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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How does the R function amira() calculate its residuals?

I am new to time series and I am trying to figure out exactly what does on beyond the scenes in R. Say I have the MA process: $$y_t - \mu = a_t+\theta_1 a_{t-1} + \theta_2 a_{t-2}$$ where $a_t$ are ...
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13 views

On estimating ARIMA models on artificially made time series data

For each day, I observe my variable, y(t), for a period of 12 hours. In order to understand the data and make predictions, I want to put together these data and ...
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1answer
31 views
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9 views

ARIMA versus a Mixed model for trend detection

I am trying to find any evidence of warming in monthly times series data of water temperature over a 21-year period that is serially correlated. Essentially I am looking to determine a global trend, ...
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10 views

auto.arima and DLM give different values for loglikelihood

I want to estimate an ARIMA model on my timeseries, then represent it in state space format, mainly because it will be more responsive to change in pattern. I used ...
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16 views

How ARIMAX model is presented in R

I have a relatively simple problem, but yet taking some time to solve it. I am suing ARIMAX{TSA} function. This is the model ...
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23 views

Why no MAX models?

I'm diving into the field of system identification, black box modeling and forecasting. A lot still has to become clear to me, but one question that came to my mind (and to which the answer might ...
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13 views

Are the data stationary or non-stationary and seasonality?

I want to use Arima model for forecasting wind speed.I plot my data. Then i plot ACF and PACF. I used ADF test and KPSS test and they said that data are stationary and doesnt need differencing but ...
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1answer
74 views

Why can't my (auto.)arima-model forecast my time series?

For testing I generated a very simple time series with a clear recurring pattern. I expected that auto.arima will generate a model, that can forecast that pattern, but óbviously it doesn't. Can anyone ...
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18 views

Constant in arima model whether to include or exclude?

I have a very basic question on including constant in Arima models. I'll illustrate this by an example. I have the following ACF and PACF of a weekly time series that is differenced at lag 1 (trend) ...
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11 views

ARIMA possible with multiple groups?

I’m looking to build an ARIMA model in R to help me predict the number of shots a football player is going to take in a game. I have last season's data to analyse to determine the optimal lags for ...
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28 views

How to analyse transfer function using R? [closed]

I want to learn about using transfer function time series in R. But I don't know how to do it. Anyone know how to do it? Anyone know some references about using transfer function using R?
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1answer
39 views

How to identify the seasonality of a timeseries from the Periodogram?

I need to identify seasonality/ periodicity of a dataset so as to develop an ARMAX model. This is what the original time-series looks like I have plotted the periodogram of the dataset. Ps: I used ...
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17 views

How can I intepret and compare ARIMAs from different data sets?

I have human chromosome data. I have 23 chromosomes that consist of equally spaced windows of 100,000 base pairs with a dependent variable attached. I am treating this like a 1 dimensional spatial ...
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9 views

How to include seasonality in the data ARMAX model that has multiple periodicities?

I am doing regression with ARIMA errors. The residuals are as shown in the figure below. Clearly, the scatter plot shows that this time series has some sort of periodicity or seasonality, but its very ...
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1answer
27 views

comparing ARIMA and AR with external regressor

Consider the following models fitted to the same time series: ARIMA(0,1,1) ARIMA(1,0,0) (that is, AR(1)) with an external regressor Can I use the AIC (or any other information criteria) to decide ...
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1answer
34 views

ARIMA modeling white noise probabilities vs. residual autocorrelation/PACF

I have moderate understanding of statistics and time series analysis. I trying to forecast a weekly time series with lots of outliers and trend shifts. After correcting all of the outliers, I'm left ...
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25 views

Conditional versus Unconditional MLE parameters estimation?

I have read about both conditional and unconditional MLE parameters estimation for ARIMA models but I have problem understanding the concept from the statistical books . Does conditional MLE mean that ...
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1answer
87 views

Multiple ARIMA models fit data well. How to determine order? Correct approach?

I've got two time series (parameters of a model for males and females) and aim to identify an appropriate ARIMA model in order to make forecasts. My time series looks like: The plot and the ACF ...
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1answer
121 views

Understand order of time series

I am trying to build a time series model. I looked at the ACF/PACF and adf test of the series and thought that an ARMA(p,q) model will be suitable for the data. However when I run auto.arima(), it's ...
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1answer
31 views

Does the Dickey-Fuller test for a Random Walk?

Is it valid to say that the Dickey-Fuller test, tests for a random walk? Since the AR(1) process $Y_{t} = \rho Y_{t-1} + e_{t}$ with $\rho = 1$ is the same as the random walk. (Next value is maximum ...
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1answer
87 views

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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13 views

Time Series Modeling: How to get a more stable time series model that captures postive/negative runs?

I am trying to fit a time series to a data set that contains both positive and negative values. A key metric that I need to use to determine the quality of the fit is the distribution of positive and ...
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1answer
86 views

time series - Poor prediction using ARIMA model

I am trying to fit and forecast log returns of a price data using ARIMA model in R. For reproducibility, data is provided here. Steps Followed, Code and Results obtained Check for outliers ...
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1answer
36 views

How to combine multiple time series or linear models?

