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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45
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2answers
11k views

Is it unusual for the MEAN to outperform ARIMA?

I recently applied a range of forecasting methods (MEAN, RWF, ETS, ARIMA and MLPs) and found that MEAN did surprisingly well. (MEAN: where all future predictions are predicted as been equal to the ...
51
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4answers
48k views

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{ \...
4
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1answer
7k 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 ...
9
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3answers
7k views

Transfer function in forecasting models - interpretation

I am occupied with ARIMA modelling augmented with exogenous variables for promotional modelling purposes and i have hard time explaining it to business users. In some cases software packages end up ...
62
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2answers
17k views

Real-life examples of moving average processes

Can you give some real-life examples of time series for which a moving average process of order $q$, i.e. $$ y_t = \sum_{i=1}^q \theta_i \varepsilon_{t-i} + \varepsilon_t, \text{ where } \varepsilon_t ...
23
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4answers
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 ...
7
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3answers
19k 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? <...
26
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5answers
6k views

Seeking certain type of ARIMA explanation

This may be hard to find, but I'd like to read a well-explained ARIMA example that uses minimal math extends the discussion beyond building a model into using that model to forecast specific cases ...
4
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1answer
3k views

ARMA/GARCH estimation in sequence

I have a time series that shows a nonstationary seasonal autoregressive component as well as known heteroshedasticity. In order to model the series, I have fit a seasonal ARIMA model for the mean with ...
39
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1answer
46k views

Detecting Outliers in Time Series (LS/AO/TC) using tsoutliers package in R. How to represent outliers in equation format?

Comments: Firstly I would like to say a big thank you to the author of the new tsoutliers package which implements Chen and Liu's time series outlier detection which was published in the Journal of ...
2
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1answer
10k views

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

I would appreciate if someone could help me write the mathematical equation for the seasonal ARIMA (0,2,1) x (0,0,1) period 12. I'm a little confused with how to go about this. I would prefer an ...
8
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1answer
4k views

Why does default auto.arima stop at (5,2,5)?

The function auto.arima in the forecast package of R is a powerful tool to identify the best ...
7
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2answers
954 views

Explosive AR(MA) processes are stationary?

According to Theorem 8.8 in Time Series A.W. van der Vaart an ARMA process $$\phi (L)X_t=\theta(L)\epsilon_t$$ has a unique stationary solution $X_t=\psi(L)\epsilon_t$ with $\psi=\theta/\phi$ if $\...
35
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3answers
62k views

How to fit an ARIMAX-model with R?

I have four different time series of hourly measurements: The heat consumption inside a house The temperature outside the house The solar radiation The wind speed I want to be able to predict the ...
21
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2answers
65k views

Auto.arima with daily data: how to capture seasonality/periodicity?

I am fitting an ARIMA model on a daily time series. Data are collected daily from 02-01-2010 to 30-07-2011 and are about newspaper sales. Since a weekly pattern in sales can be found (the daily ...
19
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2answers
17k views

stochastic vs deterministic trend/seasonality in time series forecasting

I have moderate background in time series forecasting. I have looked at several forecasting books, and I don't see the following questions addressed in any of them. I have two questions: How would I ...
5
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2answers
4k views

How to use Dynamic Regression models in R to forecast future sales

I want to forecast the sales having 2 independent variables, x1 and x2. I want to choose between different combinations and lags, e.g: sales ~ x1 sales ~ lag(x1,-1) sales ~ lag(x1,-1) + lag(x2,-1) ...
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1answer
6k views

ARMA GARCH estimation process in practice

I am trying to build an ARMA GARCH model and since I haven't found much information about the actual process I'll try it here. So, what have I allready done? I have tested my data for stationarity ...
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2answers
2k views

How to determine order of sarima?

hey, I have a dataset that contains hourly wind speeds. When I plotted my original acf, it showed seasonality at every 24 lags so I applied a difference of 24 to remove seasonality and another ...
14
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2answers
15k views

How to use auto.arima to impute missing values

I have a zoo series with many missing values. I read that auto.arima can impute these missing values? Can anyone can teach me how to do it? thanks a lot! This is ...
24
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4answers
7k views

Is this an appropriate method to test for seasonal effects in suicide count data?

I have 17 years (1995 to 2011) of death certificate data related to suicide deaths for a state in the U.S. There is a lot of mythology out there about suicides and the months/seasons, much of it ...
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2answers
14k views

Forecasting hourly time series with daily, weekly & annual periodicity

Major edit: I would like to say big thanks to Dave & Nick so far for their responses. The good news is that I got the loop to work (principle borrowed from Prof. Hydnman's post on batch ...
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5answers
26k 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 ...
32
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4answers
53k views

When to log transform a time series before fitting an ARIMA model

I have previously used forecast pro to forecast univariate time series, but am switching my workflow over to R. The forecast package for R contains a lot of useful functions, but one thing it doesn't ...
13
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2answers
11k views

Timeseries analysis procedure and methods using R

I am working on a small project where we are trying to predict the prices of commodities (Oil, Aluminium, Tin, etc.) for the next 6 months. I have 12 such variables to predict and I have data from Apr,...
17
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3answers
4k views

Auto.arima vs autobox do they differ?

