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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1answer
155 views

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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1answer
11k views

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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1answer
2k views

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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1answer
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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1answer
19 views

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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3answers
178 views

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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29 views

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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1answer
215 views

One step-ahead forecasts in R

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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11 views

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 ...
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1answer
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 ...
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2answers
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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123 views

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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11 views

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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1answer
22 views

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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1answer
16 views

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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1answer
25 views

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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27 views

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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70 views

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 ...
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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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1answer
72 views

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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14 views

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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1answer
356 views

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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12 views

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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1answer
79 views

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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2answers
2k views

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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2answers
2k views

Multistep prediction interval for ARMA(p,q) process

How do I find an $h$-step prediction interval (forecast interval) for a zero-mean ARMA(p,q) process $$ x_t = \varphi_1 x_{t-1} + \dots + \varphi_p x_{t-p} + \varepsilon_t + \theta_1\varepsilon_{t-1} +...
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1answer
27 views

ARIMA accuracy measures, rolling forecast

Regarding ARIMA model selection and especially accuracy measures several questions came into my mind. To shortly summarize, in my understanding, after necessary transformations/differencing, p and q ...
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1answer
381 views

Derive MA (Moving average) representation of a first-difference-process

I have a non-stationary AR(1)-process. After taking the first difference, how can I derive the MA representation of the resulting „difference process“ Delta_xt? As an example, consider xt = 1.5xt-1 ...
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1answer
41 views

ARIMA: Understanding how time series analysis is focused on mathematical properties as opposed to best forecasts

Rob Hyndman states: "The paper describing the competition [M] (Makridakis et al, 1982) had a profound effect on forecasting research. It caused researchers to: ... treat forecasting as a ...
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1answer
326 views

How to find multicollinearity in SARIMAX model

I am working on Malaria cases vs. Meteorological variables. I want to fit a SARIMAX model using met vars to predict cases. My query is how to find multicollinearity between them (Independent) to ...
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2answers
2k views

Outlier detection in seasonal time series via forecasting with ARIMA model

I am trying to find Outliers in a contextual time series data using ARIMA model. My data contains the Hourly Average Speed and Volume of vehicle traffic for ...
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1answer
32 views

SARIMA without seasonal differencing

I am trying to forecast daily data with (S)ARIMA, having observations for the last 180 days. STL decomposition clearly shows seasonality and ACF plot shows spikes at 7, 14, 21, etc. days so that I ...
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What is the difference between GARCH and ARMA?

I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ? Here is the (G)ARCH(p, q) process $$\sigma_t^2 = \underbrace{ \underbrace{ \...
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2answers
616 views

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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1answer
31 views

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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0answers
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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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1answer
2k views

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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1answer
71 views

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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1answer
439 views

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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1answer
45 views

In ARMA models, Is the withe noise "correlated" with the process?

I know that an ARMA(p, q) refers to the model with p autoregressive terms and q moving-average terms. For example: $$ X_t = c + \varepsilon_t + \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \...
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26 views

Prewhitening before cross-correlation

i have a question concerning cross correlation and prewhitening of two time series. I understand the common procedure to avoid spurious correlation is to model your input series x and filter the ...
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2answers
128 views

What are the downsides of ARIMA models?

I recently worked with ARIMA models and realized how common they are in economics and other sciences. You can find dozens of articles on the Internet that use ARIMA models, but you can find relatively ...
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12 views

Predicting 2 steps ahead with ARMA [duplicate]

How does one forecast 2 steps ahead in an ARMA model? If my training data is $y_1, ..., y_T$, and I have an ARMA(1, 1) model, then I have $$\hat{y}_{T+1} = \alpha*y_T + \beta*(\hat{y}_T-y_T)$$ but ...
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2answers
47 views

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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1answer
65 views

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 ...
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1answer
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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0answers
32 views

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) ...
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2answers
297 views

ARMA model coefficient Interpretation

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 $AR(1)$ ...
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1answer
427 views

General forecasting equation for ARIMA(p,d,q)(P,D,Q)s

what is general forecasting equation for ARIMA(p,d,q)(P,D,Q)s.? I wrote this equation, can someone confirm if it is a correct one? If not, can someone correct it? Thank you in advance! $\overline{...

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