# 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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### ACF and PACF Plot

I am a first year stat student. We are tasked to create a SARIMA model from trial and error using ACF and PACF plot. Now here is my generated plot: Now I am trying to understand the plot but I don't ...
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### How to select a time series model based on this ACF?

I think that I am missing some concepts because I am not able to model adequately this series. It is a times series over 12 years. I tried with multiple AR and MA models, nevertheless, I can't model ...
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### Conflicting ACF/PACF after first-difference

I have yearly data. When I do a Dickey-Fuller test it gives me insignificant results, indicating that the series are non-stationary. After differencing them the DFT tells me they are now significant ...
1 vote
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### Slowly decaying ACF plot = indicative of trend or AR(1) process?

I am required to interpret a suitable ARIMA model for the above ACF and PACF plot. My first instinct from the slowly decaying ACF plot and the sharp drop after lag 1 of the PACF tells me this is an AR(...
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### Stationary time series having unusual ACF and PACF plots

I'm analysing a highly stationary time series and while plotting ACF and PACF I noticed a strange bump at a later lag very close to the 0.5 threshold level. Does it affect the AR degree=2 and AM ...
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### p/q/d from ACF and PACF

I'm new to time series. I am still not able to read ACF and PACF plot to determine p, q or d. The series is now stationary as confirmed by ADF and KPSS test after logarithm transformation to reach ...
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### Need help interpreting ACF and PACF plots for ARIMA

Based on my understanding, we can identify the order of an AR process based on where there is a drop in the PACF and for the MA process it is when there is a drop in the ACF. Both these two graphs are ...
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1 vote
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### Unsure If I should do a seasonal difference in my dataset

I'm doing my final project for my bachelor's on Time Series, I'm using a dataset for precipitation for São Paulo City here in Brazil. My goal is to divide the dataset into training and testing and ...
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### What to do with time series model, if residuals are autocorrelated for a certain lag?

I'm doing a time series forecast (with hourly data), and after plotting the autocorrelation of the residuals, I get a bigger value for every 24th lag (the pikes in the picture). I tried to include the ...
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### decompose function show a seasonal graph but there is no correlation in the correlation plot past lag 12 for a monthly dataset. What does it mean?

I generated a TS out of a monthly data. TQ_volume_ts <- ts(csv_file[4:39,"Volume"], start=c(2019,01), frequency = 12) When i apply the decompose function I get the following result: Now ...
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### What do my first difference ACF/PACF show me? Is it white noise process?

I am quite new to econometrics, so not sure how to intepret the following acf/pacf function on log financial time series after first differencing; The level data showed a AR(1) process, how would I ...
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### The correct pre-processing of time-series data when using LSTM

I have a time-series data that I would like to use for forecasting the data trend using LSTM. I followed https://towardsdatascience.com/the-complete-guide-to-time-series-analysis-and-forecasting-...
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### Stationary time series and ARMA process

Based on the shown tests ADF, ACF and PACF is the differenced time series stationary and could it be characterized by an ARMA process? Thanks!
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### Different Colours for the test for Autocorrelation Time Series

I have been doing a project on Time Series data and one of the items was to test for AutoCorrelation and found the charts in a different color than what I expected. I also don't see the shaded part ...
1 vote
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### What AR and MA values should I choose from my ACF, PACF plots

I have plotted ACF and PACF plots for my data, as I am trying to justify my hyperparameters chosen for my ARIMA model. The data is energy prices every day, with data taken every 30 minutes (48 points ...
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### Which criteria should I use to evaluate a time series for stationarity?

I have been given two criteria to evaluate the stationarity of a time series: A stationary series will have no sample acf (SAC) or sample pacf (SPAC) values outside of confidence bounds on the chart. ...
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### How to fix the issue of the correlogram value being outside the 95% CI?

I am working on predicting the quarterly population of Ontario. After fitting the model using SARIMA, I get the following model diagnostics results: With regard to the correlogram, how do I fix the ...
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1 vote
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### ACF and volatility clustering

Can someone explain me the interpretation of volatility clustering from ACF of the absolute returns? I got two graphs of ACF of the absolute returns (first one for daily returns, second one for weekly ...
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### Does autocorrelation means harmonic analysis?

They have very different algorithms, the first easier I'd say. Autocorellation shows no significant lag. while the periodogram shows an entirely different story at "lag" 11. So which shall ...
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### Create a time series with a known autocorrelation in R

I would like to create a time series in R that is going to have a known auto correlation. I tried creating two correlated variables and then parsing the time series (as shown below) but when i run <...
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### Why does autocorrelation function for trend in data decrease with increasing lag?

Forecasting: Principles and Practice, 3rd edition by Hyndman and Athanasopoulos states in section 2.8, Autocorrelation that, for trend in data the autocorrelation function has positive values that ...
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### Why is the difference between 2 time series drawn from the same process not White Noise?

I take the difference between 2 time series (each with 200,000 observations) drawn from the same ARMA(2,1) process and find that (at least the first 1000 observations of) this difference looks like ...
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### How to check assumptions of an AR(1) process

My question is, if a model allows the errors to follow an AR(1) process, how to check for the model adequacy? Can we use ACF and PACF plots?
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### How to detect an AR(1) process of residuals from a correlogram?