From reading posts on this site I know there is an R function auto.arima (in the forecast package). I also know that IrishStat, ...
19
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1answer
22k views

A proof for the stationarity of an AR(2)

Consider a mean-centred AR(2) process $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+\epsilon_t$$ where $\epsilon_t$ is the standard white noise process. Just for sake of simplicity let me call $\phi_1=b$ and $\...
5
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1answer
4k views

Procedure for fitting an ARMA/GARCH Model

I want to try fitting an ARMA/GARCH model but want a methodological approach rather than fitting different models and picking the best one. However, I'm not sure how to choose my AR and MA terms for ...
21
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1answer
4k views

Regularization for ARIMA models

I am aware of LASSO, ridge and elastic-net type of regularization in linear regression models. Question: Can this (or a similar) kind of penalized estimation be applied to ARIMA modelling (with a ...
18
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2answers
7k 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 Log-...
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3answers
26k views

Seasonality not taken account of in `auto.arima()`

I am having basically the same issue than in this thread, except one thing: The difference, in my case, is that my data is measured weekly and not daily, so the argument of a too high seasonality (> ...
6
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3answers
11k views

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 ...
7
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4answers
10k views

forecast using arima models [closed]

I am trying to predict values using arima(0,1,1). After doing predict(mod,n.ahead=5) (in R) am getting the same value for all ...
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2answers
3k views

How to include control variables in an Intervention analysis with ARIMA?

I want to conduct an Intervention Analysis using SPSS. Thereby, I want to find out if a specific regulation introduced in 2013 has an effect on leveraged loan volume. Thus, the dependent variable is ...
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2answers
889 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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1answer
990 views

Order of ARMA models [duplicate]

Why we usually do not exceed ARMA(5,5) models in practice? Is there any mathematical justification for this?
20
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1answer
44k views

How to setup xreg argument in auto.arima() in R? [closed]

I am working on a small project with one time series which measures the customer visit data (daily). My covariates are a continuous variable Day to measure how many ...
52
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2answers
10k views

Why are MA(q) time series models called “moving averages”?

When I read "moving average" in relation to a time series, I think something like $\frac{(x_{t-1} + x_{t-2} + x_{t-3})}3$, or perhaps a weighted average like $0.5x_{t-1} + 0.3x_{t-2} + 0.2x_{...
13
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4answers
21k views

Difference time series before Arima or within Arima

Is it better to difference a series (assuming it needs it) before using an Arima OR better to use the d parameter within Arima? I was surprised how different the fitted values are depending on which ...
25
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3answers
71k views

Analyse ACF and PACF plots

I want to see if I am on the right track analysing my ACF and PACF plots: Background: (Reff: Philip Hans Franses, 1998) As both ACF and PACF show significant values, I assume that an ARMA-model ...
15
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1answer
10k views

Time Series Forecasting with Daily Data: ARIMA with regressor

I'm using a daily time series of sales data that contains about 2 years of daily data points. Based on some of the online-tutorials / examples I tried to identify the seasonality in the data. It seems ...
12
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4answers
9k views

Can a trend stationary series be modeled with ARIMA?

I have a question / confusion about stationary series required for modeling with ARIMA(X). I am thinking of this more in terms of inference (effect of an intervention), but would like to know if ...
13
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2answers
5k views

State space representation of ARMA(p,q) from Hamilton

I have been reading Hamilton Chapter 13 and he has the following state space representation for an ARMA(p,q). Let $r = \max(p,q+1)$.Then the ARMA (p,q) process is as follows: $$ \begin{aligned} y_t -\...
8
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1answer
18k views

How can I calculate the R-squared of a regression with arima errors using R?

If I have an arima object like a: ...
6
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1answer
9k views

How To Write Seasonal ARIMA model mathematically

I'm trying to write a seasonal ARIMA model ARIMA(1,0,3)(1,2,0) period 5 mathematically but I don't seem to be able to follow what this resource is saying otexts arima The example they use is ARIMA(1,...
5
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1answer
3k views

How does R's auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA errors?

The authors' paper about the method (Hyndman and Khandakar 2008) states that an extended an extended Canova-Hansen test is used, although the helpfile updates this to say than an OCSB test is used. ...
2
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1answer
1k views

Ljung-Box finite sample adjustments

What is the intuition behind the finite sample adjustments in the Ljung-Box test: $Q = n\left(n+2\right)\sum_{k=1}^h\frac{\hat{\rho}^2_k}{n-k}$? Degrees of freedom adjustments usually involve ...
6
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2answers
2k views

ARIMAX model's exogenous components?

Does anyone know, considering an ARIMAX model that fitting a stationary process Y, then do the exogenous components for the model need to be (weakly) stationary? I think exogenous components can be ...
1
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2answers
875 views

Seasonal adjustment for a series that has already been adjusted

A dataset I am working with (from the OECD), for harmonised unemployment seems to be seasonally adjusted: The unemployment rates shown here are calculated as the number of unemployed persons as a ...
6
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1answer
12k views

Forecasting a seasonal time series in R

Forecasting airline passengers seasonal time series using auto.arima() I am trying to model some airline data in an attempt to provide an accurate monthly forecast ...

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