ARMA is an acronym for auto regressive moving average; a stochastic process modelling time series. It adds moving average terms to the AR model.

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Model for prediction of binomial probabilities based on time series events with variable duration

I am new to this field, so sorry if I am not precise with the nomenclature I use. :) I am trying to develop a statistical model that will allow me to calculate the outcome probabilities of a binary ...
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ARMA ROLLING IN THE SAMPLE FORECAST [on hold]

I am trying to develop a loop for a rolling forecasting with an ARMA model. this is the part of the script I am interested in: PREVISIONE IN-THE-SAMPLE dlogRet_VIX.sub <- dlogRet_VIX[1:3000] ...
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36 views

Similarities between Pade approximations and ARMA(p,q) in time series [closed]

I am wondering if someone would mind explaining how Pade approximations in calculus and ARMA(p,q) in time series are similar.
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25 views

ARMA(2,1) autocovariance functions

I have an ARMA(1,2) model: $$x_t = 0.6 x_{t-1} + u_t + 0.1 u_{t-1} - 0.2 u_{t-2} + 5$$ and I figured out the ($\delta$ = autocovariance functions) $\delta(0)= \beta_1\delta(1) + ...
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How to calculate a probability that a time series takes values in a given interval?

So I have a time series $X_t$, where $X_t$ is the number of sales of a product at day t. I would like to be able to calculate some probability like this $P(X_t>10)$ for $t \in [5,20]$ : this means ...
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81 views

What can go wrong using lagged terms as instrumental variables?

Can anybody give one example of when the set of all lagged $X$ can (or can't) be a good choice of IV's for $X_{t}$?
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15 views

ARIMAX with changing regressor values for t+1, t+2,

I have a question on a quite complicated rolling forecast model Objective I am trying to forecast the number of calls to a hotel. The forecasts I made are t+1 days, t+2 days, up until t+60 days. I ...
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257 views

Different AIC definitions

From Wikipedia there is a definition of Akaike's Information Criterion (AIC) as $ AIC = 2k -2 \log L $, where $k$ is the number of parameters and $\log L$ is the log-likelihood of the model. However, ...
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How to Calculate Standard Error and Prediction Intervals for ARMA Forecasts on Transformed Data?

I have been recently learning about the Box-Jenkins process for ARMA modeling, and I ran into a bit of a wall when it comes to error analysis. In a lot of my data sets, I have to apply a log ...
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55 views

Time series analysis (ACF, PACF)

I have this monthly time series with pronounced seasonality and a bit of trend: The ACF and PACF for 4 years (48 months) are: Can I suppose that the data don't need transformations like: ...
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29 views

How to configure p and q parameters in ARMA (Auto-Regressive Moving Average) model

I have a stationnary time series on which I want to execute an ARMA(Auto-Regressive Moving Average) model to predict next values of my time series. The ARMA model have two parameters: p: for ...
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1answer
55 views

ARMAX model and validation

I am new to time series and am trying to fit some time series data. I understand the general concept of ARIMA model. However, as I read more textbooks and articles from Rob Hyndman, I realized I ...
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1answer
37 views

How will ARMA be affected if a non-stationary time series is not made stationary?

Which components or statistics of ARMA will be affected - and how - if the stationarity condition is violated?
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1answer
78 views

Adjusting daily time series data for the seasonal component

I have a time series data containing roughly 13 000 daily observations, and the initial plan is to fit them to an ARMA model. I have adjusted the data for deterministic trend with a regression model, ...
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2answers
46 views

How to show that any Gaussian time-series is linear one?

In this paper I saw the following statement: If the time series is Gaussian (i.e., normally distributed) then the best linear forecast is in fact the best of all possible forecasts: No ...
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What nonlinear extension of ARMA and State Space Model do exist?

In ARMA model we postulate that predictions of time series can be calculated as a linear function of $N$ previous observations (AR part) and $K$ differences between the previous observations and the ...
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41 views

Am I doing this right - choosing the order of p and q for an ARMA model (time series)?

