New answers tagged time-series
0
votes
MA best estimate depending on $\sigma$
$X_t = X_{t-1} + \epsilon_t$. So $\text{E}(X_t | X_1,\dots,X_{t-1}) = X_{t-1}$. Therefore choosing $\alpha = 1$ is optimal, regardless of the variance of $\epsilon_t$.
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0
votes
Stationarity Conditions VECM
Based on some simulations, I found that that if $I+\Pi$ does not have any eigenvalues with modulus greater than 1, then the original companion matrix will not have eigenvalues with modulus greater ...
- 2,297
1
vote
Analysis of proportions over time
When a proportion is transformed using the Anscombe transform $A$, its sampling distribution is normal (for $n$ larger than 20) and its standard error is theoretically given to be (Anscombe, 1948) :
$$...
- 351
2
votes
Testing forecasting accuracy - outliers [ with example]
I agree with Rob Hyndman that you should definitely use residuals, not actuals. After all, you are interested in "where the forecasts are significantly different from the actual values" (...
- 131k
0
votes
Testing forecasting accuracy - outliers [ with example]
Take a look at Grubbs test for outliers. It's similar to your approach, but takes into account the tail analysis. You would apply it to residuals.
I have a problem with this approach though. I don't ...
- 62.3k
3
votes
Accepted
Testing forecasting accuracy - outliers [ with example]
You should definitely use residuals, not the actual data, because the data could show patterns such as trend, seasonality, or other types of non-stationarity. The residuals will be what's left after ...
- 58.3k
2
votes
How to calculate autocorrelation manually
Next to the points about starting values raised in the comments, there is another issue related to the "manual" formula for a deterministic difference sequence of the type you use that, ...
- 34.8k
4
votes
Accepted
How to approach time series forecasting
Lots of questions here. I recently wrote an answer here that addresses many of your points: https://stats.stackexchange.com/a/658061/1352. Regarding the points not addressed there:
Due to the high ...
- 131k
0
votes
Ecological temporal statistical analysis question
A Friedman's test is used when your data are repeated measures / related - that is each measure is taken from one unit (animal, person, place). It doesn't sound to me like the measures are repeated / ...
- 19k
1
vote
Why are exponential smoothing models not considered auto-regressive?
Hi: As Juan and Rob said, the ARIMA(0,1,1) is equivalent to exponential smoothing of the response in terms of the respective predictions, assuming that $\lambda$ is equal to $(1-\theta)$.
But, even ...
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0
votes
Why are exponential smoothing models not considered auto-regressive?
It is a commonly held myth that ARIMA models are more general than exponential smoothing. While linear exponential smoothing models are all special cases of ARIMA models, the non-linear exponential ...
1
vote
How to best forecast a time series showing level changes and square wave kind of behavior with noise
You have multiple-seasonalities: load varies within days, but this is modulated by the day of week. Depending on where you are in the world, you may have a third seasonal component for the time within ...
- 131k
6
votes
Accepted
Is there a way to forecast by subgroup without forecasting each subgroup separately?
If you can cut your data into MECE (mutually exclusive and collectively exhaustive) subsets, you can use the by now well-established machinery of hierarchical forecasting, which in my experience ...
- 131k
2
votes
Is my time series exhibiting stationarity?
The problem here is the presence of seasonality, the series exibit a seasonal bahaviour that is itself non-stationary.
2
votes
Accepted
"Strength" of cointegration
A function of this first eigenvalue is a test statistic for the null of no cointegration, see The eigen values of Johansen's cointegration procedure, viz.
$$
-T\log(1-\hat\lambda_1)
$$
To the ...
- 34.8k
0
votes
Is it possible to train Neural networks for time series forecasting using elastic distances (such as dtw) as a loss function?
My answer is certainly not covering all aspects of your question, but here are some thoughts about it.
i) DTW is not differentiable as is, due to the MIN operator.
ii) you could have a look as softDTW ...
2
votes
Why are the HAC (Newey-West) standard errors smaller than the ordinary standard errors in my regression?
Christopher Hancks answer is an option. Another option would be the following:
Robust standard errors are biased towards 0, which effects them a lot if sample sizes are small. What's your ratio of ...
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4
votes
Why are the HAC (Newey-West) standard errors smaller than the ordinary standard errors in my regression?
The issue can arise under negative serial correlation, see What does it mean when newey-west standard errors are much larger than other types of standard errors for the respective formulae. There, I ...
- 34.8k
0
votes
Problems with using ACF and PACF for ARMA modelling
I used the ADF test, the PP test, the Schmidt Phillips test and the DFGLS test, and got the same result that my variable $\Delta y_t$ was integrated of order 0, but from what we've been taught, these ...
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0
votes
Difference Between Simultaneous Equation Model and Structural Equation Model
Structural equation modeling (SEM) represents the structure - the causal relationships between variables - using equations, graphs, and other tools. As a framework for causal inference, SEM ...
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0
votes
Fitting an ARIMA subset model in R
If you look at the help for the arima function, you will see an option "fixed". It says, in part,
optional numeric vector of the same length as the total number of
coefficients to be ...
- 523
0
votes
Fitted values of initial observations in auto.arima for non-stationary models
Looking in the source code of the arima function, it appears as though the initial conditions are treated as additional parameters to be estimated via Maximum ...
- 523
0
votes
How to statistically compare two time series?
You can consider using matrix profile-based approaches that leverage z-normalized Euclidean distances to find similar-looking (nearest neighbor) time series.
STUMPY appears to be a robust and well ...
4
votes
Accepted
Uncertain serial autocorrelation in GAM count model residuals
Your mvgam model doesn't have any autoregressive components in it, so these two models should be roughly equivalent apart from the better handling of uncertainties in mvgam. But there are a few tweaks ...
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1
vote
Wold decomposition
Write the processes in lag operator notation, i.e.,
$$
\phi(L)Y_t=\epsilon_t,
$$
where
$$
\phi(z)=1-\phi_1z-\ldots-\phi_pz^p
$$
and
$$
Y_t=\psi(L)\epsilon_t,
$$
where
$$
\psi(z)=\psi_0+\psi_1z+\psi_2z^...
- 34.8k
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