Questions tagged [box-jenkins]

The Box-Jenkins procedure is used to identify the orders of an ARIMA model to apply to a time series.

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Searching for Clive Granger's 1972 paper on time series decomposition from the Budapest Conference

In 1972 Clive Granger presented a seminal work on the Box-Jenkins Time Series methods as a conference paper: C. W. J. GRANGER, Time Series Modelling and Interpretation, Paper presented to the European ...
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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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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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I’m having issues to make this data Stationary [duplicate]

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 are ...
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How to choose between these 2 Arima models

I have two Arima models with interventions. Both used automatic procedures to find the interventions. The forecasts diverge a lot, mostly because of the drift term in model 1. How can I ...
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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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calculating truncated infinite AR weights in practice for Arima model

I am trying to figure out how to form the truncated infinite AR weights for a general time series process. $(1 - \phi_1 B - \phi_2 B^2 - ... - \phi_p B^p)(1 - B)z_t = (1-\theta_1 B - ... - \theta_q ...
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What is the proper ARIMA model for the data?

I'm doing a project about inflation forecasting. I do the seasonal differencing of the log of CPI (log(cpi)-log(cpi(-)). After that series still exhibit the nonstationary nature, so I need to ...
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136 views

Over-fitting SARIMA model

I am currently running an iterative process(for loop) to determine best ARIMA model for monthly sales data according to smallest AIC and MAPE. Box-Jenkins methodology clearly states to choose the ...
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331 views

Selecting ARIMA orders based on ACF-PACF vs. auto.arima

I use R to fit an ARIMA model to a time series (yearly granularity): ...
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65 views

Is Box-Jenkins approach to time-series prediction and forecasting similar to Unobserved Components models approach?

How I understand the Box-Jenkins Method in a nut-shell is that a time-series model has signals that can be identified by weighting its own past lagged values, or weighting its owned past errors or ...
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Are Box-Cox and differencing redundant or complementary?

I was always under the impression that differencing and Box-Cox were two ways to achieve the same goal: Making a time series stationary so that it can be modeled using an ARMA process. However, ...
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655 views

The theory behind fitting an ARIMAX model

I'm very familiar with the theoretical underpinnings of ARIMA/SARIMA models but I've been struggling to understand the theory behind fitting an ARIMAX model. I'm not looking for a practical ...
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831 views

How to interpret these acf and pacf plots?

I don't know which model to fit to these ACF and PACF. Is it an AR(3) or something else?
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76 views

Why would you introduce a constant in a moving average model, when you already have the option of differencing?

In the online forecasting book of Hyndman (https://otexts.com/fpp2/MA.html) firstly the use of differencing is explained. After that he shows the formula for a moving average model: $$y_t = c + \...
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Parsimony and Box Jenkins

Suppose that you want to estimate volatility of stock returns with the arch/garch family. An important step is to estimate the mean equation. Suppose that you estimated e.g. an ARMA(5,4) model for ...
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Problem of extremly increasing Partial Autocorrelations in time series data

I'm currently trying to make a forecast of the use of prepaid payment instruments using ARIMA modelling in Stata. I have a time series data set, containing monthly oberservations from April 2011 to ...
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207 views

Parsimony in Box -Jenkins model

Book of Enders says: A parsimonious model fits the data well without incorporating any needless coefficients. I am confused with this tradeoff, coefficients ...
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What can cause autocorrelation in higher lag orders of returns?

I am fitting an AR(p) model to the daily time series of S&P500 returns. I have examined AIC/BIC up to 5 lags and both show that model with 2 lags is optimal. However, when I examine the residuals ...
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851 views

I have correlogram ACF and PACF below for a temperature time series. Can I say it is MA(2) from ACF? What about AR?

ACF and PACF for monthly average temperature time series:
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Interpretation of this ACF plot

Currently I am trying to determine whether a sample of monthly returns can be seen as the outcome of a random sample. I plotted the ACF for 20 lags and got the following plot: I am uncertain by the ...
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1answer
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Could somebody help me read these ACF and PACF plots?

So, I have this time series that I have already forecasted using an ARMA model, but I am new to this and am therefore not at all sure whether or not I did this (somewhat) correctly. I got the best ...
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1answer
270 views

Issues on analyzing a time series, ACF and PACF quite the same

I'm attending a econometric course and I'm new to time series analysis. They gave me a time series to analyze and I'm trying to apply all the things I learnt (and understood) to an actual time series. ...
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ARIMA model with splitted data

Question: When analyzing a time series of size $N$ assume that you fit models for data in the intervals $[1,N/2]$, $[N/2+1,N]$, $[1,(2/3)N]$ and $[(2/3)N+1,N]$. Discuss what this approach is for. ...
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ARIMA Analysis (Box Jenkins Method) In R

