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.
Questions tagged [arima]
2935 questions
16
votes
2 answers
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 what I have tried, but without success:
fit <- auto.arima(tsx)
plot(forecast(fit))
user3730957
- 171
7
votes
2 answers
How would you fit ARIMA model with lots of autocorrelations?
This is really puzzling...
I have this data which has a lot autocorrelations...
The data is about 60000 data points of 15min data.
I tried fitting it to ARIMA(6, 0, 6) and even GARCH(1, 1) with mean model ARMA(6, 6), still there are lots of…
Luna
- 2,345
6
votes
1 answer
Fitting an ARIMA model with conflicting indicators
I have a time series data set to which I want to fit an ARIMA model.
In looking at the plot of the data, it seems stationary, albeit perhaps marginally so. No trends, no seasonal effects, somewhat constant variance, etc. But despite the marginality,…
rwjones
- 365
3
votes
1 answer
ARIMA model parameter
For the ARIMA (0,0,1) model, some books write the equation as
$$Z_t = \mu - \theta Z_{t-1}$$
whereas some books write the equation as
$$Z_t = \mu + \theta Z_{t-1}$$
Why is there either a negative sign or positive sign before the moving average…
user41760
- 31
- 1
3
votes
1 answer
Let $X_t$ be an ARIMA(1,1,1) process and $Y_t = Y_{t-1} + X_t$. What kind of process is $Y_t$?
Q: Let $X_t$ be an ARIMA(1,1,1) process and $Y_t = Y_{t-1} + X_t$. What kind of process is $Y_t$?
$X_t$ is an ARIMA(1,1,1), i.e $\nabla X_t = X_t - X_{t-1} = Z_t $ where $Z_t$ is a casual ARMA(1,1) process and satisfies $(1-\phi_1 B)Z_t =…
Oskar
- 245
3
votes
2 answers
How do I prove that ARIMA(0,1,1) is equivalent to simple exponential smoothing?
this is an exam question of mine, but I am really struggling with it.
I have seen proofs online but they are too vague and do not connect the dots explicitly. Would someone be able to post a proof which shows the steps exactly?
Student
- 31
3
votes
1 answer
Time series - Classic decomposition model
A decomposition model widely used in practice is
$$Z_t = \mu_t + N_t + a_t$$
where $\mu$ captures the deterministic part of the series and $N_t$ is a stationary process that can be adjusted by ARMA(p, q).
The series I'm studying shows no trend, only…
jassis
- 562
3
votes
1 answer
Using OLS to estimate an ARMA(1,1)
Is it possible to obtain a consistent OLS estimator of an AR-parameter, given that the true process is an ARMA(1,1)? - It is purely a theoretical question regarding whether the AR-parameter is consistently estimated in the presence of moving average…
Armageddon
- 33
3
votes
1 answer
Find Arima equation using auto.arima, daily long-term data (msts), 3 seasonal regressors, and calculating K in fourier
I am working with daily data (variables include: temperature, salinity, wind, etc...) from 2002-2013 (msts), and I want to identify the ARIMA equation describing the whole data set, while also considering covariates unique to each variable, then use…
2
votes
1 answer
What are we trying to predict with ARIMA if we remove non-stationarity in data
I am beginning to learn time series analysis and I read that for ARIMA models, one needs to have a stationary process...that would mean removing periodicities and trends in the data....but isn't that what we are trying to predict in the first…
2
votes
1 answer
Selecting ARIMA p,d,q paramerters for hourly data with 24 hour cycle
I am working with an ARIMA model using data with hourly resolution and a 24 hour cyclical pattern. When I run an ACF on the data I can see a peak at a lag of 24. Does this mean I set p to 24 or am I missing something. I have found this slow to run.
Shug
- 21
2
votes
1 answer
Rearranging VARMA(1,1)
Can
$$
X_t - a X_{t-1} = Z_t + Z_{t-1}
$$
be written with recursion as
$$
X_t - a^2 X_{t-2} = Z_t + (1-a) Z_{t-1}
$$
where $a =
\begin{pmatrix}
0 & 1/3 \\
1/3 & 0
\end{pmatrix}
$?
I wasn't sure of how to find the autocovariance when the…
2
votes
1 answer
ARIMA Modeling on specific time series
i have some time series example that i want to predict, lately i was applying
ARIMA and Bayesian Forecasting method. But i really am interested in making a further best ARIMA Model (or just knowing some suggestion about the time series), so here is…
Jovan
- 159
2
votes
1 answer
ARIMA: how to do prediction when the data is detrended by subtracting the moving average?
Before fitting an ARIMA model, we found the trend of the ts is clearly nonlinear, so we remove the trend by subtracting the moving average (calculated by moving a sliding window over the ts and compute the mean of the numbers in the window) from the…
user112758
- 758
- 5
- 13
2
votes
2 answers
What ARMA model is this?
\begin{aligned}
Y_t &= a Y_{t-1} + e_t, \\
Z_t &= Y_t + H_t, \\
\end{aligned}
where $H_t$ is independent of $Y_t$.
I'm trying to understand what ARMA model $Z_t$ corresponds to but I'm not really sure.
Can someone provide a quick explanation?
tryingtolearn
- 539