I have a time series and have to come up with the ARMA(p,q) model that fits best to the data. (I have read ARIMA model identification, which was helpful, but doesn't completely resolve my question). ...
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1answer
33 views

Estimate the best ARMAX model with one lagged independent variable (time series)?

I have two time series to work with, let's say X1 and X2. First I have to estimate the best pure ARMA model for X1; which is no problem. For that I perform the following steps: Stationarize (if ...
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2answers
54 views

How are the values of residuals (white noise) calculated in ARMA model?

I am trying to implement ARMA model in Java. I have trouble with calculating residuals (white noise) in Moving average part of the model. From the answer on this question (Fitted values of ARMA model) ...
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1answer
46 views

ARMA-GARCH model initial parameters for optimizer

I am implementing a program to fit an ARMA-GARCH model to given data. My model parameters are optimised by maximizing the Maximum Likelihood function using a nonlinear algorithm. The algorithm ...
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13 views

Deriving log likehood of AR vs MA

To derive the log-likelihood function of an MA(1) we condition on $\epsilon_0$. But when deriving the log-likelihood function function for an AR(1) we don't. Why not? Is it just because $\epsilon_0$ ...
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Is AR(1)-ARCH(1) covariance stationary?

Say I have the following model: $$ y_t = c+\phi y_{t-1} +\epsilon_t \,, \epsilon_t|\Omega_{t-1} \tilde{} WN(0,\sigma_t^2 ) $$ $$ \sigma_t^2=\alpha_0+\alpha_1\epsilon_{t-1}^2 $$ $$ |\phi|<1 \,, ...
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105 views

How to reconstruct a stock price from ARMA/GARCH fit

In this GIST, you will find simple R code that calculates Microsoft's daily stock price based on an ARMA(1,1) + GARCH(2,2) using "rugarch" library and the data from 2008 to 2015. It compares the ...
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Autocorrelation function decay for AR(p), how to proof

How can I demonstrate that the Autocorrelation function (ACF) for an AR(p) decay exponentially? It seems so simple but neither Enders' book nor Greene's has such proof.
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35 views

Yearly restrictions on quarterly forecast in ARMA

I was thinking, is it possible to implement a quarterly forecast for one year ahead such that its sum over year equals some constant number? This problem may arise if we have, for example, some ...
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17 views

General PACF for MA(1) process [duplicate]

This following question is a sample question from my notes. I have the equation $X_t=w_t+\theta w_{t-1}$. I want to prove the general equation for PACF for the MA(1) process at lag n $\phi_{nn} = ...
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18 views

Time Series ARMA Covariance

The equation is $Z_t=\theta Z_{t−1} + a_t + \alpha a_{t−1} + \beta a_{t−2}$ $\alpha, \beta, \theta=\text{constants}$ $\text{E}(a_tZ_t)=\text{E}[a_t(\theta Z_{t−1} + a_t + \alpha a_{t−1} + \beta ...
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28 views

Difference between actual curve and the curve estimated by ARIMA

I'm trying to use ARIMA model to forecast the next point in my measurements. I have a vector with $\{x_1, x_2, \ldots ,x_t\}$ measurements. I'm trying to forecast the $x_{t+1}$ element. I'm using the ...
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1answer
103 views

ARIMA(2,1,3) - insignificant coefficients?

I estimated an ARIMA (2,1,3) model and found that AR(1), AR(2) had both significant coefficients however my MA tests were unexpected - both the MA(2) and MA(3) were significant yet the MA(1) was ...
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34 views

AR(4) - show E(Yt) = 0

I was wondering if anyone could help me show that $E(Y_t) = 0$? I have had a go myself but have got stuck. Could someone please point me in the right direction? Consider the stationary AR(4) model ...
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31 views

GAMM choice of k basis dimension with temporal correlation

I have univariate time series data that I am fitting a gamm to. I am using 10-fold cross validation to choose the best temporal correlation structure in the data. The lowest RMSE value tends to come ...
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44 views

Why should the roots of an ARMA (p,q) process be different?