So I have a time series which I cannot share with you all, but I have a few questions about the proper proceedings to fit the correct ARIMA model for my data. I have successfully written a loop to ...
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ACF and PACF in Box Jenkins

guys! I know this might be a silly question, but I am really curios if my interpretation is correct. I have some stock returns and try to fit and ARMA model I took the log difference and I want now ...
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498 views

auto.arima() fits a different model than ACF/PACF plots suggest

I have a data set that is transformed to stationarity and I'm trying to fit it to an ARIMA model. I found that variance is lowest when the transformed set is differenced to 1, and here are my ACF and ...
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Building an ARIMA model using ACF, PACF, etc

I wish to better understand the details of ARIMA models and how to interpret ACF and PACF graphs in determining what type of ARIMA model to use. From my studies so far, I understand that there are ...
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117 views

Check the stationarity of a time series [duplicate]

I've a time series, 100 observations. I'm following the the Box-Jenkins method in order to find a model that fit the data. My questions (I'm a bit confused): if I plot in a graph time vs observation ...
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696 views

ARIMA Box-Jenkins analysis with no significant ACF/PACF lags

I am analysing the stock index returns data for few countries. From observation of the ACF and PACF there seem to be no significant peaks at any lags. However, applying the auto.arima function from ...
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1answer
594 views

What is the ARIMA model for this data?

I have made my series stationary by using one difference and have plotted the following acf & pacf: So I have decided to test the following models: • ARIMA(0,1,1) since the acf cuts off after ...
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Box-Jenkins to prove model

Suppose the $X_t$ satisfies: $$\phi_1 (B) X_t = \theta_1 (B) Z_t, \tag{$*$}$$ where $\{Z_t\},$ $WN(0, \sigma_Z^2)$ and $\phi_1 (\cdot)$ and $\theta_1 (\cdot)$ are polynomials of order $p_1$ and $q_1$...
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Fitting a Multivariate ARIMA Model (in R) [closed]

I've been working on a high school project attempting to determine whether or not there exists a relationship (and if it exists, information on the strength and duration of the relationship) between ...
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763 views

Find state space model to compare with Box-Jenkins ARIMA model

I asked a question here about how to get predictions for the random-walk component of an ARIMA model. Are there time series models in the state-space framework that might be suitable for the kind of ...
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Determining order of ARIMA model using Box-Jenkins. Correct approach / argumentation?

I obtained a couple of time series from estimating my (mortality-)model which I now aim to forecast with an appropriate ARIMA(p,d,q) model, which should be chosen with the use of the Box-Jenkins ...
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Box-Jenkins Forecasting With ARIMA(p,d,q) models

I want to check that I understand the general theme of forecasting with ARIMA models using box-jenkins, so I am going to take an example and then proceed from there. We will use $B$ notation for the ...
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ARIMA Specification from Correlogram

How should I determine the data generating process from the correlogram below? This is non-seasonally adjusted monthly data that has been 1st differenced. I am trying to conduct univariate time ...
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Review of Box-Jenkins methodology

i just finished developing an ARMAX model with python (mostly statsmodels) in order to forecast some data. My next step is to test the data (24 time series) with the given ARMAX model. As i need to ...
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What exactly is the Box-Jenkins method for ARIMA processes?

The Wikipedia page says that Box-Jenkins is a method of fitting an ARIMA model to a time series. Now, if I want to fit an ARIMA model to a time series, I will open up SAS, call ...
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Determining parameters (p, d, q) for ARIMA modeling

I am fairly new to statistics and R. I would like to know the process to determine the ARIMA parameters for my dataset. Can you help me figure out the same using R and theoretically (if possible)? ...
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2k views

Determining the order of a Box-Jenkins modeling process

I have a problem on what model class (AR, MA, ARMA, ARIMA, etc.) will I use on my data, i.e., what order (say 1,0,1) will I use, using a Box-Jenkins procedure. I have already done many ...
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ARIMA estimation by hand

I'm trying to understand how the parameters are estimated in ARIMA modeling/Box Jenkins (BJ). Unfortunately none of the books that I have encountered describes the estimation procedure such as Log-...
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What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?

What are the assumptions of ARIMA/Box-Jenkins modeling for forecasting time series?
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Is ARMA model possible for series with non significant ACF/PACF?

I am playing around with SP500 data from the MASS package. From observation of the ACF and PACF there seem to be no significant autocorrelation. Now I want to model ...
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1answer
391 views

Is this explanation of the Box-Jenkins approach correct?

Can someone please tell me what they think of my explanation of the Box-Jenkins approach to modeling time series? Do you have anything to add (in particular to my explanation as to the intuition ...
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Relation and difference between time series and regression?

What are relation and difference between time series and regression? For models and assumptions, is it correct that the regression models assume independence between the output variables for ...
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Poisson regression with (auto-correlated) time series

I have a time series dataset which shows, for each day, the number of complaints received by an organization about a particular problem. I also have a number of other time series for the same period (...
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How can I check if my time series data is zero mean, stationary and independent identically distributed?

I have time series data which is international monthly tourist arrival to Malaysia (N=264). My objective is to forecast tourist arrival for 6 months ahead. After analyzing my data pattern, I found ...
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21k views

Moving-average model error terms

This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values $Y$ against previous error terms $e_t,..., e_{t-n}$. That is, the ...