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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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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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Estimation of autocorrelation from unevenly sampled time series

Consider $n$ distinct time series $X^{(1)}, \ldots, X^{(n)}$, indexed by time (time ranging from 0 to 1), such that: each time series $X^{(i)}$ has a different number of observations, the time ...
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Why the differenced at lag 12 time series of a SARIMA(0,0,0)(0,1,1)_12 model follow the MA(1) pattern with step 12?

I am trying to understand why the ACF of the seasonally differenced series reveals the AR of MA structure of the original series. For example: The following lines creates a SARIMA(0,0,0)(0,1,1)_12 ...
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What does a significant PACF and insignificant ACF plot mean about autocorrelation?

I am new to time-series analysis and have been trying to understand how to correctly identify different types of autocorrelation in my seasonal data. I have run a gam and am now looking at the ...
Jcarroll's user avatar
3 votes
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How to determine (the lag order of) MA from these plots?

I am using time series to analyze the price of a commodity. Characterizing is the fact that the price of the good is determined per hour, one day prior to the day of delivery. For now, I have ...
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Prove the convergence of the sample PACF

I'm looking for a proof that the sample PACF converges in probability to the PACF in probability as T goes to infinity when m = p. Moreover, I am looking for a proof that when m > p, that the ...
Jerry Qu's user avatar
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Difference transformation and Stationarization of Moving Average

I have a temperature sensor data, I want to denoise it. The first thing that came to my mind was to take the moving average, it was very smooth but it is still not stationary. If I take the log ...
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ACF and PACF plots to estimate SARIMA orders

I have some data (sales of a particular item at a particular grocery store) which exhibits both trend and seasonality. I fit these trend and seasonality components by doing a linear regression of the ...
Steven Gubkin's user avatar
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How to choose the order of differencing?

I have a time series that looks like this I was asked to display the autocorrelation function and perform ADF test and based on that suggest a d for further analysis. I get plots like this and can ...
moon's user avatar
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What critical level to use in diagnostic tests for model selection in forecasting?

I have been reading Hyndman & Athanasopoulos "Forecasting: Principles and Practice" (newest edition here) recently, and I noticed something that I regard as a possible inconsistency. On ...
Richard Hardy's user avatar
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What modeling approach should i use AR, MA, ARMA?

those are my ACF and PACF plots for my time series after two differentiating. I watched a couple of tutorials but I cannot figure out what method I am supposed to use. Also, an interpretation of the ...
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What does this autocorrelation plot mean? [duplicate]

Is there any definitive meaning to a sinusoidal (above and below zero line) autocorrelation v lag plot? What does it tell us, if anything, about the realization it came from?
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ESS with many short, parallel chains

I have a curious problem I would like to share and ask for references and advice about. I am working on a MCMC problem and I realized that I have big economies of scale when I am drawing many chains ...
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ARIMA model on yearly data using R

Im new to time series forecasting, and I was trying to model the folowing time series data using ARIMA model in R, so that I can predict for the future 10 time periods. data: cereal_dataset When I ...
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The time series shows random walk behavior from PACF and ACF plot but adf test shows its stationary

I am new to time series and wanted to practice it by forecasting an hourly time series. The adf and kpss test results show that the series is stationary. ADF test results ...
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Very narrow confidence interval in ACF and PACF graphs

I am trying to forecast electricity consumption using hourly consumption data over a span of 4 years. However, when I plot the ACF and PACF graphs, the confidence interval turns out to be very narrow, ...
Sila Sefer's user avatar
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ARIMA - Identifying an outlier in residuals

I am trying to perform an ARIMA (SARIMAX in fact) and when looking at the residuals I see a large outlier. I am using python statsmodels.tsa.statespace.sarimax. I ...
Solebay Sharp's user avatar
2 votes
1 answer
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standardized residuals GARCH

I am having a hard time understanding ACF and PACF. I estimated a GARCH(1,1) model and now I am checking its standardized residuals. This is what I get: I can not really understand why the lag 0 has ...
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How to determine the theoretical ACF of a SARIMA model?

