Questions tagged [arima]

Refers to the AutoRegressive Integrated Moving Average model used in time series modeling both for data description and for forecasting. This model generalizes the ARMA model by including a term for differencing, which is useful for removing trends and handling some types of non-stationarity.

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Why the seasonality of daily time series is not predicted correctly in R with arima model?

I have a question related to the estimation of arima models in R. I have estimated a model with daily simulated data where Mondays have a lower value than the rest of the days. I have simulated two ...
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Do I have to add the seasonal effect and trend back to ARIMA forecast?

I'm a newbie in Time Series Analyses. I'm using ARIMA to make a prediction about my monthly data. So sorry that I cannot post my data here, you can just dump the ...
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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 ...
249 views

ARIMAX - predict

I have the monthly number of patients in a psychiatric facility from Jan 2010 to Dec 2018 - the data shows a seasonal pattern. I want to forecast the number of patients in the facility from Jan 2019 ...
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Interpreting why a VAR produces lower error than VARMA?

I trained various VARMA models on the same dataset consisting of different number of AR and MA terms, from $VARMA(0,1)$ and $VARMA(1,0)$ to $VARMA(6,6)$ and all the combinations in-between. After ...
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How do I restrict coefficient values to ensure stationarity and invertibility of ARMA(p,q)?

I am trying to simulate an ARMA series but I am concerned about it being conformed to ensure invertibility of $\text{ARMA}(p,q)$ in addition to stationarity. I know of the following conditions for MA ...
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SARIMA(1,1,1)(0,1,1)7 Math Formula

Would the correct mathematical way to write a SARIMA(1,1,1)(0,1,1)7 Model be: $$(1-\Phi_1B)(1-B)(1-B^7)y_t= (1+\Theta_1B)(1+\Theta_1B^7)\varepsilon_t$$ I am new to the ARIMA world and I am trying to ...
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I would like to compare one-step ahead forecasts on a given time series for ARIMA and UCM (using KFAS library). I have split my time series in train and validation, that I will use to understand which ...
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Implications of using an ARIMA model with non-significant coefficients

I am a beginner with time series analysis, and I got confused when I encountered an ARIMA model with a non-significant coefficient. I have my time-series data that is log-transformed and differenced ...
565 views

ARIMA(1,1,1) Model - Forecast

How does one write the mathematical equation for the ARIMA(1,1,1) model with the estimated coefficients below and use the ARIMA(1,1,1) model and time series points below to produce a forecast value ...
689 views

Alternative construction of ARMA(1,1) process

My question is related to the exercise 2.9, p. 79 in Brockwell & Davis, An Introduction to Time Series Analysis and Forecasting, 2nd edition, New-York, Springer, 2002 (It is also related to ...
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Prediction intervals from Linear regression and Arima for DYNAMIC forecasting

I am comparing prediction intervals from linear regression and ARIMA for a simple AR(1) model: p = lag(p) The models were built on monthly data from 2003-2013 years. Predictions were made for 2014 ...
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Backcast time series using Python [closed]

I have time-series data from 2016 to 2021, how could I backcast to get the data from 2010 to 2015 using ARIMA in Python? Could you guys give me some sample Python code? Thank you very much
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1 step ahead timeseries prediction with ARIMA python [closed]

I want to train my arima model on my training set and then use in-sample prediction to predict the values of my testing set. Here is what I do : ...
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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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Time Series Forecasting with Different Time Horizon for Comparing Models?

At the moment I am dealing with a time series problem. The data I have is about 6 years and in daily frequency. I want to try out different models on the data and I came up with an experiment: ...
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Is the sum (in some sense) of ARMA processes an ARMA process?

Given an ARMA(1,1) process $$X_t = \phi X_{t-1} + \varepsilon_t + \theta \varepsilon_{t-1},\quad \varepsilon_t \sim WN(0,\sigma^2)$$ Let $N \sim Po(\lambda)$ a poisson random variable. Consider the ...
26 views

non gaussian residual distribution for ARIMA

I have a few theoretical and practical questions regarding residual distribution of ARIMA models. I made quite a few for various purposes and I don't think I ever found gaussian distributed residuals. ...
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Is the third moment of an AR(1) dependent on $t$?

