggests an ARIMA(0,1,1) model but I am still confused as to how ...
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Is this data stationary ? I’m having issues with the correlogram

I have run the augmented dickey fuller test and the NGperron test , I have taken the first difference ,the data seems stationary however the correlogram is still exactly the same and the values as ...
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What is the ACF plot of $x_t = 0.9 x_{t-2} + w_t$

I am just learning time series, and I am wondering about the following AR(2) model: $x_t = 0.9 x_{t-2} + w_t, w_t \sim N(0, \sigma_w^2)$ Please show me the plot of its Autocorrelation Function, or ...
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55 views

How to estimate a single AR model for multiple time series?

I have ACF of a time series data, I want to interpolate the ACF using AR model for which I need to calculate the coefficient of the AR model The problem is I have (6000x6000) matrix of ACF and I cant ...
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37 views

Accounting for autocorrelation in descriptive analyses?

I understand the need to account for/model autocorrelation in predictive analyses, but is it necessary to account for/model autocorrelation in descriptive analyses? For example, I have built a GAM to ...
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GEEs for temporal autocorrelation and the ACF plot

I have a dataset with temporal autocorrelation in it. The response variables consists of 0s and 1s, and I used a binomial GLM first. However, when I used: residualsmodel <- resid(model) acf(...
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50 views

How AR model parameters are estimated?

I know that AR(p) is defined like this: $$ y_{t} = c + \phi_{1}y_{t-1} + \phi_{2}y_{t-2} + \dots + \phi_{p}y_{t-p} + \varepsilon_{t}, $$ From what I understood, this means $y_{t}$ value is predicted ...
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35 views

When not to use autocorrelation structure in time series?

I have time series data of animal carcasses submitted to a testing laboratory on a monthly basis for three years to test for disease. This disease acts very quickly and kills the host within a couple ...
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69 views

Determining order of SARIMA model by ACF/PACF (and dealing with seasonality)

I have a ts that has the average monthly measure of pollutants in the air and i'm trying to use a SARIMA$(p,d,q)(P,D,Q)$ to model it but I'm having trouble determining the order because I'm somehow ...
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Can you help me derive PACF for moving average process MA(1)?

I am really lost with the task. Can someone provide literature or possibly the derivation for the following: Assuming that the best linear predictor of $X_{h+1}$ can be estimated as $\hat{X}_{h+1} = \...
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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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61 views

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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33 views

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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53 views

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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38 views

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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48 views

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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24 views

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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102 views

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 ...
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293 views

How to set (p,d,q) and (P,D,Q) for SARIMA time series model

I have a time series dataset of monthly average temperature in Cayman from year 1823 to 2013, with dickey-fuller test = 0.008275 (I assume the series to be stationary since the test doesn't exceed 0....
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37 views

Do the following ACF and PACF plots show a ARIMA(1,0,0) model?

I am trying to find the correct ARIMA model for a time series without seasonality that produce the following ACF and PACF plots. Looking at these plots my initial hypothesis is that an ARIMA(1,0,0) ...