I need to determine the ACF for a SARIMA(0,0,1)(0,0,1)12 model with $\Theta=0.7$ and $\theta=0.4$. However, I am unsure what parameters to use.
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Specifying parameters for SARIMAX model with significant ACF / PACF at tails

I have hourly data that has a period of 1 day or 24 hours / time steps and I hope to do short term forecasting for a few days in advance. The ACF of the raw time series was periodic (see last figure) ...
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How to interpret those ACF & PACF?

I have some problems when analyzing my time series dataset. Basically, the dataset is about the daily sales volume of an FMCG company (they work from Monday to Saturday with Sunday being a day off, so ...
Khoi Le's user avatar
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How to intepret ACF and PACF plots? I'm trying SARIMA MODEL

I tried to put p=5 and q=7 but it's not working.
Alexandra's user avatar
1 vote
1 answer
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ARIMA flattens out on one order and works perfect on another

I am implementing an ARIMA model on a time series data. I have confirmed that the data is stationary with the adfuller test. I plotted my ACF and PACF graph as below with a lag of 40. Here, I see the ...
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Time series ACF PACF vs SARIMA results

My SARIMA gives the following result but my acf and pacf plot shows a different story. Is it because of heteroskadiscity of the model also my model has a seasonality of 365 days how do I handle it?
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How to interpret autocorrelation charts?

Provided the following examples of data, p-value and autocorrelation charts: How are we supposed to interpret the charts on the rightmost column? Just by looking at these charts, what can we say ...
evilmandarine's user avatar
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Different PACF plots with different statistical software

I was attempting to replicate the results of a paper and ran PACF plots through R Studio, Stata, and EVIEWS for the UK debt-to-GDP ratio. I received quite different plots in return. Can anyone shed ...
steve's user avatar
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Interpretation of ACF plot of a Hidden Markov Model

I am trying to interpret the ACF plot of a 3 state HMM model but as it is my first time dealing with any kind of HMM it is causing a lot of trouble. I have also had a hard time finding a ressource on ...
Emma GoldB's user avatar
2 votes
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104 views

Interpretation of ACF and PACF functions

ADF testing showed that the series are I(1) stationary. After taking a first difference, the ACF and PACF looks the following way, which is nothing I have came across in the literature, where mostly ...
Johanna W's user avatar
1 vote
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26 views

How to calculate the PACF of a time series using provided regressions?

I have been provided a table of regressions of an AR(1) model and asked to calculate the PACF. I know that the PACF is the additional information about the process y_t accounting for the previous lags....
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How can I interpret this ACF PACF?

Data I am using is Relative Humidity from 2004-01-01 to 2022-12-01 (day is always 01 as it is a monthly average). I established a linear regression model to find a trend. Used the residuals and ...
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arima model for time series prediction based on the given acf and pacf plots

I have just started learning fitting arima model for time series. So I am not very sure what AR and MA order I should use. May I know what are some possible arima models for the following ACF and PACF ...
lucy's user avatar
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2 votes
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How to test for statistical independence on non-stationary time series?

I have multiple time series on which I want to identify statistically significant (if any) trends. To that end, I started by conducting the Augmented Dickey Fuller (ADF) test to identify which series ...
joaocandre's user avatar
1 vote
1 answer
96 views

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 ...
eork's user avatar
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ACF and PACF vs Ljung Box test

I have a time series with realized sales prices on monthly basis in a large European city which comes as an index and I would like to do 1 period ahead forecasting. I have run ADF and KPSS for unit ...
mbih's user avatar
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1 answer
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ACF and PACF graphs - MA, AR, ARMA, ARIMA?

The data are for areas. How would I interpret these ACF and PACF graphs, and what model could I use? To me, this is a non-stationary series and therefore an ARIMA would be suitable, but I don't know ...
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What do you do when the lags in ACF are on the edge of significance? How would you descibe this ACF and PACF plot?