Given an AR(1) process: $$X_t = \phi X_{t-1}+ \epsilon_t, \quad \epsilon\sim WN(0, \sigma^2)$$ I know that if $|\phi|<1$, then the process is stationary (weakly). Thus, the first and second ...
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How to predict monthly data from quarterly seasonal data?

I have a dataset that contains the price of a vegetable for each quarter-end day since 2000-01-01. Now I want to get(predict) the monthly values of the month-end prices. I am not a student of stat, by ...
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Issue with forecasting a time series that is a white noise using ARMA

I am working on stock prices and stock returns and I'm supposed to do some forecast on these data. The stock prices series is not stationary and even if the stock returns series is, it is a white ...
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Formulation of ARIMA(1,1,1) as markov process by extended state space [duplicate]

my question is: How can I formulate ARIMA(1,1,1) as Markov Process by extended state space? i.e. if $$s_t = \mu + \sum_{i=1}^p\beta_i s_{t-i} + \varepsilon_t$$ Define$$S_t = (s_t,\ldots,s_{t-p+1})$$ ...
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Types of noise processes and the one assumed in arima() estimation in R

Here is a time series class defining white noise incorrectly as an independent sequence of random variables. source Aside from the widespread mix-up of White noise and iid noise, a further ...
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How to make $h$-step interval forecasts from an ARMA-GARCH model?

I recently wrote various Python functions to fit ARMA models and make forecasts from them. I am now trying to do the same for ARMA-GARCH models. To make $h$-step forecasts from ARMA models, I used ...
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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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Detecting MA order - ARMA Modelling

I have the following problem of detecting the MA order in usage of the ACF plot. Note: The process is stationary and the lags display monthly data. I am not really able to say which order suits the ...
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Exogenous variable having opposite effect on forecasted values in SARIMAX model

I'm modeling how many plays are made on arcade machines at a store, using the number of active machines as an exogenous variable. I'm forecasting the number of plays into the future while keeping the ...
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Determine paramaters for SARIMA model

I have the following timeseries with a frequency of 12 (months). Since there is both a trend and seasonality, I differenced the timeseries. To determine the parameters p, q, P and Q for the SARIMA(p, ...
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Calculate $E [ Z_{t-1}| X_{t-1}]$ in an ARMA process

Suppose I have an ARMA(1,1) model: $$X_t = \phi X_{t-1} + Z_t + \theta Z_{t-1}, \quad Z_t \sim WN(0,\sigma^2)$$ Indeed, I want calculate $E[X_t | X_{t-1}]$. For this: \begin{align} E[X_t | X_{t-1}] &...
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SARIMAX doesn't fit the model

I used this tutorial to find optimal coefficients for my ARIMA model and still it pretty bad (see picture). How can I improve it? ...
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How to deal with negative forecast values in time series forecasting?

Data - Monthly Rainfall of a region for the past 20 years Objective - To Forecast for the next 2 years I have used a SARIMA model and predictions have been done using R. but one of the forecast value ...
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Do Time Series Models fall under GLM?

I have the following question: Can Time Series Models (e.g. ARMA, GARCH) be considered as GLM's? For example, below is the standard form of a GLM: At first glance, Time Series Models have some ...
656 views

ARIMA generation of a time series

I'm trying to understand the ARIMA process by generating a sequence manually, then fitting an ARIMA model from statsmodel.tsa to check my results I've found an example there (not in english but doesn'...
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Is non-invertibility a problem for (AR)MA processes?

I'm reading Time Series Analysis: Forecasting and Control (3rd ed.) by Box, Jenkins and Reinsel. There are some arguments about invertibility that I can't wrap my head around. Considering a MA(1) ...
How do I interpret the phi and theta in the $SARIMA$ model? I know that they are both parameters of the model, but I am having a hard time trying to interpret them. For example, the phi in the $AR(1)$ ...