17
Time series decomposition helps us disentangle the time series into components that may be easier to understand and, yes, to forecast.
In principle, yes, you can see pretty much everything in the original plot, but teasing things apart makes your life easier sometimes. For instance, there may be spikes that are due to some drivers, but the spikes may not be ...
5
Here is what your call to pm.auto_arima() writes to the console:
Best model: ARIMA(0,1,0)(0,0,0)[0]
That is, it fits a non-seasonal (that's the trailing (0,0,0)[0] part, and it's not surprising, since you specified seasonal=False) ARIMA(0,1,0) model. This is an ARMA(0,0) model on first differences, or
$$ By_t = y_t-y_{t-1} = \epsilon_t, $$
where $B$ is the ...
3
Presence of a unit root in a higher-order autoregressive process does not imply unpredictability as in the case of a random walk. Here is a counterexample. If the first-differenced process is AR(1)
$$
\Delta x_{t}=\varphi\Delta x_{t-1}+\varepsilon_t,
$$
then the original process is AR(2) with a unit root
$$
x_{t}=(1+\varphi)x_{t-1}-\varphi x_{t-2}+\...
3
Note that you are not getting a flat line. You are getting forecasts that show seasonal variation, specifically weekday patterns.
Your forecasts vary less than the historical data simply because there is little regularity that ARIMA can fit (especially since you pre-specify the model order - you may want to use an automatic order selection method, as in ...
3
Your outcome variable is measured wind speed, while the predictor is wind speed calculated from a numerical weather forecast model. So, input and output has the same units of measurement, and, assuming the forecasting model is good, the result of the model should be some small adjustment (maybe also depending on some other predictors).
The identity link than ...
3
How to fit a copula GARCH model?
For each series (margins):
(a) fit a univariate GARCH model (e.g. using ugarchspec followed by ugarchfit from the rugarch package in R),
(b) obtain standardized residuals,
(c) apply probability integral transform (PIT) to obtain Uniform[0,1] pseudo observations.
The latter two steps can be acomplished by a single function ...
2
A simplified answer, as indicated by Cagdas Ozgenc, might be: whenever you do not aim for the true predictive distribution.
A second aspect is the difference between fitting/estimation, inference, and forecast comparison. When you fit by minimizing a proper scoring rule and then add a penalty to deal with overfitting, your objective is usually no longer a ...
1
It depends, there definitely can be some positives in going to the monthly level. First off, as you pointed out, you can actually build a model at the monthly freq. With 3 points you will just use some naive forecast for the annual level which can work unless the annual freq is masking an underlying trend which would be evident at the monthly level.
It all ...
1
On the one hand, I am unable to recreate Excel's calculation.
One part of the problem is that SES crucially depends on how the level component is initialized. Common ways of doing so are using the first observation (as you do in your calculation), or using the average of all observations, or - especially if we operate in a state space framework - estimating ...
1
This depends on a lot of things but I would say that this is fairly typical. Mostly due to at your lower level (sku level) you probably have more intermittent demand as well as a less stable seasonal signal for more items which makes it harder to do more complex forecasting methods. And, most importantly, you are taking averages across these items where ...
1
Electricity price forecasting is a very active field of research. I would recommend you take a look at recent papers. Off the top of my head, two recent reviews are Nowotarski & Weron (2018) and Weron (2014). The electricity load forecasting literature may also be inspirational, e.g., Hong et al. (2016) or Hong et al. (2019) or Hong & Pinson (2020). ...
1
I am not sure what you mean by
assume I set a ARIMA model to forecast n-ahead = 20 (using dynamic regression not one step forecast)
In any case, the role of $h$ is as follows:
at time $t$ you predict $y_{t+h}$,
at time $t+1$ you predict $y_{(t+1)+h}$,
...,
at time $t+s$ you predict $y_{(t+s)+h}$.
Note that the forecast horizon is constant and equal to $h$...
1
Consecutive Date class dates always have a frequency of 1 since consecutive dates are 1 apart. xts does not support this. A quick ts(xts.object, frequency=12, start = 1976) call when passing to forecast functions takes care of the frequency issue.
# xts
unemployment_xts <- xts(x=US_indicators$"Unemployment Rate", order.by=US_indicators$Date, frequency=12)
...
1
On the one hand, you can forecast each series separately. There is little you can do for time series with only ten observations. You can try the historical mean, or the historical median, or use the last historical observation as a forecast. No special tools or libraries are necessary. See Best method for short time-series.
On the other hand, you may be able ...
1
Absolutely! If you want your work to be serious, you should never blindly trust the methods you use. This means analyzing the residuals but also other tests. Always check the validity of your models. There are several reasons for this:
There could be an unknown bug in the third-party software.
There could be a bug in your own code. Gathering as much ...
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