I have caluclated the first differences of a process and now created an ACF and PACF plot and I honestly don't know how to interpret it. I thought that it is an AR(1) process but I see some ...
user386345's user avatar
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Convert ARMA(p,q) to MA$(\infty)$ and find ACF

$Xt-0.4X_t+0.03X_{t-2}=Zt-0.4Z_{t-1}$ This process is causal and invertible. For the $MA(\infty)$ representation, I wrote it as $X_t=\frac{1-0.4B}{1-0.4B+0.03B^2}Z_t$, where $\psi(B)=\frac{1-0.4B}{1-0....
eddie's user avatar
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How Can One Test for Significance of a Particular Lag of Coefficient of ACF and PACF of Time Series Data Using R

I have this time series data presented in the R code below, I want to test for the significance of the first and second lag of auto-correlation and partial auto-...
Daniel James's user avatar
2 votes
1 answer
298 views

Understanding ACF and PACF plots for model selection for AR(1) vs AR(2)

Good afternoon all, I've got a model that models a time series and I am trying to decide which how the residuals are correlated. The first model, called $m1$ is models $AR(1)$ residuals and the second ...
Warhawk1987's user avatar
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1 answer
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Modelling temperature: seasonality, stationarity, differencing

I have temperature-related time daily time series. I plot the time series and found that the plot have seasonal variations. Thus I differenced the series. When I did Dickey-Fuller test for both ...
soba's user avatar
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Differenced data still showing seasonal pattern in ACF Plot

I was given an oil time series dataset (quarterly). I was trying to build an ARIMA Model in Stata. There is trend and seasonality in the data I am trying to plot acf and pacf plot to determine the ...
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Autocorrelation function of AR(1)-GARCH(1,1) [duplicate]

How can I derive the Autocorrelation function of AR(1)-GARCH(1,1) process which is the combination of AR(1) with GARCH(1,1) process?
Neda Fathi's user avatar
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285 views

Interpreting ACF and Partial ACF Plots with Python

I have time series data which is measured in each 5 second. I am trying to forecast the data. But, ACF and PACF results are seems to different than other plot that I have seen. I am using statsmodels ...
MrsHelios's user avatar
1 vote
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ACF/PACF of my residuals from the cointegration model shows a perfect 1-lag autocorrelation?

I'm performing a cointegration test + OLS regression on 2 assets' prices. If I check the correlogram of the model residuals (training set, but also happens with the test set residuals) it looks like ...
Hiperfly's user avatar
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278 views

Seasonality from ACF

I'm trying to determine whether there is seasonality in some data or not. When I apply the ACF the data doesn't seem to be correlated but, with a 1st order diff, there might be with a lag of 7. Since ...
Kondor Kondorowski's user avatar
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Partial auto-correlation function (PACF)

I wonder how to calculate the partial auto-correlation function of the AR(2) process $Y_t = 0.2 Y_{t−2} + \varepsilon,$ where $\varepsilon_t ∼ \text{N}(0, \sigma^2)$? I found ACF as $\rho_h=0.8\rho_{(...
Neda Fathi's user avatar
1 vote
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Partial autocorrelation significant at regular lag distance

I am trying to forecast inflation with a simple AR model. I took the natural logarithm of the CPI and subtracted the 12th lag, thus obtaining a measure of inflation. The PACF is significant at the ...
Khairon's user avatar
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How to choose model parameters based on ACF and PACF in SARIMA model?

I have some monthly data which show the number of visitors to a country whose plot is given below Since there seems a non-constant variance, I took the log, which stabilized the variance. To remove ...
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How to calculate ACF from PACF?

I have tried to search a lot on Google but could not find any information regarding the relationship between ACF and PACF. Say I have PACF at lag 1, 2, and 3. How could I calculate the ACF for lag 1, ...
mommomonthewind's user avatar
2 votes
1 answer
126 views

Autocovariance of ARMA-GARCH vs. that of pure ARMA

Is the autocovariance of an ARMA-GARCH process the same as that of the ARMA part of that process? If this is too difficult/cumbersome to show, analysis of a special case like MA(1)-GARCH(1,1) or AR(1)-...
Richard Hardy's user avatar

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