I am estimating a dynamic factor model which allows the errors to follow an AR(1) process. Thus, an approximate dynamic factor model. So for residual diagnostics I plotted the correlogram of residuals....
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### Impact of residuals on forecast

I'm working with ARMA models right now and I was wondering about the following case: If we have late significant lags in the residuals ACF and the rest of the earlier residual lags weren't significant,...
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### Why I cannot find suitable ARIMA model for the dataset?

I have a monthly dataset. I applied ADF test and saw that this dataset is stationary. Also, Canova-Hansen test is applied to see if there is stochastic or deterministic seasonality. As you see below ...
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### How to properly select AR, MA, or ARMA structure for time series data?

I am attempting to model seasonal and diel changes in fish depth over time. Previous work has used ARMA correlation structures, which makes sense logically. I have processed my data to weekly means of ...
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### Autoregressive Timeseries (AR-1) and interpretation of autocorrelation plots

My understanding is as follows: ACF-Plot: AR-k model shows highest correlation at lag k PACF-Plot: PACF to only describe the direct relationship between an observation and its lag, so that there would ...
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### Strange and very low results in Ljung-Box test

I have been reading some posts about the Ljung-Box test and I am applying it to some of my databases. However, I am not really understanding the outputs, I think I am doing something wrong. I have a ...
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### Detecting autocorrelation of residuals using ACF and PACF plots

How to identify autocorrelation of residuals in the fitted VAR model. I have provided the ACF and PACF plots below. There are some significant lags in the PACF plot. Does it mean that my model has ...
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1 vote
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### PACF-like plot but between x and y, and not y and y?

I’m interested in generating a PACF-like plot but between two separate time series x and y, with significance levels included. Just as the PACF tells us the best lagged predictors of y using lagged ...
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### Finding the $k^{th}$ partial autocorrelation of 100 observations

So, to find $\alpha_{kk}$, do I use the following? And would the order for the ARIMA underlying model be (2,0,0)?
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### Is my data set stationary

Here is what I obtain when I plot my data set in R. I am now wondering whether this data set is stationary or not. I'm assuming it is stationary since it has no visible trends or seasonality. However, ...
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### Interpreting ACF and PACF for data which have had its seasonality removed

I'm currently working on a project and trying to figure out how to interpret my ACF and PACF plots. I have removed seasonality from the data in order to establish the trend, now when plotting my ACF ...
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### PACF on Smooth Time Series

I have generated a heatmap of sorts from events occurring on certain dates. This heatmap is made as a Gaussian mixture with a fixed standard deviation of 50 days for each event. The heatmap looks like ...
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### How to select P and Q in ARIMA

I am new to using ARIMA and I would like to know how to determine the p, q values of ARIMA by PCF and PACF. Here is the raw data figure. The raw data is a human glucose data collected.The blue data is ...
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### Identification Problem of SARIMA

I am trying to make time series analysis with SARIMA and I have a question. My dataset is a seasonal dataset. I validated that I have stationary series by KPSS test. I also found the following ...
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### Interpreting Autocorrelation plots in R

I am trying to interpret the following plots I got in R using the checkresiduals() function. The first plot is the model I am replicating without any correction for autocorrelation, while the second ...
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### Sales forecasting. What model to choose and how to interpret ACF/PACF?

I have the following raw sales timeseries: Clearly it's not stationary since it does have somewhat of an increasing trend (non-stationarity also verified by DF-test). By differencing I obtain the ...
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### How to interpret ACF/PACF plots with no recent lag correlations?

I have a time-series data that looks like this: There is obviously an upward trend in this data, so I do differencing with lag of 1, i.e., Series = Y(t) - Y(t-1) The differenced series looks as ...
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### Showing that pacf of an AR(2) process is $0$ for $h > 2$

I am trying to complete this exercise An AR(2) process has $\rho(1) = 0.75$, $\rho(2) = 0.475$ and $\rho(3) = 0.275$. Calculate its pacf for every $h$. I have no problem computing $\phi_{11}$ and \$\...
1 vote
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### Should we consider MA(7)? How to interpret the ACF and pACF here?

Getting very confused by these two plots. Can one from first ACF plot conclude that this is MA(7)? But why does the ...
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### You are given PACF for a stationary process: φ11 = −0.60, φ22 = 0.36, φkk = 0 for k ≥ 3. What time series model could have this PACF?

You are given PACF for a stationary process: φ11 = −0.60, φ22 = 0.36, φkk = 0 for k ≥ 3. What time series model could have this PACF? Identify model’s coefficients and write model equation. I am very ...
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### Does my ACF and PACF suggest no random noise?

I have 77 observations in my time series data which I obtained from the tsdl library in R. I have also reduced the time window. The data is quarterly average earnings. ...
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### Potential issue in partial autocorrelation in smoothed data using centered moving average in R

I'm new to time series analysis. I finds that if the data is smoothed by centered-moving average, its ACF will becomes significant(which is understandable), while its PACF will have peak at the lag ...
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### ACF plot of differenced and transformed data

I am analysing time series data from the tsdl packages (specifically data number 94), my target time series is the time series named "real". I have shortened the time from to 1956 to 1975. <...
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### Is my time series exhibiting stationarity?

I'm a beginner in time series analysis so I'm uncertain whether or not this data is stationary according to the ACF plot; I can observe a fast decay but on the other hand, a lot of the lines exceed -0....
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### AR and MA terms for a highly irregular time-series?

I have been fussing over the ACF and PACF plots with 1 order of differencing (passed the ADF test) but I haven't found any information that deals with ACF and PACF plots that have lags as large as ...
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