What would be the best suited method to analyze the following: ...
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12 views

ARIMA Fitting: CSS vs CSS log likelihood

Can someone explain to me: in estimating the parameters for an ARIMA model, what is the advantage of optimizing the CSS log likelihood(pg 2), versus optimizing CSS (pg 3)? Are there any ...
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19 views

forecasting imputed data

My data set consists of a 15 year time series of monthly water quality measurements (10 different measurements). The data set has ~30% missingness. I applied multiple imputation using the Amelia II ...
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38 views

R : arima : plotting regression line of autocorrelated time-series data when d > 0

I'm interested in determining both the slope regression coefficient and plotting regression lines for autocorrelated time-series datasets of rainfall. Specifically, I'd like to identify the best ...
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1answer
34 views

Does ARIMA(0,1,11)4 exist?

I have, without luck, searched to find what an ARIMA model that is differenced once, and have two moving average terms (one at lag 1 and one at lag 4) is called. The equation for what i am asking ...
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2answers
42 views

ARIMA (with xreg) vs GLS

I am fitting both an arima model (with xreg variables) and a gls model to my data in R software. They both have the same ARMA structure and variables. The ARIMA model fits to the data better. Does ...
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21 views

How are the ARIMA forecasted values calculated?

If I have data for 10 days and want to predict the data for the next day based on the previous ones, how does ARIMA find the predicted value? Is it just the average of the last 10 days, or are other ...
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27 views

Data forecasting; which method should I use?

I am interested in predicting the data for a day, based on the data given from the 14 previous days. The data I am working with is the number of subscriptions to a website per day. Each day, the ...
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1answer
36 views

Stationarity in ARIMA modeling

I am working on a problem that I think ARIMA modeling could be useful for, and am researching the theory behind ARIMA. I came across this website that says: ARIMA(p,d,q) forecasting equation: ARIMA ...
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1answer
23 views

comparing arima(1,0,0) model to lm produces very similar ar(1) coefficients and very different intercepts

I'm diving into arima models and was trying to repreduce the results of auto regression. here is a reproducable example: ...
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1answer
31 views

Outlier detection with ARIMA models?

I have several different time series with monthly values for 8 years, where I fit an ARIMA model. And the purpose is to forecast the next year and indicate possible outliers in a fancy way. Is the ...
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0answers
39 views

ARIMA models for mortality modelling (Box-Jenkins methodology)

Fitting the Lee-Carter model of mortality to data provides a time series for the period-related effect, which is subsequently often modelled as an ARIMA(p,d,q) process in order to make forecasts. p,d ...
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2answers
59 views

How to deal with a single Yearly spike with ARIMA?

I have a time series which shows an yearly spike around summer but otherwise is predictable by an AR(1) model. The tests on the data also show that the time series shows stationarity and is ...
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19 views

A comprehension question to conditional heteroscedasticity/GARCH

I have a time series with strong seasonality. At specific time periods/seasons there is also a stronger Variance than in other time periods/seasons. Is that an example of conditional ...
2
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1answer
102 views

ARMA-GARCH model selection / fit evaluation

I'm trying to fit an ARMA-GARCH model to a data set of FTSE 100 log returns (which I've uploaded here). However, I'm not able to find a well-fitting model. Below are the ACF and PACF of the log return ...
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12 views

Can the inclusion of exogenous variables in an ARMAX control for non-stationarity?

I have a non-stationary time series. If I run an OLS regression, the residuals appear non-stationary but serially correlated. Can I then run an ARMAX model on this time series, since the inclusion of ...
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1answer
32 views

Simulate ARIMA Model in R using same starting values as original time series?

I have built an ARIMA model in R with the forecast package's auto.arima() function. I want to simulate the ARIMA model with the same starting values as the original time series. For example, if my ...
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1answer
19 views

Cross-validating the tbats/bats function in forecast

Is there a way to cross validate the tbats/bats function in the forecast package in R? I have been trying to get CV weighted parameters which then I can pass to a function for revised estimates. ...
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1answer
40 views

Forecasting: Turn a basic formula to an ARIMA model

What ARIMA model best represents a formula like this one. $$R_{T_i}=\frac{R_{T_{i-12}}+R_{T_{i-24}}}{2}\times{TREND}$$ I thought that an ...
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1answer
25 views

Forecasting with no seasonality

I have a set of data, let's say average weight of employees, captured every month over a period of 5 years (2010 - 2014). I cannot find a seasonality trend in the data over these years. Also, I have ...
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13 views

Prerequisites for time series and ARIMA

I am working on forecasting sales for 2016. The details of the problem is: 2014 - sales happened only between Jan-Apr 2015 - Sales happened only between Jan-Apr The sales in rest 8 months of the ...
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14 views

Which time series model to use?

Hi I have a large data set of objects, each containing a list of the same attributes. The data is arranged in a time series so that the value for an attribute for an object is indexed by its time. ...
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22 views

linear regression with autoregressive errors ~ARMA(1,0)(2,1)[12]

I am fitting monthly data that are expected to be auto-regressive (streamflow), but I want to include other independent variables (in my case it is a multivariate regression, with about 4 variables). ...
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23 views

Transfer function of pure ARMA time series model

Is it theoretically justifiable to calculate/use the transfer function of a pure ARMA model? I would like to be able to use the transfer function representation to put the state equations into their ...
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1answer
43 views

Modeling Time-Series with a lower bound

I am trying to fit a model to a time series that has a lower bound (at around -150). Using an ARIMA model, running simulations often leads to the time series hitting (and going underneath) this lower ...
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8 views