# Tagged Questions

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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### Does ARIMA require normally distributed errors or normally distributed input data?

I have two questions related to time series forecasting with ARIMA: Does ARIMA require normally distributed errors or normally distributed input data ? Are there any assumptions on input time series ...
285 views

### What are disadvantages of state-space models and Kalman Filter for time-series modelling?

Given all good properties of state-space models and KF, I wonder - what are disadvantages of state-space modelling and using Kalman Filter (or EKF, UKF or particle filter) for estimation? Over let's ...
12 views

### How to extract bootstrap forecasts from forecast.Arima in the R package forecast?

In a forecasting context, I have two different time series: y = {y1, y2, .., yn} and z = {z1, z2, ..., zn}. In R, let's say that the two series are as follows: y <- arima.sim(list(order = ...
39 views

### Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf? [on hold]

** What is the "order of difference" to achieve stationary? what is the "lag" value? what does [12 ] in ...
71 views

### ARIMA vs ARMA on the differenced series

In R (2.15.2) I fitted once an ARIMA(3,1,3) on a time series and once an ARMA(3,3) on the once differenced timeseries. The fitted parameters differ, which I attributed to the fitting method in ARIMA. ...
60 views

### ARIMA Representation using polynomial long division

I have 2 questions from Tsay's book, dealing with ARIMA representation. I. How does the division of the polynomial work - what are the steps that lead to the solution they show? They show a "simple" ...
173 views

### ARIMA with seasonality in Statsmodels

I'd like to have a seasonal ARIMA model implemented with Statsmodels ARIMA. Specifically, I'd like to log before the weekly seasonality and then be able to make forecasts. Perhaps an example with ...
32 views

### What are some examples of real-world processes that are well-described by AR, MA, ARMA, or ARIMA?

Subject says it all - AR/MA/ARMA/ARIMA are often described as workhorses of time series analysis. But what are some real-world examples where these methods gave great results, and another more modern ...
75 views

### Auto-Regressional & Moving Average Model Formula Properties

I seeking help in understanding specific values underlying the formula's for the MA(p) model & the AR(q) model. I am attempting to implement the models (building up to the combined ARIMA model) in ...
123 views

### 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 ...
363 views

### Performance evaluation of auto.arima in R and UCM on one dataset

I started evaluating and comparing some methods in forecasting. I used Price of dozen eggs in US, 1900–1993, in constant dollars in the R software FMA package. I held out the last 10 years for ...
171 views

### How do I write a mathematical equation for ARIMA (2,1,0) x (0,2,2) period 12

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (2,1,0) x (0,2,2) period 12. I'm a little confused with how to go about this. I would prefer an ...
68 views

### Transfer functions in R (TSA package)

In Time Series models’ transfer functions there is a decay parameter in the formula (let’s call it b). In TSA package that decay parameter is not mentioned. When I used other software before (such as ...
16 views

### Trying to Refine SARIMA models

I have a SARIMA forecast from statewide Real Estate Sales data.. but I'm not happy with it. The SARIMA parameters are confusing to say the least. I am finding that the current model is not ...
29 views

### ARIMAX order stock price predictions

I am implementing the ARIMAX model for stock price predictions. To select the order, I looped through 0<=p,d,q<=10 and found the best order to be (1,0,10). I'm a bit confused how to interpret ...
11 views

### ARIMAX feature selection

I am implementing the ARIMAX model and need to implement feature selection. I have >100 features and a lot of data, so I need a method that isn't too computationally expensive. I tried a wrapper, ...
54 views

### How can I form ARIMA equation given MA and AR terms

Above is output from SAS. What would be the corresponding ARIMAX equation? I would appreciate if someone could help me write the mathematical equation, preferably in the following form:  Y(t)= ...
22 views

### ARIMA model sensitivity

Just wondering if a model was sensitive to the overall assumptions made when building the ARIMA model, what would be the impact on the model if any of these assumptions were violated?
23 views

### Does this model make any sense?

I have fitted data of user activity per day to an arima(1,0,1)x(1,0,0). It's a nice fit. But does it make any sense?
169 views

### SARIMA estimation

I am trying to manually estimate the non-seasonal components of an SARIMA (p,d,q)x(P,D,Q)[s]. I thought the estimation is going the same way like in ARIMA, but the output says somehow something ...
23 views

### Feature Selection ARIMAX

I am trying to implement the ARIMAX model. I have a lot of exogenous features and I have no clue which ones are important in predicting my endogenous variable. Does ARIMAX have some sort of native ...
55 views

### ARIMA continuous forecasting

I am learning about the ARIMA model and trying to implement it and had some questions. From my understanding, ARIMA forecasts better for short-term projections rather than long-term projections (is ...
381 views

### ARIMA model fitting and forecasting implementation

I am new to time series modelling and I am trying to build a simple time series model using ARIMA methodology and forecast. I could write an R program to do the same, but I am more interested in ...
29 views

