Statistical Analysis Stack Exchange
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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.

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. Typically, ACF and PACF are plotted and the plots are inspected visually, but numerical summaries are also used.

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Estimate ARMA coefficients through ACF and PACF inspection

How do you estimate the appropriate forecast model for a time series by visual inspection of the ACF and PACF plots? Which one (i.e., ACF or PACF) tells the AR or the MA (or do they both)? Which part of the graphs tell you the seasonal and…
4everlearning
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ACF and PACF of residuals to determine ARIMA model

I'm having trouble interpreting an ACF/PACF plot of the residuals of a regression to determine what the corresponding ARIMA model would be for the error term. This is the plot of the ACF/PACF of the regression. Since the ACF trails off at a lag of 4…
Benjamin Krause
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How to interpret ACF and PACF plots

I just want to check that I am interpreting the ACF and PACF plots correctly: The data corresponds to the errors generated between the actual data points and the estimates generated using an AR(1) model. I've looked at the answer here: Estimate…
Baz
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ACF and PACF plot analysis

I am new to ARIMA, and I am trying to understand these lag plots. Are the following ACF and PACF suggesting that the lag of my time series is 4? If I am wrong, please help me understand these plots.
Stephen Saidani
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What to do if time series are non-stationary?

Data: I have a time series data of 2528 daily observations for OMXS.30 (Stokholm) closing price. The aim is to fit proper ARCH/GARCH models and use for forecast daily Value at Risk. Here is a plot of my data, and the daily log returns. By looking…
gabobo
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Procedure for fitting an ARMA/GARCH Model

I want to try fitting an ARMA/GARCH model but want a methodological approach rather than fitting different models and picking the best one. However, I'm not sure how to choose my AR and MA terms for my mean equation, same thing for my variance…
ankc
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Exponential decay of ACF of AR(p) process

I was wondering why I always read that the decay of the ACF of an AR(p) process should be exponential. I am confused because the theoretical ACF of a stationary AR(1) process $y_{t} = \phi y_{t-1} + \epsilon_{t}$, $\mid\phi\mid < 1$ is $\phi^{h}$…
corianne1234
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Autocorrelation in Poisson model's residuals - Is my model not specified correctly?

I am fitting a poisson regression model in R to count time series data to perform an Interrupted Time Series Analysis, the aim of my analysis is to see if an intervention affected the counts. I am basing my analysis on this tutorial:…
Undergraduate413
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Autocorrelation of an AR(1) process

I am learning about this AR process. According to the book I'm reading, the autocorrelatio function of a stationary process: $$y_t = c + \phi y_{t-1} + \varepsilon_t, \quad \quad |\phi|< 1$$ is as follows: $\rho(h)= \frac{\gamma(h)}{\gamma(0)} =…
Fam
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Why is the ACF diagram showing seasonal patterns when they should have been removed by `decompose`?

I'm reading the book Introductory Time Series with R where the following code is given: > data(AirPassengers) > AP <- AirPassengers > AP.decom <- decompose(AP, "multiplicative") > acf(AP.decom$random[7:138]) A screenshot of the ACF diagram…
Chris Snow
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Ljung-Box always significant for ARIMA models - what now?

Sorry in advance if this is too basic of a question - I've been struggling with this data set for almost a month and feel like I'm going in circles, and the more I Google the more confused I get. I have a time series of hourly activity levels (mean…
sitka
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How to calculate the ACF and PACF for time series

I just started with time series analysis and I would like to know whether there is a formular for calculating the autocorrelation function (ACF) and the partial autocorrelation function (PACF) for time series data. While there are forumlars for…
PeterBe
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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 is equivalent to $Y_t =…
David Waterworth
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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 0.05). Link to dataset:…
Jess
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ACF vs PACF in ARIMA

Given a time series problem, Should ACF and PACF be done before or after differencing that make the time series stationary? If ACF and PACF has shown different results, should the number of orders of AR/MA follows ACF or PACF?
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