I understand that an ARMA process is a linear combination of an AR and MA process, but why should the roots of the two characteristics polynomials be different? I'd like both an intuitive insight and ...
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27 views

Analytical formula for the variance of ARMA(2,1) model [duplicate]

I'm looking for methods to derive an analytical formula for the variance of an ARMA(2,1) model. Given $$(1-\phi_1B-\phi_2B^2)Z_t=(1-\theta_1B)a_t, $$ I've tried the usual "trick" ...
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characterizing a financial return stream

Hello this might be a rookie stats question as I am not a seasoned stats user. Here is the problem context: I was sitting in a meeting and some one dropped a very generic question along the lines of ...
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65 views

Which ARIMA parameters fit my data?

I have the following data; ...
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16 views

How to calculate first three orders of PACF function given ARMA model?

Is there a way to calculate the first three orders (i.e. $\phi_{11}$ $\phi_{22}$, and $\phi_{33}$) of PACF given the estimated form of ARMA model, for example: ...
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1answer
130 views

Why do sample ACF/PACF suggest different TS models after box-cox transformation?

I use auto.arima function in R to fit a TS model to a annual data composed of electricity demand. The series is transformed w.r.t Box-Cox lambda due to the prevailing heteroscedasticity and then it is ...
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1answer
59 views

Increasing ACF results when fitting AR(1) or ARMA(1,1) structure to correlated residuals from mixed-effects model

So, I am trying to understand some odd results in one of my mixed-effects models. I am fitting data from 50 individual units over 20 timepoints each. There is also a time varying covariate $C$ which ...
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26 views

In which languages can I estimate a VMA model?

In which languages/environments are there tools to estimate a VMA model of a given order? That is, given $q\in\mathbb{N}$ and a multivariate time series $y_t\in\mathbb{R}^d$, $t=1,\dots,T$, a function ...
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41 views

AR(2) model, convert to smaller step size

Given an AR(2) model with coefficients $\varphi_1$ and $\varphi_2$ and step size of 1.0, is there a possibility to compute new coefficients, but with a different step size (e.g. smaller, 0.5) so that ...
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23 views

Can Hurst Exponent be applied to non-stationary series?

I have a set of non-stationary time-series which I want to model with ARMA models. Can I apply the Hurst Exponent to the time-series or should I apply it to the differenced time-series (assume ...
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40 views

Clarification in the differences between several time-series analysis models

Can anybody give me a simple explanation of the differences among the following: ARIMAX model Regression with ARIMA errors Transfer function model Please provide some references if you can.
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1answer
144 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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186 views

Why is forecasting of ARMA models performed by Kalman filter

What are the advantages of expressing an ARMA model as a state-space-model and do forecasting using a Kalman filter? This methodology is for example used in the SARIMAX implementation of ...
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58 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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41 views

Covariance of ARMA (2,1)

I am preparing for an exam and need help. Consider the following estimated ARMA(2,1) model, $$y_t = 0.05 + 0.83y_{t-1} + 0.13y_{t-2} - 0.15e_{t-1} + e_t$$ Given the unconditional variance and 1st ...
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2answers
158 views

AR(2) model is causal

AR(2) model is: $$X_t=\phi_1X_{t-1}+\phi_2X_{t-2}+W_t$$ Where $W_t\sim N(o,\sigma^2)$ I want to prove AR(2) model is causal. So, I tried as: $$X_t-\phi_1X_{t-1}-\phi_2X_{t-2}=W_t$$ $$\Rightarrow ...
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78 views

AR(1) model - which prior to use?

I want to use the following univariate model: $y_t = \mu_t + \epsilon_t, \ \epsilon_t \sim N(0,1)$ $\mu_t = \phi \mu_{t-1} + \omega_t, \ \omega_t \sim N(0,\sigma_\omega^2)$ That is, $\mu_t$ follows ...
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95 views

corARMA specification in a date*DayNight model

I'm working on a model of animal movement speed as a function of date and day/night. For each animal (50 individuals), I have 2 values for each date an animal was present - a day value and a night ...
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101 views

Using ARMA model for future forecasting

I just started learning about times-series modeling and I'm confused by the following scenario: Let's assume we train a ARMA(p, q) model on a time-series $\{x_1, x_2, ..., x_t\}$. Later in a test ...