### Weighting time series coefficients using model's likelihood

I have a question regarding to time series forecasting. In particular I've been working with a Bayesian approach, but I think the question is independent from that. I have several time series which ...
47 views

### ARIMA unusual forecasts

I am trying to implement the ARIMA model using statsmodels. I get really unusual results for my predictions, and was hoping for advice on fixing this. ...
99 views

### Why does differencing time-series introduce negative autocorrelation

For example, this mentioned here: link. I also saw this in my data. I wonder - does anyone know a good reference where this is explained and justified more rigorously with some math and for some ...
46 views

### Control charts of seasonal data

I have been asked to develop control charts for my company - or some other means of quickly identifying when ticket sales are "out of control" and not just a random blip. The data we are looking at ...
52 views

### How can I replicate R forecasts for seasonal ARIMA?

I have obtained the following estimations and forecasts in R for a seasonal ARIMA(1, 0, 1)(1, 0, 1)[7] model1 Series: PO ARIMA(1,0,1)(1,0,1)[7] with zero mean Coefficients: ...
43 views

### Time series for network matrices?

Let's say I have two people. Each of whom I create a network matrix for daily for some of their daily habits $(i.e. A, B, C, D)$. I do this for, let's say $60$ days. I didn't bother to change the ...
1k views

### What are the values p, d, q, in ARIMA?

In the arima function in R, what does order(1, 0, 12) mean? What are the values that can be assigned to ...
122 views

### What are the assumptions of ARIMA modeling for forecasting time series?

What are the assumptions of ARIMA / Box-Jenkins modeling for forecasting time series?
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### How to apply an AR(MA) model to a prewhitened signal?

I have two (vehicle velocity) signals that should consist of similar "latent" drivers, but have different autocorrelation structures. The driver-signals are quite nasty statistically, so I'm not ...
70 views

### Predicting a baseline response using ARIMA forecasts

I have a modelling dilemma. I am creating a model that attempts to predict demand (leads not sales) based upon the correlation to advertising spend. We know that without advertising spend, demand is ...
71 views

### Estimate single ARIMA for multiple timeseries

I have two groups of time-series, each group represents one type of data. However within each group, each time series may be fitted with a different ARIMA(p,d,q) from the other time series in the same ...
2k views

### Problem with ARIMA in Minitab

I have made non-stationary data stationary by differencing at lag 1 and then differencing the differences at lag 11. The data values for months 1/06 through 6/11 are in an Excel file at ...
940 views

### Ljung-Box Statistics for ARIMA residuals in R: confusing test results

I have a time series I am trying to forecast, for which I have used the seasonal ARIMA(0,0,0)(0,1,0)[12] model (=fit2). It is different from what R suggested with auto.arima (R calculated ...
79 views

### Moving average ARIMA error term

Lets say that I have a time series data $Y_{t}$. I'm trying to forecast using am moving average MA(1) model using Box Jenkins methodology. The following is the equation for an MA(1) obtained from a ...
149 views

### Extract BIC and AICc from arima() object

Problem: I would like to extract the BIC and AICc from an arima() object in R. Background: The arima() function produces an output of results, which includes the estimated coefficients, standard ...
185 views

### Pandas Statsmodels Time series seasonal forecasting

Using Stats models and Pandas (and requests for the data) I'm working on a forecast model.. my 1st step is just getting the Arma function working and understood. My data is available publically and is ...
103 views

### Generating IMA(1,1) series

I'd like to generate a series that follows an IMA(1,1) process, where $θ$ is the moving average parameter. I generated the series based on different representations and I got different results, I'm ...
140 views

### How to remove seasonality from daily electricity demand

I want to remove seasonality from daily electricity demand (a time series). My understanding is there is weekly (high demand on Tue, Wed, and low demand on Sat, Sun) and annual seasonality (high ...
81 views

### What is the minimum historical data/sample data required for a time series forecasting analysis?

Are there any statistical power analysis/sample size deteminations methods for time series data analysis/forecasting? For example if I have time series of 30 data points, how can I with confidence ...
698 views

### Moving-average model error terms

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

### Log or square-root transformation for ARIMA

With the below dataset, I have a series which needs transforming. Easy enough. However, how do you decide which of the SQRT or LOG transformations is better? And how do you draw that conclusion? ...
88 views

### Interpreting ACF and PACF for ARIMA model estimation for SAS

The following output is for a data set for monthly airport arrivals that have been log transformed, with first difference & seasonal difference. My interpretation from the SAS output is p=P=2 ...
86 views

### Time Series Modeling with Lagged Variables

I have a dataset with columns that represent lagged values of predictors. To illustrate with a simple example, suppose we had car sales data for 3 years and the only predictors available were income ...
119 views

### Arima residual calculation and comparison with R

I have simulated an ARIMA(1,0,1) process using R. Below is the code. ...
587 views

### Initialize ARIMA simulations with different time-series

I have a fairly long time-series of annual abundances ($N_t$) of a wildlife species (73 years of abundances). To forecast the population’s trajectory, I have used ARIMA modeling. Examination of the ...